Arthur Vigan

Je Soussignée

Mona El Morsy
email: mona.elmorsy@lam.fr

Ferdaws Khadr

Mohamed Bachandy

Omar & Fatheya

Ateya Khalil

Ahmed Mohamed El

Morsy El

Salhy To

Howayda & Maged

El Morsy

M El Morsy

M Lopez

G P P L Otten

E Choquet

F Madec

A Costille

J.-F Sauvage

K Dohlen

E Muslimov

R Pourcelot

J Floriot

J.-A Benedetti

P Blanchard

P Balard

G Murray

É Choquet

Validation of strategies for coupling exoplanet PSFs into single-mode fibres for high-dispersion coronagraphy

Keywords: instrumentation, high angular resolution -instrumentation, spectrographs -instrumentation, adaptive optics Experimental validation of exoplanet centring strategies for high dispersion coronagraphy instrumentation, high angular resolution -instrumentation, spectrographs -instrumentation, adaptive optics

On large ground-based telescopes, the combination of extreme adaptive optics and coronagraphy with high-dispersion spectroscopy, referred to as high-dispersion coronagraphy (HDC), emerged as a powerful technique for the direct characterisation of giant exoplanets. The high spectral resolution of this method brings a major gain in terms of accessible spectral features and enables a better separation of the stellar and planetary signals. The instrument HiRISE, the main topic in this thesis, aims to exploit these anticipated success factors. It bases its observing strategy on the use of a few science fibres: one is dedicated to sampling the planet's signal, while the others sample the residual starlight in the speckle field. For precision and stability purposes, single-mode fibres (SMF) are optimal for feeding light into spectrographs, as achieved on HiRISE. They are used in the focal plane of telescopes for their spatial filtering effect. However, efficiently coupling a PSF into a SMF is inherently challenging due to their intrinsic properties described throughout this thesis.

"Mille viae ducunt homines per saecula Romam qui Dominum toto quaerere corde volunt". Tout comme cette expression qui date du XIIe siècle, il m'est aujourd'hui possible de dire que je suis arrivée à l'aboutissement de mon doctorat. Ces lignes, que j'ai d'abord noircies à la main lors d'un trajet Marseille-Paris, traduisent mon désir de remercier sincèrement ceux avec qui un instant de vie a été partagé. Je les ai spontanement écrit en mélangeant le français, l'anglais et l'italien. Je m'excuse d'avance pour ces inombrables aller-retours linguistiques.

Je tiens tout d'abord à remercier les membres de mon jury d'avoir acceptés d'évaluer mon manuscrit de thèse et pour leurs disponibilités à échanger sur mes travaux. Je tenais également à remercier mon directeur de thèse Arthur Vigan pour avoir encadré mon travail de thèse, pour nos échanges sur l'instrumentation et pour avoir créer ce beau projet qu'est HiRISE.

Au cours de ma thèse, j'ai évolué dans le groupe d'Imagerie Haut Contraste, donc je souhaiterais remercier ceux qui le composent: Faustine, Eduard, Chen, Jean, Lisa, Mathis. Élodie, merci pour nos discussions scientifiques, tes relectures toujours très pertinentes et pour tes raclettes party que j'adore. À Maxime, mon co-bureau, mon acolyte de l'instru, merci pour ton soutien, nos moments de rigolades, les "tkt ça va aller Mony" et d'avoir partagé ton espace avec une thésarde qui écoute régulièrement Claude François, Eminem et de la musique égyptienne.

Je voudrais remercier les membres du GRD pour nos échanges: Benoit, Thierry, Manu, Marc, Thibault. J'ai également eu l'opportunité d'échanger à de nombreuses reprises avec le service optique, merci donc à Edgard, Zalpha, Kacem, David, Amandine. Johan, merci pour ta grande expertise instrumentale, et nos nombreux fous rires, je t'attends pour voir un match des Spurs. Kjetil, nombreuses ont été nos discussions sur la natation et la Norvège, mais je tenais surtout à te remercier pour ta grande pédagogie à transmettre ta passion de l'optique. Merci pour ta vision poétique de l'instrumentation: " Écoute MITHiC chanter et tu trouveras la source des vibrations".

Participation aux conférences et écoles d'été au cours de la période de thèse :

Résumé étendu en français Introduction À la fin du 19ème siècle, l'existence de planètes hors du système solaire était envisagée par la communauté scientifique, bien qu'aucune n'ait été détectée en raison du manque d'instruments capables de faire une image directe de ces planètes. En effet, la difficulté réside dans la faible séparation angulaire entre l'étoile hôte et les planètes et leur différence de luminosité. Les scientifiques ont donc décidé de contourner ce problème et ont cherché à détecter ces exoplanètes de manière indirecte en observant les potentiels effets qu'une exoplanète aurait sur son étoile hôte. Diverses méthodes indirectes (par exemple, la vitesse radiale, les transits planétaires, etc.) ont conduit à plusieurs découvertes au cours des dernières années.

Les récentes avancées technologiques nous ont permis de construire de nouveaux instruments capables d'utiliser des techniques d'imagerie directe. L'imagerie directe est une technique efficace pour étudier l'atmosphère des planètes. Cependant, cette technique est plus performante pour imager les planètes orbitant près de leur étoile hôte (< 5 -1000 UA). La première image directe d'une exoplanète orbitant autour d'une naine brune (NB) a été faite par [START_REF] Chauvin | A giant planet candidate near a young brown dwarf. Direct VLT/NACO observations using IR wavefront sensing[END_REF] [START_REF] Macintosh | Discovery and spectroscopy of the young jovian planet 51 Eri b with the Gemini Planet Imager[END_REF]. La limitation de cette technique réside dans la différence de magnitude entre la planète et son étoile hôte et dans le fait que pour un observateur sur Terre, elles semblent orbiter très près l'une de l'autre. Nous définissons l'observation par imagerie directe par la résolution angulaire entre la planète et son étoile hôte, qui est limitée par la résolution angulaire du télescope et le contraste de luminosité, qui est limité par la sensibilité de l'observation. Pour atteindre la séparation angulaire et le contraste nécessaires à l'imagerie directe des exoplanètes, une des techniques les plus utilisées est l'imagerie à haut contraste qui combine l'optique adaptative extrême (ExAO, e.g., FUSCO et al., 2006), qui permet de mesurer et compenser la distorsion atmosphérique depuis les observations au sol, avec la coronagraphie qui a pour but d' atténuer la lumière des étoiles sur l'axe (GUYON et al., 2006 ;[START_REF] Mawet | Direct imaging of extra-solar planets in star forming regions. Lessons learned from a false positive around IM Lupi[END_REF]. Cette technique est principalement limitée par des tavellures quasi-statiques dans le plan focal (SOUMMER et al., 2007), couvrent ainsi le signal planétaire. Pour relever les défis de l'HCI, une nouvelle génération d'instruments a été mise en place sur de grands télescopes terrestres au cours de la dernière décennie : VLT/SPHERE (BEUZIT et al., 2019), Gemini/GPI (MACINTOSH et al., 2014), et Subaru/SCExAO [START_REF] Jovanovic | The subaru coronagraphic extreme adaptive optics system: enabling high-contrast imaging on solar-system scales[END_REF].

Bien qu'ayant pris en considération tous les progrès réalisés jusqu'à présent, notre compréhension des exoplanètes est encore limitée en raison de la taille de l'échantillon des paramètres tels que la masse, la séparation, le rapport signal/bruit de la planète et la couverture de longueur d'onde. L'observation de planètes avec de grands télescopes permettrait d'ajouter une pièce au puzzle très complexe des mécanismes de formation et d'évolution des exoplanètes, notamment en permettant l'utilisation de spectrographes pour les observations. La spectroscopie est déjà utilisée pour caractériser l'atmosphère de mini-neptunes, d'exoplanètes géantes en transit, de super-Terre (SING et al., 2016) et de jeunes exoplanètes géantes [START_REF] Bonnefoy | First light of the VLT planet finder SPHERE. IV. Physical and chemical properties of the planets around HR8799[END_REF][START_REF] Chauvin | Discovery of a warm, dusty giant planet around HIP 65426[END_REF][START_REF] Macintosh | Discovery and spectroscopy of the young jovian planet 51 Eri b with the Gemini Planet Imager[END_REF]. L'avantage d'utiliser la spectroscopie en imagerie directe est qu'elle permet de sonder des couches plus profondes de l'atmosphère, et donc de détecter des biosignatures [START_REF] Morley | Thermal Emission and Reflected Light Spectra of Super Earths with Flat Transmission Spectra[END_REF] en comparaison avec les méthodes de spectre en transmission utilisées pour étudier les atmosphères d'exoplanètes en transit comme HD 209458 b décrite dans [START_REF] Charbonneau | Detection of an Extrasolar Planet Atmosphere[END_REF]. En complément des spectrographes embarqués sur les télescopes spatiaux (tels que STIS/HST), divers instruments imageurs au sol permettent de combiner des coronographes à haut contraste avec des spectrographes à champ intégral (IFS). Par exemple ces instruments (P1640, SPHERE, GPI, SCExAO+CHARIS) combinent des AO et des coronographes avec des IFS à faible résolution spectrale, tandis que VLT/MUSE, VLT/SINFONI et Keck/OSIRIS utilisent l'optique adaptative extreme (ExAO) avec des IFS à moyenne résolution spectrale. Les imageurs d'exoplanètes SPHERE et GPI nous permettent de détecter et de caractériser grâce à leurs IFS, des objets peu lumineux tels que [START_REF] Gilmozzi | The European Extremely Large Telescope (E-ELT)[END_REF] L'augmentation de la résolution spectrale permet non seulement d'améliorer la caractérisation des exoplanètes, mais aussi d'augmenter leur détection comme le démontre Sparks Ford [START_REF] William | Imaging Spectroscopy for Extrasolar Planet Detection[END_REF]. Simultanément, à l'imagerie haute contraste (HCI), la spectroscopie à haute dispersion (HDS) s'est avérée être une technique puissante pour caractériser l'atmosphère des exoplanètes en utilisant des spectrographes infrarouges tels que Keck/NIRSPEC (MCLEAN et al., 1998) ou VLT/CRIRES (KAEUFL et al., 2004). La HDS dans le proche infrarouge (NIR) dans le cas d'observations au sol, a fourni un grand nombre d'informations essentielles, telles que la vitesse du vent ou la vitesse de rotation de certaines exoplanètes en transit (I. A. G. SNELLEN et al., 2010). Elle a également été utilisée pour caractériser les exoplanètes en résolvant spectralement les caractéristiques moléculaires des espèces présentes dans l'atmosphère (BROGI et al., 2013 ; DE KOK et al., 2013). La combinaison de la haute résolution angulaire utilisant l'AO pour d'abord séparer spatialement la planète du signal stellaire et la mise en oeuvre d'une spectroscopie de moyenne à haute résolution pour filtrer spectralement la lumière stellaire de celle de la planète a été démontrée avec succès en utilisant l'instrument VLT/CRIRES avec une résolution de R = 100 000 dans la bande K. En utilisant le système AO MACAO (ARSENAULT et al., 2003), CRIRES a été utilisé pour détecter les lignes CO à 2.3 µm dans β Pictoris b et pour mesurer ses vitesses orbitales et rotationnelles (I. A. G. SNELLEN et al., 2014). Cependant , ces résultats ont été en partie limités par la performance relativement faible de CRIRES, qui n'a pas été conçu à cet effet.

La combinaison de HCI et HDS a été proposée pour la première fois par (RIAUD et al., 2007) pour améliorer la sensibilité en contraste, et une étude plus approfondie a été réalisée plus tard par I. SNELLEN et al. (2015) dans le cadre de l'instrumentation ELT. En théorie, pour les observations au sol, HCI et HDS peuvent respectivement atteindre un contraste planète-étoile de 10 -3 et 10 -4 donc en combinant les deux pour réaliser de la coronagraphie à haute dispersion (HDC), on pourrait théoriquement atteindre des contrastes de 10 -7 ou mieux. Plus récemment, l'étude de WANG et al. (2017a) a développé un modèle détaillé des observations HDC et a analysé le compromis entre la suppression de la lumière des étoiles et la résolution spectrale pour la caractérisation des exoplanètes géantes jeunes dans le NIR.

Ce travail a ouvert la voie à la technique de HDC, qui est maintenant mise en oeuvre dans plusieurs projets sur des télescopes existants : Keck/KPIC (J.-R. [START_REF] Delorme | Keck Planet Imager and Characterizer: a dedicated single-mode fiber injection unit for high-resolution exoplanet spectroscopy[END_REF], Subaru/REACH (KOTANI et al., 2020), et VLT/HiRISE (KOTANI et al., 2020). Les trois projets mentionnés ci-dessus consistent à coupler des instruments haut contraste existants avec des spectrographes à moyenne ou haute résolution. Ces projets proposent d'échantillonner le signal planétaire avec une fibre monomode (SMF) et de l'envoyer vers un spectrographe (COUDÉ DU [START_REF] Coudé Du Foresto | Very High Angular Resolution Imaging[END_REF]JOVANOVIC et al., 2017).

Pour des raisons de précision et de stabilité, les SMF sont optimales pour alimenter les spectrographes en lumière (CREPP, 2014 ;JOVANOVIC et al., 2016) et ils sont utilisés dans le plan focal des télescopes pour leur effet de filtrage spatial (GHASEMPOUR et al., 2012). Cependant, le taux de couplage d'une fonction d'étalement de point (PSF) dans une SMF est difficile en raison des propriétés intrinsèques des fibres monomodes. Une SMF est conçu uniquement pour accepter un mode fondamental quasi-gaussien (LP01). Selon la théorie du champ des ondes électromagnétiques, l'efficacité optimale du couplage se produit lorsque l'intégrale de recouvrement entre le champ électrique du faisceau d'entrée et le mode LP01 est maximisée (BARRELL et al., 1979 ;[START_REF] Jeunhomme | Single-mode Fiber Optics. Principles and Applications Jovanovic[END_REF]NEUMANN, 1988). Cela implique que l'amplitude complexe de la composante transversale du champ électrique au plan focal du télescope doit correspondre au mode LP01 de la SMF (COUDÉ DU FORESTO et al., 1993). Dans le cas idéal d'une pupille non obstruée, une tache d'Airy est formée dans le plan focal et est composée d'une tâche entourée d'anneaux concentriques sombres et brillants successifs où la phase est inversée de π. L'efficacité de couplage maximale d'une tâche d'Airy dans une SMF se produit lorsque seul la tâche central s'apparente au mode quasi-gaussien. L'efficacité de couplage maximale théorique d'une ouverture circulaire non obstruée dans une SMF est de ∼81% (SHAKLAN et al., 1988). Cependant, la plupart des télescopes terrestres ont des ouvertures circulaires obstruées et des araignées. La présence d'une obstruction centrale et d'araignées dans la pupille a un impact significatif sur l'efficacité du couplage. Les observations au sol sont également limitées par les aberrations optiques, qui sont classées en deux catégories : les aberrations quasi-statiques causées par des défauts optiques (e.g. N'DIAYE et al., 2013) et les aberrations atmosphériques causées par l'atmosphère turbulente. Les deux types d'aberrations perturbent le front d'onde et requièrent l'utilisation d'un système d'OA pour rétablir un front d'onde le plus plat possible. Une correction ExAO a démontré qu'elle augmentait le rapport de Strehl, minimisait les aberrations, et donc permettait d'obtenir une efficacité d'injection proche de son maximum théorique (JOVANOVIC et al., 2017).

Combiner l'imagerie à haut contraste avec la haute dispersion coronographique : le cas d'HiRISE

La transmission globale du signal de la planète dans une SMF connectée à un spectrographe détermine le rapport signal/bruit de la détection des molécules et des mesures d'abondance. Le couplage d'une PSF d'exoplanète avec une SMF a été le coeur de mon travail de doctorat. Ce travail a été réalisé dans le cas spécifique du projet HIRISE qui vise à connecter deux instruments phares installés sur les plateformes Nasmyth du télescope unitaire 3 (UT3) du VLT : l'imageur d'exoplanètes SPHERE d'un côté, et le spectrographe à haute résolution en proche infrarouge CRIRES+ (DORN et al., 2023) de l'autre. Cela permettra de caractériser des exoplanètes géantes jeunes connues par imagerie directe à des résolutions spectrales allant jusqu'à R = 10 5 dans la bande H. HiRISE est composé de trois parties indépendantes : (i) le module d'injection de fibres (FIM) qui sera implémenté dans le bras IFS de SPHERE, (ii) le toron de fibres (FB) qui reliera SPHERE et CRIRES+, et (iii) le module d'extraction de fibres (FEM) qui sera installé sur l'étage de calibration de CRIRES+. HiRISE bénéficiera de l'infrastructure de SPHERE pour l'imagerie à haut contraste et de CRIRES+ dans le proche infrarouge pour la haute dispersion spectroscopique. Sur le plan conceptuel, HiRISE dévie le faisceau SPHERE/IFS en aval de l'ExAO et du coronographe et injecte la lumière d'une exoplanète connue dans une SMF. Cette fibre est connectée au spectrographe CRIRES+ placée sur la plateforme Nasmyth opposée, et qui est utilisé pour disperser la lumière de la planète avec une haute résolution spectrale. La mise en oeuvre pratique requiert trois éléments interconnectés : le FIM implémenté dans SPHERE qui se charge d'injecter correctement le signal planétaire dans la la fibre scientifique, le toron de fibres (FB) qui passe autour du télescope et qui achemine la fibre scientifique et les fibres supplémentaires entre les deux plateformes Nasmyth et le FEM implémenté dans CRIRES+ qui ré-image la fibre scientifique à l'entrée du spectrographe avec les bonnes propriétés optiques.

Le FIM est implémenté sous la forme d'un banc vertical immédiatement en aval de la roue de Lyot dans le bras IFS de SPHERE (BEUZIT et al., 2019). Le FIM comprend un miroir de renvoi qui peut être inséré dans le faisceau IFS pour envoyer la lumière vers le FIM au lieu de l'IFS. La pupille SPHERE est ré-imagée sur un miroir collé sur une plateforme piézoélectrique S335 de Physik Instrument. Le faisceau est ensuite recollimaté à l'aide d'un doublet achromatique et passe par un filtre dichroïque qui réfléchit les courtes longueurs d'onde (0.95-1.3 µm ; bandes YJ ) dans la " branche de suivie (science)" et transmet les plus grandes (1.4-1.8 µm ; bande H) vers la "branche d'injection". Dans la branche science, une image du plan focal est formée à F/40 sur une caméra C-RED 2 de First Light Imaging [START_REF] Gibson | [END_REF], et nous l'appelons la caméra de science (tracking) dans cette section. Cette image est échantillonnée à 12,25 mas/pix, ce qui correspond à un échantillonnage de Nyquist à 0,95 µm. Bien que l'on ne s'attende pas à ce que les images de la caméra de tracking soient utilisées pour une interprétation astrophysique, elles seront néanmoins d'une qualité suffisante pour permettre un traitement de base. Dans la branche d'injection, le faisceau est refocalisé avec un doublet très rapide à F/3.5, conçu pour correspondre à l'ouverture numérique (N A = 0.16) des fibres scientifiques utilisées dans le faisceau. Le système optique est conçu pour être télécentrique dans la branche d'injection afin de maximiser l'efficacité de l'injection, et ceci, en tenant compte des fibres situées hors axe. Bien que la fibre scientifique soit placée sur l'axe optique pour maximiser la qualité du front d'onde et, par conséquent, l'efficacité de l'injection (JOVANOVIC et al., 2017), trois fibres supplémentaires seront placées hors axe pour échantillonner le signal de l'étoile dans le champ de tavelures. En pratique, le FB reste statique après l'alignement du système, et l'image du plan focal est déplacée par rapport à la fibre scientifique à l'aide d'un mirroir, de manière à ce que la lumière stellaire ne soit pas perdue. Le miroir bouge en tip et en tilt, de manière à placer le PSF d'un compagnon connu sur la fibre. En plus des fibres dédiées à la science, le FB comprendra également des "fibres de rétroéclérage", qui sont connectées à une source de calibration à ∼1.3 µm et utilisées pour rétro-injecter un signal dans le système. En raison de l'orientation du filtre dichroïque, le signal rétro-injecté est réfléchi sur le filtre dichroïque, puis sur un coin de cube qui permet de repasser par le filtre dichroic et d'être envoyé vers la branche de suivi.

Les sorties des fibres de retro-injection sont finalement ré-imagées sur la caméra de science en superposition de l'image coronographique en plan focal. La position des fibres de retro-injection par rapport à la fibre scientifique est calibrée, ce qui permet de les utiliser pour un centrage précis sur la fibre scientifique. Cette solution a été proposée précédemment pour optimiser le centrage sur la fibre scientifique dans une situation où le signal de la planète reste indétectable lors de courtes expositions [START_REF] Mawet | [END_REF].

Le module d'injection de fibres a été conçu en tenant compte de (i) l'espace disponible à l'intérieur de l'enceinte de SPHERE et (ii) la meilleure position pour profiter pleinement de SPHERE dans le bras NIR. Pour injecter efficacement la PSF d'une planète dans une SMF, il est nécessaire d'avoir le meilleur front d'onde possible et une PSF très stable donc placer le FIM en aval de l'AO, du DTTS et du coronographe était le meilleur choix pour répondre à ces exigences. Le volume a également été optimisé pour être le plus compact possible, avec un volume approximatif de 530 (l) x210 (l) x 810 (h) mm 3 . Le FIM sera pré-aligné en laboratoire avec un SPHERE simulateur, puis implémenté verticalement dans SPHERE. L'un des défis du couplage de SPHERE et de CRIRES+ réside dans la réussite d'injecter avec succès le signal d'une exoplanète connue détectée par SPHERE dans une SMF avec une précision de centrage de 0.1 λ/D. Puisque la PSF de la planète ne sera généralement pas visible sur l'image de la caméra de tracking en raison du rapport signal/bruit, l'acquisition de la planète sera effectuée en aveugle sur la base de son astrométrie relative déjà connue par rapport à l'étoile et sur les calibrations effectuées pendant la journée.

Prototypage d'une procédure de centrage sur MITHiC

Pour étudier la meilleure approche de centrage, j'ai utilisé le banc d'essai MITHiC au LAM, que j'ai mis à jour pour reproduire la configuration utilisée dans HiRISE. Avec cette configuration, trois stratégies ont été mises en oeuvre et testées sur MITHiC pour évaluer la faisabilité d'obtenir une spécification de 0.1 λ/D. La première stratégie repose uniquement sur une fibre de centrage dédiée, située à proximité de la fibre scientifique. Dans la configuration non coronographique, la première étape consiste à placer la PSF stellaire au-dessus de la fibre de centrage puis d'affiner le centrage avec un algorithme d'optimisation qui maximise l'efficacité du couplage de l'étoile dans la fibre de centrage. Il s'agit ensuite d'appliquer un décalage entre la fibre de centrage et la fibre science (ce dernier a été calibré au préalable lors de la validation en laboratoire de l'instrument) afin de placer l'étoile sur la fibre fibre scientifique. Et enfin, à l'aide de la matrice d'interaction et en utilisant les données d'ascension droite et de déclinaison (RA et DEC), le miroir de tip-tilt est bougé pour déplacer la planète sur la fibre scientifique. La deuxième stratégie, également dans la même configuration non coronographique, utilise la fibre scientifique et quatre fibres de rétro-injection qui rétro-injectent de la lumière dans le système via le filtre dichroïque et le coin de cube. Les quatre fibres sont ré-imagées sur la caméra de suivi superposées à la PSF de l'étoile. En théorie, l'intersection de leurs diagonales (I), fournit la position de la fibre scientifique sur l'image en plan focal.

Par conséquent, la première étape de la procédure consiste à allumer les diodes qui allimentent les quatre fibres de rétro-injection pour acquérir une image avec la caméra de suivi, de trouver le centre des points de rétro-injection et déterminer la position de la fibre scientifique. Cependant, un décalage peut se produire entre I et la position de la fibre scientifique. Il est dû à un décalage d'alignement entre la branche scientifique et la branche de rétro-injection, et devra être calibré au préalable lors de la validation de l'instrument en laboratoire. Ensuite, la PSF de l'étoile est positionnée sur la fibre scientifique en déplaçant le miroir de tip-tilt et, comme décrit pour la première stratégie, un décalage est appliqué pour déplacer la planète dans la fibre scientifique. La troisième stratégie combine la première et la deuxième stratégie en utilisant les quatre fibres de rétro-injection, la fibre de centrage et la fibre scientifique. La première étape consiste à allumer les diodes qui alimentent les fibres de rétroinjection pour trouver le centre des quatre fibres et l'intersection I. Le miroir de tip-tilt est utilisé pour placer l'étoile sur la fibre de centrage. En utilisant le décalage précalibré en laboratoire, l'étoile est placée sur la fibre scientifique. Ensuite, un décalage est appliqué pour placer la planète sur la fibre scientifique. J'ai réalisé une étude de performance pour vérifier le centrage de la PSF de la planète sur la fibre scientifique S pour plusieurs séparations angulaires et pour plusieurs angles autour de l'étoile. Les résultats montrent que la stratégie la plus performante est la première ; nous n'atteignons jamais un taux de réussite de 1,0 pour une précision de spécification de 0,1 λ/D ou 0,2 λ/D pour tous les angles de position, alors qu'un taux de réussite de 1,0 est atteint pour tous les angles de position en considérant une précision de spécification de 0,3 λ/D. Pour une spécification de 0,1 λ/D, le taux de réussite peut descendre jusqu'à 0,2, mais se situe en moyenne autour de 0,7. Pour une spécification de 0,2 λ/D, le taux de réussite est nettement amélioré, avec une valeur de 1,0 pour la plupart des angles et chute à 0,8 pour un seul point de mesures. Indépendamment de la stratégie, j'ai conclué qu'atteindre une précision de 0.1 λ/D est extrêmement difficile. Elle nécessite un haut niveau de précision à chaque étape de calibration, ce qui est difficile à atteindre, surtout dans un système non optimisé construit à partir de composants du commerce. Dans notre cas, la performance finale sur plusieurs positions angulaires de la planète ou sur les separations angulaire peut s'expliquer par une précision moindre des calibrations utilisées pour réaliser les première et troisième stratégies de centrage. Certains aspects liés à la performance peuvent être expliqués par les limitations du système, telles que l'instabilité de la PSF et la précision de la fonction d'interpolation. La fonction d'interpolation est utilisée dans les trois stratégies pour placer le PSF de l'étoile à n'importe quelle position dans le champ de vue de la caméra de suivie. Même si la distribution de l'incertitude de la fonction d'interpolation est en grande partie conforme à la spécification de ± 0,1 λ/D, la présence de valeurs aberrantes a un impact négatif sur le fonctionnement idéal de la fonction d'interpolation dans certaines zones. Ces valeurs aberrantes proviennent des limitations inhérentes au banc d'essai MITHiC, qui, espérons-le, ne seront pas présentes pour HiRISE.

Développement du processus d'assemblage, d'intégration et de test de l'instrument HiRISE

A la lumière de l'étude des performances réalisés sur MITHiC et en considérant le point de vue opérationnel, la première stratégie est celle considérée pour HiRISE. Cependant, il sera nécessaire d'attendre les AIT pour vérifier la faisabilité de la stratégie dans le cas de HiRISE. Les AIT auront lieu dans différentes localisations. La première sera au Laboratoire d'Astrophysique de Marseille, où l'équipe HiRISE effectuera, dans l'atelier mécanique, l'assemblage à blanc du FIM et du FEM pour préparer les deux sous-systèmes à être montés et testés dans une salle blanche ISO 8. La deuxième localisation est à l'UT3/VLT, où les AITV auront lieu dans le hall d'intégration et dans le télescope. L'AIT au LAM sera divisé en plusieurs étapes et consistera à mettre en oeuvre, tester et valider les différents sous-systèmes qui composent HiRISE. L'implémentation du SPHERE simulateur, du FIM et du FEM, ainsi que leur assemblage et leur alignement ont été réalisés indépendamment. Pour la première partie des AIT, le FB ne peut pas être testé car il n'a pas encore été reçu. Lorsque le système sera prêt à être mis en service sur le site du VLT, deux types de vérifications sont prévus. Pour vérifier la validation fonctionnelle de l'ensemble du système, y compris SPHERE et CRIRES+, nous avons l'intention d'effectuer des vérifications de jour, par exemple des tests de calibration du système en utilisant la source interne de SPHERE. Les vérifications sur le ciel seront consacrées à la validation des performances de HiRISE sur des cibles définies au préalable.

Conclusion

HiRISE a pour but de coupler SPHERE et CRIRES+ se situant sur l'UT3 du VLT avec un toron de fibres monomode. Cela permettra de caractériser des exoplanètes géantes jeunes détéctées au préalable par imagerie directe à des résolutions spectrales allant jusqu'à R = 10 5 dans la bande H. Les résultats préliminaires de la mise en service sur le ciel auront lieu au printemps 2023. Une fois la mise en service terminée, le premier ensemble d'observations sera analysé afin d'améliorer les futures mises en service d'HiRISE et de maximiser le flux de photons dans la fibre scientifique en bande H. Dans le cadre de ma thèse, j'ai développé des solutions expérimentales, algorithmiques et de calibration pour parfaitement centrer une PSF sur une fibre monomode, ce qui permet d'optimiser l'efficacité du couplage dans le cadre de la haute dispersion coronographique. J'ai proposé une compréhension fine du budget d'erreur concernant le centrage de la PSF sur des fibres monomodes en exploitant les limitations. En seconde partie de thèse, j'ai travaillé sur la conception finale de l'instrument HiRISE ainsi que sur les aspects d'assemblage, d'intégration et de tests. Dans les prochains mois, HiRISE sera testé sur ciel et il s'agira, lors du commissioning de l'instrument, de vérifier quelle stratégie de centrage se confronte le mieux lors des tests de vérifications mais aussi lors des observations. En raison de la forte dépendance des performances à la transmission globale du système (OTTEN et al., 2021), les procédures de centrage sont cruciales pour HiRISE. Dans ce cas particulier, nous travaillons avec des systèmes existants, ce qui implique de fortes contraintes sur les spécifications afin de maximiser le flux transmis. Ces contraintes seront sans doute assouplies pour les futurs instruments optimisés de bout en bout pour la HDC. Le développement d'instruments IFS offrant une très haute résolution spectrale est difficile et coûteux, il est donc probable que la HDC restera largement basé sur des spectrographes alimentés par des fibres dans un avenir proche. Notre étude prépare donc le terrain pour des instruments tels que RISTRETTO sur le VLT [START_REF] Lovis | [END_REF] et, à plus long terme, PCS sur le ELT (KASPER et al., 2021), HISPEC sur Keck (2025), MODHIS sur TMT -ou des missions phares post-JWST telles que le concept IROUV-Astro2020, récemment rebaptisé "Observatoire des Mondes Habitables".

Résumé

Sur les grands télescopes terrestres, la combinaison de l'optique adaptative extrême et de la coronagraphie avec la spectroscopie à haute dispersion, appelée coronagraphie à haute dispersion (HDC), est apparue comme une technique puissante pour la caractérisation directe des exoplanètes géantes. La haute résolution spectrale apporte un gain important en termes de caractéristiques spectrales accessibles, et permet une meilleure séparation des signaux stellaires et planétaires. L'instrument HiRISE, sujet principal de cette thèse, vise à exploiter ces facteurs de succès anticipés et base sa stratégie d'observation sur l'utilisation de quelques fibres scientifiques : l'une est dédiée à l'échantillonnage du signal de la planète, tandis que les autres à échantillonner la lumière résiduelle des étoiles dans le champ de tavelures. Pour des raisons de précision et de stabilité, les fibres monomodes (SMF) sont optimales pour alimenter en lumière les spectrographes, comme c'est le cas sur HiRISE. Elles sont utilisées dans le plan focal des télescopes pour leur effet de filtrage spatial. Cependant, l'efficacité de couplage d'une PSF dans une SMF est difficile en raison de leurs propriétés intrinsèques.

L'un des défis d'HiRISE réside dans le centrage, dit à l'aveugle, de la PSF d'une planète déjà connue et détectée par SPHERE dans une SMF. Le module d'injection de fibre (FIM) joue un rôle critique puisqu'il va récuperer la PSF de la planète dans SPHERE et l'injecter dans une SMF située dans le toron de fibres afin d'alimenter le spectrographe. Pour maximiser l'efficacité du couplage, la PSF de la planète doit être positionnée avec une précision meilleure que 0,1 λ/D (4 mas dans la bande H pour SPHERE) afin de minimiser les pertes de flux. Il est donc essentiel de définir la meilleure stratégie possible pour HiRISE afin de centrer la PSF d'une planète sur une SMF. Trois stratégies de centrage sont prévues, basées sur la rétro-injection de fibres pour localiser la position de la fibre scientifique, sur une fibre de centrage ou sur la combinaison des deux. J'ai mis en oeuvre ces approches et comparé leur précision de centrage en utilisant une configuration améliorée du banc d'essai MITHiC, qui reproduit la configuration de l'instrument utilisé dans HiRISE.

Mes résultats démontrent qu'il est difficile d'atteindre une précision de 0,1 λ/D, quelle que soit la stratégie de centrage choisie. Cela nécessite un haut niveau de précision à chaque étape de la procédure de centrage, qui peut être atteint avec des instruments très stables. J'ai étudié les facteurs contribuant à l'erreur de centrage et j'ai proposé une quantification des termes ayant le plus d'impact. En outre, je contribue actuelement à la préparation de la phase AIT de HiRISE au LAM et je contribue à établir une procédure de validation des stratégies de centrage sur le ciel. L'alignement du système est basé sur un SPHERE simulateur qui reproduit les principales caractéristiques du faisceau IFS dans SPHERE et permet de vérifier la qualité de l'image et du front d'onde. Le but de mon travail est d'analyser les différences entre le travail effectué sur MITHiC et son implémentation sur HiRISE, et d'extrapoler celà aux défis que nous rencontrerons sur le ciel. Une validation concernant la meilleure stratégie de centrage pour HiRISE émergera de la phase d'AIT, mais la décision finale concernant la stratégie de centrage sera prise après les premiers tests sur le ciel.

Il est probable que le HDC continuera à utiliser des spectrographes alimentés par des fibres dans un avenir proche. Mon étude prépare donc le terrain pour des instruments comme RISTRETTO/VLT, PCS/ELT, MODHIS/TMT -ou des missions phares post-JWST.

Mots clés : haute résolution angulaire, spectrographes, optique adaptative, coronographie à haute dispersion, exoplanètes One of the challenges of HiRISE resides in blindly centring the planet's signal of a previously known exoplanet detected by SPHERE into a SMF. The FIM part plays a critical role since it will pick up the planet's PSF in SPHERE and inject it into a SMF located in the fibre bundle to feed the spectrograph. To maximise the coupling efficiency, the planet's PSF must be positioned with an accuracy better than 0.1 λ/D (4 mas in the H band for SPHERE) to minimise light losses. Therefore, defining the best possible strategy for HiRISE to centre the planet's PSF on a SMF is essential. Three centring strategies are foreseen, based on retro-injecting calibration fibres to localise the position of the science fibre, on a dedicated centring fibre, or on a combination of both. I implemented these approaches and compared their centring accuracy using an upgraded setup of the MITHiC HCI testbed, which emulates the instrument setup used in HiRISE.

My results demonstrate that reaching a specification accuracy of 0.1 λ/D is challenging regardless of the chosen centring strategy. It requires a high level of accuracy at every step of the centring procedure, which can be reached with very stable instruments. I studied the contributors to the centring error and proposed a quantification for the most impactful terms. In addition, I contribute to the AIT phase preparation of HiRISE at LAM and investigate how to validate the centring strategy on sky. The alignment of the system is based on a SPHERE simulator that reproduces the main characteristics of the SPHERE IFS beam and enables to verify the image and wavefront quality. The goal of my work is to analyse the difference between the work done on MITHiC and its implementation on HiRISE and to extrapolate to the challenges we will meet on sky. Some validation regarding the best centring strategy for HiRISE will emerge from the AIT phase, but the final decision regarding the centring strategy will be taken after the on-sky tests.

It is likely that HDC will continue using fibre-fed spectrographs in the foreseeable future. My study, therefore, prepares the ground for instruments like RISTRETTO/VLT, PCS/ELT, MODHIS/TMT -or post-JWST flagship missions.

Keywords: high-angular resolution, spectrographs, adaptive optics, high-dispersion coronagraphy, exoplanets Un gargantuesque merci à Jeff pour ta disponibilité, ta pédagogie exquise et pour l'interêt que tu as porté à mes travaux. C'était un réel plaisir intellectuel d'échanger avec toi. Anne, il est difficile de ne pas utiliser tous les superlatifs que j'ai en tête pour te remercier. Mille merci pour ton soutien, ton expertise pointue de l'instrumentation et de m'avoir permis de réfléchir à "haute voix" sur ton tableau. Fabrice, il y a tellement à dire que je sais pas par où commencer alors je vais faire simple. Merci pour ta disponibilité, de m'avoir transmis ta passion de coder de façon pythounesque, ton expertise immense sur l'instrumentation, nos échanges passionnant sur les sous systèmes et les voyages. Last but not least, Gilles. It was a tremendous pleasure to have you in our team. Thank you so much for your kindness, constant support, and educational way of teaching instrumentation and exoplanets. Thank you for all the work you achieved for HiRISE, your brain is comparable to an encyclopedia. I am looking forward to seeing you soon and wish you and Sasha a lot of happiness. Je voudrais remercier les personnes au LAM avec qui j'ai partagé des discussions au détour d'une pause: Alexandre Santerne, Olivier Moussis, Stéphane Basa, Vincent Hue. Thank you also to all the PhDs students, Postdocs, CDDs, I met and with whom I had fun: Gayathri, Artem, Isabelle, Antoine, Jean-Charles, Mahawa, Nicolas, Divin, Hugo, Steven, Lorena, Pia, Diana, Sia, Mathilde, Meriem, Alessandro, Ilias, Raissa, Maxime, Arnaud, Camille, Nour, Arielle, Valentina, Iris, Pierre and Julia.

Aux services méca et essais: Pat, Phillipe, Jean-Antoine, Alain, merci pour vos expertises et pour ces bons moments passés dans l'atelier méca. José, promis je ne verrais plus la méca de la même façon désormais, merci pour ton oeil avisé, ton professionnalisme et ta bonne humeur. Aux services informatique et administratif, merci de nous rendre la vie plus facile au LAM: merci à Françoise, Nataly, Pascal, Christine, Solange, Fabrice, Vincent, Samuel, Jean-Luc et tout le personnel du LAM qui nous a permis de travailler en sécurité lors de cette pandémie.

To my mentors: Glenn Orton, Conor Nixon, Daniel Rouan, Raphaël Galicher, and Thierry Fouchet, thank you for the opportunities and your constant support. Thank you also to the people who welcomed me during my US tour: the Keck team in Hawai'i: Peter Wizinowich and Jacques-Robert Delorme, Dimitri Mawet's team at Caltech, Rémi Soummer and Laurent Pueyo at the STScI, Rebecca Jensen-Clem's team at USC, Vanessa Bailey and Gareth Ruane at JPL, Tyler Groff, Scott Will and Avi Mandell at NASA Goddard.

Lorsque je suis arrivée à Marseille, j'ai été accueilli par un super-groupe d'amis, avec qui j'ai partagé beaucoup de bons moments: Mel, Olive, Yoyo, Mich, Lucie, Sabri pour toutes les fois où tu m'as fait rigoler à en pleurer, Romain pour le temps que m'as consacré et nos discussions autour du Japon, Vincent pour ces moments funs et nos discussions lègeres-sérieuses, Taï le masry du LAM pour toutes ces fois où tu as été d'une sagesse sans nom et pour les moments de qualité que l'on a partagé. Alexis, thank you for being such an amazing friend, and for proofreading my thesis with so much dedication. Iva, I am so happy that I met you, thank you for having my back, and proofreading my thesis but mostly thank you for empowering your friends with your wisdom and soul. Romain et Thibaut, c'était un plaisir de vous avoir dans mon entourage pendant ces dernières années. Merci pour les bons moments que l'on a partagé au LAM et en dehors. À ma Faustinou, merci d'avoir été là, pour ta gentillesse, ta sensibilité et ton empathie pour autrui, pour ton amitié tout simplement. Je te souhaite une vie remplie de bonheur et de pingouins avec Horst. Manal, Manoula comme je dis si souvent. Ton arrivée au LAM a apporté une grande bulle d'oxygène dans ma vie et celle du labo. Merci d'avoir été là pour moi, pour tes conseils avisés, nos moments de complicités, pour tous les bons moments que l'on a partagé et pour ton amitié sans faille. Promis, je ne jure que d'une visite du Liban par tes soins mais surtout je vous souhaite beaucoup de bonheur à ta famille et à toi. Every time I travel the world, I found Italians and I get along with them, Marseille was not an exception. To the Italian crew: Elena, Davide, Jorge (yes, you are Italian by procuration) thank you so much for the extra life you brought to my thesis life. For the 100Kg of pasta, cheese and love you provided. I will miss our Harry Potter Marathon, our board game, our Chambord meetings, and our weekly restaurants (not the gym though), but I am sure that we will meet again. Simona, Simou, grazie mille per tutto il supporto che mi avete dato. Per tutti quei momenti in cui abbiamo riso insieme, per i tuoi saggi consigli, le tue feste di compleanno, i nostri momenti di complicità. Per aver riletto la mia tesi, e per avermi letto Dante per calmarmi. Mi mancherai terribilmente, ma prometto che ci rivedremo. Au Bazarette Marseillaise: Fanny, Perette, Anna, Zoé, Johanna, merci pour votre accueil et pour tous ces beaux moments que l'on a partagé. À ma Manon, je suis tellement heureuse de t'avoir rencontré, merci pour tous les moments de qualité que l'on a partagé et pour cette si belle amitié. Je vous souhaite pleins de bonheur et j'ai hâte de vous revoir.

Vous savez qui vous êtes, merci pour le soutien, et d'être toujours là: Imane Bellani aka Dr Imou, Leila, Cherihan, Paula, Clément, Stella, Issam, Alice, Savannah, Carol, Anna, Bérangère, Dahlia, Nicolas, François, Angélique, Léon, P-C. À mon love Séculaire : Sophie et Kelly, mes choupies, merci pour votre amitié, nos moments si précieux, notre complicité sans faille, d'être là même quand on est sur différents continents. À vous tous, j'ai hâte de voir ce que vous allez accomplir, car je sais que ça sera grandiose.

Viens enfin le moment de remercier ma famille au quatre coins du monde. À mon tonton Djamel, Melissa et Line, je suis très fière de vos accomplissements respectifs et je tenais à vous remercier pour vos encouragements si précieux. À ma tata Salima, que dire si ce n'est que tu es un brillant docteur et un être humain comme on en a rarement vu. Merci d'avoir été une source d'inspiration depuis ma tendre enfance et d'avoir été un modèle d'excellence académique et humain. À Sarha Zibani, merci pour le rôle déterminent que tu as joué dans ma vie. Pour cet esprit de finesse qui te caractérise si bien, mais surtout d'être ce modèle d'éminence, de savoir, de douceur humaine et de sagesse. Merci de m'avoir transmis ton amour de la littérature.

À ceux qui ne sont plus, mais qui n'ont eu de cesse de m'appeler Docteur avant l'heure et qui ont tant accomplis. Mes oncles et tantes de la famille Bachandy: Wataneya, Mahmood, Soraya, Ghada, Bataa, Moustapha, Sayeda. Mes oncles et tantes de la famille El Morsy-El Essawi: Soraya, Mokhtar, Mohamed. Je ne vous oublie pas. Merci. À ma bien aimée tante Sara et ma brillante cousine, Dr Mona emportées par le COVID-19, merci d'avoir cru en moi et de m'avoir stimulé scientifiquement et spirituellement. Enfin, à ma meilleure amie d'enfance/soeur Marina, merci de m'avoir toujours encouragé à me surpasser. Je suis certaine que de là où tu es, que d'une façon ou d'une autre ces quelques lignes te parviendront, toi qui étais impatiente de lire ma thèse. J'espère que tu auras ce sourire qui te va si bien. "May flights of angels sing thee to thy rest" À mes grands-parents et mes parents. Mille mercis pour votre amour. Il mêle votre passion de la science et de l'art, vos valeurs de respect, d'empathie et de bienveillance. Merci de m'avoir soutenu dans mes choix, de m'avoir encouragé et porté pendant mon cheminement professionnel et humain.

À l'art sous toutes ces formes, merci pour ces nombreux voyages de l'esprit.

"There is a tide in the affairs of men Which, taken at the flood, leads on to fortune; Omitted, all the voyage of their life: Is bound in shallows and in miseries. On such a full sea are we now afloat; And we must take the current when it serves, Or lose our ventures."

The High-Resolution Imaging and Spectroscopy of Exoplanets:

HiRISE 74 is to be glued on the tip-tilt platform. The Fizeau Phase-shifting laser interferometer is on the left on the picture with the reference surface directly implemented in the device (black ring). On the right side of the picture, we see the tested mirror on its mount. The mirror has been tilted only when the picture has been taken. . . . . . . . . . . . . . . . . 3.20.Screenshot of the metrology wavefront error for the selected mirror. . . Temperature elevation with respect to the ambient air for the tip-tilt stage controller and its power supply. The black rectangle on top of the controller is the aluminium tape that holds the temperature sensor, which has a different emissivity than the rest of the controller surface.

Prototyping of a centring procedure on MITHiC

Assembly, integration and testing process of the HiRISE instrument164

Conclusions and perspectives

Bibliography ANNEXES

List of Figures

Introduction

Over the past decades, numerous exoplanets have been detected beyond the Solar System by indirect or direct methods. This allows us to target different populations and retrieve their physical key properties (Mayor et al., 1995). One of the main advantages of directly imaging exoplanets is that it allows quantifying the chemical compositions and abundances of their atmospheres (Brogi et al., 2019; I. A. G. Snellen et al., 2014), and establishing their formation and evolution mechanisms (Crepp et al., 2012;Piso et al., 2016). High-contrast imaging (HCI) focuses on the direct detection of young (<300 Myr), giant (>1 M Jup ) exoplanets orbiting at relatively large orbital separations (>10 au) from their host star. The high contrast (>10 mag) and small angular separation (<1 ′′ ) of these planets with respect to their host star are a severe limitation to their detection, but especially to their atmospheric characterisation.

Is there life out there?

"The count of confirmed exoplanets just ticked past the 5,000 mark, representing a 30-year journey of discovery led by NASA space telescopes." This statement has been made by NASA's Exoplanet Exploration Program in 2022. Figure . 1.1 shows the cumulative number of discoveries as a function of the year and the discovery methods. Figure . 1.2 enables to visualise the number of exoplanet discoveries in mass-period space from 1989 through January 2023. 1.1. Is there life out there?

State of the art and methods of exoplanet detection

At the end of the 19th century, the existence of planets outside of the solar system was considered by the scientific community, although none had been detected due to the lack of instruments capable of making a direct image of these planets. Indeed, the challenge lies in the small angular separation between the host star and the exoplanets and their difference in brightness. Therefore, scientists decided to circumvent this problem and sought to detect these exoplanets indirectly by observing the potential effects that an exoplanet would have on its host star. Various indirect methods have led to several discoveries. In the following sections, I briefly present these different methods.

Pulsar timing

In 1965, Burnell and Hewish [START_REF] Hewish | Observation of a Rapidly Pulsating Radio Source[END_REF] recorded a short pulse signal (0.3s) repeated on a period of 1.3 s with a radiotelescope. The origin of the signal was traced back to a neutron star, which originates from an explosion of a massive star and which is rotating rapidly around itself. These neutron stars, commonly called pulsars, were predicted by Lev Landau in 1930. The gravitational effects of an exoplanet around a pulsar affect the period of the pulsar signal and detecting them thus implies the presence of a planet -this effect is called pulsar timing. For many years, astronomers [START_REF] Lyne | No planet orbiting PS R1829-10[END_REF][START_REF] David | Pulsating Radio Sources near the Crab Nebula[END_REF]) have announced the discovery of a planet around a pulsar but it was in 1992 that Alek Wolszczan and Dale Frail announced the discovery of two exoplanets orbiting PSR1257+12 [START_REF] Wolszczan | Confirmation of Earth-Mass Planets Orbiting the Millisecond Pulsar PSR B1257+12[END_REF]. The first planet had 3.4 M ⊕ and a period of revolution of 66.5 days, and the second planet had a 2.8 M ⊕ and a period of revolution of 98.2 days. Two years later, Wolszcan confirmed the presence of a third planet in the same system with the lowest known planetary mass in the universe (0.02 M ⊕ ). This method has made it possible to discover other planets, but it has not been very popular due to the environment it targets. The detection of habitable planets is considered impossible because the electromagnetic environment of the pulsar is hostile and leaves few hopes that these exoplanets could be habitable.

1.1. Is there life out there?

Radial velocity

The periodic motions of exoplanets around their host star can be detected by measuring the velocity variations of the star during its orbit, caused by the planet's gravitational tug. Using spectroscopy (see Sect. 1.3), we can study the spectrum of the star and determine the velocity variations of the star along the observer's line of sight, which is defined as radial velocity. The position of the absorption and emission lines of the star vary with the relative speed of the star with respect to the observer, which is described as the Doppler-Fizeau effect and as it is shown on Fig. 1.3. When the star approaches the planet there is a shift towards blue and when it moves away there is a shift towards red part of the recorded spectrum. In 1995, Didier Queloz and Michel Mayor discovered the first exoplanet in orbit around the star 51 Pegasi (Mayor et al., 1995), which earned them the Nobel Prize in Physics in 2019. Their discovery was possible due to observations made with the spectrograph ELODIE [START_REF] Baranne | ELODIE: A spectrograph for accurate radial velocity measurements[END_REF] installed on the T193 of the Observatoire de Haute Provence (see Fig. 1.4). In the Fig. 1.5, we see the original radial velocity curve, which allowed to deduce the mass (half of the M Jup ) and the period of revolution (4 days) of the planet. As the inclination of the planet can not be constrained by this method alone, the measured mass can only be seen as a lower limit. We can cite many spectrographs that use this method of detection such as: HARPS installed at the La Silla Observatory [START_REF] Mayor | Setting New Standards with HARPS[END_REF], SOPHIE [START_REF] Perruchot | The SOPHIE spectrograph: design and technical key-points for high throughput and high stability[END_REF], and ESPRESSO on the VLT (Pepe et al., 2021). 1.1. Is there life out there?

Astrometry

By studying the astrometry of a star, i.e. by studying its position and motion projected on the sky, it is possible to detect the motion of their exoplanets. The first astrometric measurements coincided with the advent of photographic plates for astronomical observations. In 1969, Peter Van de Kamp announced the detection of two planets orbiting Barnard's star, based on the analysis of 2400 photographic plates taken between 1916 and 1963 with the Sproul telescope, which later turned out to likely be caused by instrumental errors. However, this technique is limited by its low precision (about 10-100 µarcsec), which has made only one detection possible to date (4 mas motion, Sahlmann et al. 2013). In contrast, with space telescopes such as ESA/Gaia, which was successfully launched in 2013, an accuracy of the order of a few µarcsec can be achieved. This will hopefully lead to a large number of exoplanet detections by the end of the mission (see initial estimates by [START_REF] Perryman | Astrometric Exoplanet Detection with Gaia[END_REF].

Planetary transit

Apart from gravitational effects, exoplanets in orbit around a star can cause the star's luminosity to be dimmed, as illustrated in Fig. 1.6. This event is noticeable if the planet is between the star and the observer, which is a limitation for their detection. For planets the size of Jupiter, the observed decrease in luminosity is on the order of 10 -2 , and for planets the size of the Earth, 10 -4 . This method makes it possible to constrain the radius of the planet when the radius of the star can be modelled. As it strongly sets the inclination of the planet's orbit, it can be used together with the minimum mass of the Radial Velocity method to determine the true mass of the planet. Together the radius and mass determine the density, which gives us valuable information on the composition of the planet. The first exoplanet discovered by the transit method was detected around the star HD 209458 [START_REF] Charbonneau | Detection of Planetary Transits Across a Sun-like Star[END_REF]. Since then, the space instruments CoRot (Fig. 1.7), Kepler, CHEOPS, and TESS have detected many more. A method derived from the transit method exists and is called the secondary transit method. This involves subtracting the signal from the star (when the planet is behind the star) from the star-planet system (when the planet is in front of the star). This semi-direct method allowed the detection of HD 209458 b (commonly called OSIRIS, Vidal-Madjar et al. 2004) with the Hubble telescope (HST), which allowed the detection of carbon and oxygen in the atmosphere.

1.1. Is there life out there?

. Microlensing

In 1936, Einstein introduced the notion of the curvature of space-time by a massive star as part of his theory of general relativity. His theory explains that if a planet is present between the star and the observer then it will no longer follow the geodesics of space-time. A star that intersects the line of sight of a second star (background star) will produce a lensing effect that increases the luminosity of the background star. Thus, if a planet passes in front of a background star, the same phenomenon would occur, this time with a decrease in luminosity because the planet is less massive than its host star.

High contrast imaging

Several large-scale surveys using robotic telescopes or a network of telescopes, such as OGLE [START_REF] Udalski | OGLE-IV: Fourth Phase of the Optical Gravitational Lensing Experiment[END_REF] or MOA, have made several such detections over the past decade. Some important results regarding the demography of planets at large separation from their parent star (e.g., [START_REF] Suzuki | The Exoplanet Mass-ratio Function from the MOA-II Survey: Discovery of a Break and Likely Peak at a Neptune Mass[END_REF] have been made. In a few years, the launch of the Roman Space Telescope and its wide field imager (WFI) instrument will offer significant prospects for the detection of microlensing events [START_REF] Penny | The WFIRST Microlensing Survey: Symbiosis with Galactic Bulge studies[END_REF]. It has even been suggested that a joint survey with ESA/Euclid could bring a lot of information and break some fundamental degeneracies that usually limit the microlensing technique [START_REF] Bachelet | Euclid-Roman joint microlensing survey: Early mass measurement, free floating planets, and exomoons[END_REF].

High contrast imaging

Although some interesting direct detections have been obtained through secondary transit eclipses (e.g., [START_REF] Deming | Infrared radiation from an extrasolar planet[END_REF]) and more recently with interferometry (GRAVITY Collaboration et al., 2019, 2020), I will focus solely on classical "imaging" of planetary companions in this section.

Direct imaging is a powerful technique to study the atmosphere of planets. However, this technique is more efficient to image planets orbiting far from their host star (< 5-1000 AU). The first direct image of an exoplanet orbiting a brown dwarf (BD) was made by [START_REF] Chauvin | A giant planet candidate near a young brown dwarf. Direct VLT/NACO observations using IR wavefront sensing[END_REF] and other direct detection of planets followed in the next decades, e.g Fomalhaut b [START_REF] Kalas | Optical Images of an Exosolar Planet 25 Light-Years from Earth[END_REF]

Limitations of the technique

The limitation of this technique resides in the ratio of magnitude between the planet and its host star, and in the fact that for an observer on Earth, they appear to orbit very closely to each other. We define the direct imaging observation by the angular resolution between the planet and its host star, which is limited by the angular separation of the telescope. It is also impacted by the contrast of luminosity, which is limited by the sensitivity of the observation.

Contrast

To illustrate the problem of contrast in direct imaging techniques, I take the solar system as an example. We notice in Fig. 1.9 that the luminosity is represented as a function of wavelength for different objects. In such a representation, the Sun is 1.2. High contrast imaging approximated as a black body, and the other planets of the solar system as a black body to which is added the light reflected from the Sun. At λ > 0.7µm for a hot Jupiter and at λ > 3µm for Earth and Jupiter, the planets' own emission is brighter than the light reflected from the sun. It is therefore preferable to work in this part of the spectral range when trying to detect a planet. In this part, the star-and-planet pair is spatially resolved by a telescope of a few metres in diameter. The difficulty lies in overcoming the contrast of their fluxes, which is 10 9 -10 10 for an Earth-type planet. Since we want to spectrally characterise exoplanets, we aim to cover the widest possible spectral band. However, we notice that even if we expand the spectral band, the planet flux remains faint, so it is crucial to optimise our imagers to increase the photon transmission. I define the contrast to be the flux ratio between the planet and the star at which it can be detected with an SNR of 5 (equivalent to a 5σ detection).

Angular resolution

The angular resolution of telescopes is proportional to the wavelength, thus favouring observations at shorter wavelengths.

The angular resolution of an optical system, limited by the diffraction is defined as the angle between two objects that it can resolve. It is defined as:

1.2. High contrast imaging Θ = λ D , (1.1)
with λ the wavelength and D the telescope diameter.

The Rayleigh criterion states that a telescope with a circular aperture of diameter D, observing at a certain wavelength λ, is able to separate two objects that are separated by more than 1.22 λ/D.

Directly imaging an exoplanet using a ground-based telescope comes with the challenge of observing through the Earth's atmosphere. The atmosphere is turbulent and produces spectral and spatial wavefront distortions.

Image formation through a telescope 1.2.2.1. Image formation principle

The role of an imaging instrument is to make the light coming from a light source at infinity converge into an image in a focal plane by using mirrors and lenses. This image formation is driven by the diffraction theory described by Born and Wolf [START_REF] Born | Principles of Optics Electromagnetic Theory of Propagation, Interference and Diffraction of Light[END_REF]. In the hypothesis of an angular field of "isoplanatism", i.e. the impulse response of the instrument being the same in all angular directions (the light passes through the same layers of the atmosphere), I define the image on the sensor to be the convolution of the observed object o with the impulse response of the instrument h:

i = o * h (1.2)
with * the convolution product between two functions f (t ) and g (t ) defined as:

[ f * g ](y) = f (t )g (y -t )d t . (1.3)
The impulse response of the instrument h is also called the Point-Spread Function (PSF). It describes the two-dimensional distribution of the light in the instrument's 1.2. High contrast imaging focal plane. The PSF is equal to the square modulus of the inverse Fourier transform of the complex field in the entrance pupil of the instrument. If ψ(r) is the field at the instrument entrance pupil with r = (r, θ) the vector coordinates in the pupil plane, then complex field Ψ(γ) in the focal plane is defined as:

Ψ(γ) = F -1 [ψ(r)], (1.4)
with γ = (γ r , γ θ ) the vector coordinate in the focal plane and F -1 the inverse of the Fourier transform. By definition, the PSF of the instrument is defined as:

h(γ) = |Ψ(γ)| 2 = |F -1 [ψ(r)]| 2 .
(1.5)

The Fourier transform of the PSF is called optical transfer function (OTF) and as described in Fig. 1.10, it can be calculated by the auto-correlation of the field in the entrance pupil:

h(γ) = F [h(γ)] = ψ(r) ⊗ ψ(r) (1.6)
The OTF describes the response of an imaging system as a function of spatial frequency f . In the case of an instrument of diameter D, the OTF is defined for a wavelength by a cutoff frequency f c = D/λ. In the following paragraphs and for the sake of clarity, I will not explicitly write the spatial variables γ and r.

High contrast imaging

The sensor located in the focal plane is based on a pixel matrix architecture with a pixel pitch of d p (pixel centre to pixel centre) and a noise n intrinsic to the sensor. The model to represent the system consists of the convolution of the h with h sensor , as:

i = o * h * h sensor + n.
(1.7)

The Shannon-Nyquist's sampling theorem states that the sampling frequency of a signal f s = 1/d p must be equal to or greater than twice the maximum frequency contained in that signal, to not lose any information. The theorem is described as:

f s ≥ 2D λ ≡ d p ≤ λ 2D , (1.8)
with the sampling e, equal to the ratio between f s and f c .

In the case of an ideal telescope, the complex field in the entrance pupil is constant, so the PSF is calculated by the Fourier transform of the pupil transmission function P: h Ai r y = |F -1 [(P)]| 2 , with in the case of a circular pupil with no central obstruction:

P(r ) =
1 if inside the aperture, 0 if not.

(1.9)

Effect of aberrations and decomposition in Zernike modes

Ideal telescopes are unrepresentative of real imaging instruments, which face image degradation due to aberrations. During its propagation, light passes through inhomogeneous media and encounters imperfect optics, which introduces errors in phase (Φ) and amplitude (ε). The complex field in the entrance pupil with aberrations is defined as: ψ = P.e (i φ+ε) .

(1.10)

High contrast imaging

In this thesis, I focus only on phase aberrations. We notice that in the presence of aberrations, the PSF is not an Airy pattern anymore. The resulting wavefront error corresponds to the standard deviation σ φ of the phase φ. The phase aberrations are caused by the atmospheric turbulence encountered, which distorts the wavefront by introducing optical path differences. These originate from variations in the refractive index of the optical surfaces and the air and the differences in the geometrical paths crossed by the light. To decompose the wavefront error into easier-to-understand components, Zernike polynomials are used. The first few Zernike Polynomials correspond to very well-known optical aberrations (piston, tip and tilt, defocus, astigmatism, trefoil, coma, and spherical).

The Zernike polynomials, defined as {Z k } k∈ [1,∞] are continuous and orthogonal over a unit circle (usually the pupil plane), where the aberrated phase can be decomposed. The phase φ decomposed on the base {Z k } is defined as:

φ = ∞ k=1 a k Z k , (1.11)
with a k the coefficients associated to the polynomials Z k of the base. The Zernike polynomials are defined as the product of a radial function R m n (r) with an azimuthal function Θ m n (θ), and they are defined as:

Z k = R m n (r )Θ m n (θ), (1.12
)

Θ m n (θ) =    n + 1 if m = 0 2(n + 1) if m ̸ = 0and k even 2(n + 1) if m ̸ = 0and k odd (1.13) R m n (r ) = (n-m)/2 s=0 (-1) s (n -s)! s![ n+m 2 -s]![ n-m 2 -s]! r -2s , (1.14)
with for each polynomial radial and azimuthal degrees such as n (n = 0, 1, .., ∞) and m (0 ≤ m ≤ n). The Zernike polynomials as a function of their degrees are represented in Fig. 1.11.

High contrast imaging

We notice that aberrations can evolve over time and we define three categories of aberrations. If the evolution time of the aberrations is very long compared to the image acquisition, we speak of static aberrations. If it is very short, we speak of dynamic aberrations and finally, if it is of the same order as the integration time, we speak of quasi-static aberrations. In order to compensate for these aberrations, which can be created by the atmosphere and internal optics, we use a system called adaptive optics (AO), see also Sec. 1.2.3.

Characterisation of the image quality through the atmosphere

Wavefront perturbations caused by the atmosphere can be summarised into three categories: (i) scintillation, which is a fluctuation in the brightness of a star. It is only observed for quasi-point sources; (ii) agitation, which represents a variation of the wavefront in time; (iii) spreading, which leads to images of a larger size than the size of the diffraction spot. The spatial coherence of the wavefront is reduced and this effect is responsible for a decrease in angular resolution.

Formalisms exist to interpret and quantify these phenomena. One of them is the Fried parameter, noted r o (λ), which is used to measure the quality of optical trans-1.2. High contrast imaging mission through the atmosphere. This quantity is calculated from the turbulence and makes it possible to define the disturbed image of a spot whose diameter is of the order of λ/r o , where r o is 5-20 cm in t. The seeing is defined by this ratio and thus corresponds to the size of the object on a detector acquired at long exposure. The seeing is highly chromatic and varies like λ -1/5 , which shows that its impact is reduced towards the infrared.

To estimate the quality of an imaging instrument, we use the Fraunhofer diffraction theory that computes the wave amplitude using the Fourier transform of the aberrated pupil function evaluated at the centre of the image plane. The Strehl ratio (SR) is defined as:

SR = |e i φ | 2 = |e i 2πδ/λ | 2 , (1.15)
with φ the phase error over the aperture at the wavelength λ. In the case of small aberrations, the SR can be estimated to be:

SR ≃ e -σ 2 φ , (1.16)
with σ 2 the variance. The performance of the telescopes can be characterised by the SR, ie, if SR = 1, then the performances of the instrument are limited by the diffraction.

AO system

The adaptive optics system allows to compensate the atmospheric turbulence and improves the performance of an imaging system described previously. In the fifties, the AO concept has been invented by H. W. Babcok [START_REF] Babcock | The Possibility of Compensating Astronomical Seeing[END_REF], but the concept has been developed only a few decades later at the Observatoire de Haute-Provence (OHP). It is in 1989, that the first system technologically capable of achieving an atmospheric correction appeared. This AO system named COME-ON [START_REF] Rousset | First diffraction-limited astronomical images with adaptive optics[END_REF] had paved the way for other systems such as the Nasmyth Adaptive Optics System (NAOS-CONICA), involved in the first exoplanet image with the VLT Since this first discovery, AO systems had become unavoidable on ground based-telescopes and had opened the path to active research since then.

High contrast imaging

Principle of AO

Fig. 1.12 represents the concept of AO system, which is composed of a reconstruction and control system (real-time calculator, RTC), wavefront sensor (WFS), and a wavefront corrector. The distorted light generated by the atmospheric turbulence arrives at the entrance pupil of the ground-based telescope. Then, the light is sent to a wavefront corrector to compensate for the wavefront distortions. Several wavefront correctors exist such as the deformable mirror (DM), and the spatial light modulator (SLM). Here, the DM reflects the light to a waveplate that splits the light between the wavefront sensor and the science path, where the image is formed on a focal plane camera. The role of the wavefront sensor is to measure the phase aberrations that are not compensated by the DM. Once this measurement is calculated by the WFS, the RTC adjusts the command to apply to the DM to compensate for the distortion. The atmospheric turbulence evolves with time at a high speed of typically 1ms, which induces also variations in the wavefront. The measurement of aberrations and the command to send to the DM must be refreshed as quickly as possible to maintain an accurate compensation of the atmospheric distortion. To achieve this requirement, AO is performed in closed-loop and at a high cadence. Typically the SPHERE AO system runs at 1.2 to 1.4 kHz, with a delay between measurement and correction of 1.6ms. I will introduce in the next paragraphs the different AO elements used to compensate for the phase aberrations.

Wavefront sensing

To estimate the phase aberrations, we could extract the information from this equation, ψ = P.e (i φ+ε) but if we compute the image of the pupil plane, we lose the phase contribution. Thus, the role of wavefront sensors is to provide a direct measure of the phase and amplitude of a wavefront. I will briefly describe the three main wavefront sensors used in AO system:

1. The most common type of wavefront sensor is the Shack-Hartmann wavefront sensor (SHWFS) (Shack and Platt, 1971). It combines a 2D lenslet array detector and each of the lens allows to estimate locally the slope of the wavefront (named s). By combining all the slopes, it is possible to reconstruct the wavefront to correct.

2. In 1999, Ragazzoni proposed the Pyramid wavefront sensor (PyWFS) (Ragazzoni et al., 1999), which is an optical device used to perform wavefront sensing. The PyWFS is a pupil plane wavefront sensor performing optical Fourier filtering thanks to a focal plane glass square-based pyramid. The pyramid produces four pupil images on a detector and by analysing the differences in brightness between the four pupils, it is possible to locally retrieve the slope of the wavefront.

3. The curvature sensors developed by [START_REF] Roddier | Curvature sensing and compensation: a new concept in adaptive optics[END_REF] enable to measure the curvature of the wavefront instead of its slope. The principle of this method is to form defocused images of the pupil. The purpose of the defocusing effect is to transform phase aberrations into amplitude aberrations. The wavefront curvature producing an increase of illumination in the plane before the focus will produce a decrease of illumination in the plane after the focus. By analysing the intensity variations in the obtained images, it is possible to retrieve the radius of curvature of the wavefront.

Each of these WFS offers advantages (and inconveniences). The choice to use one instead of the other is driven by the type of aberrations to compensate (need for simple AO or ExAO). However, all of three WFS provides local wavefront estimation (slope or radius of curvature) in the pupil plane.

Deformable mirrors

Once the phase aberrations are estimated, the wavefront correctors apply the opposite measured phase to compensate for the distortion. Two wavefront correctors exist, SLMs, which optics principles are detailed in this thesis, and deformable mirrors 1.2. High contrast imaging (DMs). DMs are preferably chosen over SLM due to their specificity to work with achromatic light (photons entering the telescope).

Coronagraphy

The word coronagraphy has been proposed by William Huggins [1824-1910] to the Royal Society in 1882. Its etymology is composed of the Latin "corona", which means "crown" and the Greek "graphô", which means "to write", so it can be translated to "describe the crown". The crown in question is the Sun's corona, imaged for the first time in 1851 by Johan Berkowski. In 1930, Bernard Lyot developed a method for observing the Sun's corona by blocking the Sun's light with an opaque mask whose size is identical to that of the Sun [START_REF] Lyot | The study of the solar corona and prominences without eclipses (George Darwin Lecture[END_REF], combined with a stop in a downstream pupil plane to block the diffracted light. A few years later, this technique was also applied to other stars, with the principle being based on the reproduction of a total eclipse that masks the star and allows planets orbiting close to the star to be made visible.

Coronagraphs are characterised by four quantities such as the throughput, the inner working angle, the contrast and the chromaticity. The inner working angle is the smallest angle for which a planet is detected with more than 50% of throughput. The contrast is the flux ratio between the star and a planet detected at 5 σ. The chromaticity of the coronagraphs is important in the case of spectroscopy since their performance rapidly decreases as the spectral bandwidth increases. There are different types of coronagraphs, whose role are to block the light in the pupil or focal plane, such as amplitude coronographs and phase coronographs. Among the amplitude coronographs in the focal plane, we find the Lyot coronograph, whose principle is illustrated in Fig. 1.13, and its improvement based on an apodized pupil [START_REF] Soummer | Apodized Pupil Lyot Coronagraphs for Arbitrary Telescope Apertures[END_REF]. There are also phase coronographs in the focal plane, the first one proposed was the [START_REF] Roddier | Stellar Coronograph with Phase Mask[END_REF] based on a transparent blade with an engraved circular disc in the centre. The size of the disc is adapted to the PSF of the telescope and for a wavelength produces a phase shift of π. The Dual Zone Phase Mask (Soummer, Dohlen, et al., 2003a) and the 4-quadrant mask proposed by [START_REF] Rouan | The Four-Quadrant Phase-Mask Coronagraph. I. Principle[END_REF], which principle is based on the use of a transparent mask producing a phase shift of π on half of the PSF (in amplitude) and which causes by destructive interference a luminous attenuation of the star placed on the axis of the star, while the image of the off-axis planet is unaffected. Finally, [START_REF] Mawet | Annular Groove Phase Mask Coronagraph[END_REF] presented a vortex coronagraph, which is in the form of a transparent blade with a thickness that decreases spirally from a height that produces a phase shift of 2m π (with m an integer) to a height that produces a zero phase shift. The principle of vortex coronagraph as with all coronagraphs is that an on-axis star will be highly attenuated while the off-axis planet 1.2. High contrast imaging light will be transmitted. It is a fairly powerful coronagraph, only it is limited by its manufacture mainly due to the difficulty to engrave a spiral blade whose thickness variation is continuous. Other solutions exist: see the Annular Groove Phase Mask (AGPM), based on the dispersion of form birefringence of subwavelength gratings.

An amplitude or phase modification in the pupil plane allows for reshaping the PSF by suppressing the diffraction rings. A few examples of pupil plane coronagraphs are the shaped pupil of [START_REF] Kasdin | Extrasolar Planet Finding via Optimal Apodized-Pupil and Shaped-Pupil Coronagraphs[END_REF], the apodising phase plate (APP) developed by [START_REF] Kenworthy | First On-Sky High-Contrast Imaging with an Apodizing Phase Plate[END_REF]. The Phase-Induced Amplitude Apodization (PIAA) Technology is successfully used in coronagraphy. The PIAA concept has been developed by [START_REF] Guyon | Phase-induced amplitude apodization of telescope pupils for extrasolar terrestrial planet imaging[END_REF] and employed to modify the shape of a light beam. A significant limitation of the PIAA technology is that the wavefront remapping depends on the localisation of the source with respect to the optical axis. When the PIAA is aligned with an off-axis object, such as in the case of a planet, the wavefront becomes highly aberrated, and the coma aberration deteriorates the PSF.

Coronagraphs offer many advantages and disadvantages depending on their localisation (pupil, focal plane) and on their design. Using a coronagraph in a focal plane allows to theoretically reach high contrast performance, however, they are sensitive to vibrations and difficult to install and align. Instead, pupil plane coronagraphs are achromatic, insensitive to vibrations and they only occupy a unique plane in the setup, which facilitates the installation. Many coronagraphs have an inner working angle of 1-2 λ/D [START_REF] Mawet | Direct imaging of extra-solar planets in star forming regions. Lessons learned from a false positive around IM Lupi[END_REF], which allows imaging planets close to their host star by using the diffraction limit of the telescope. A review of the design of coronagraphs described in this section is available in Mawet, Pueyo, et al. (2012).

. Substraction of the speckles

In addition to the control methods described above, post-processing methods have been developed to reduce the presence of speckles in the images. The purpose of these post-processing methods is to extract the signal of the planet from the coronagraphic image by processing the images acquired during the science observation. During my thesis, I did not work on these methods so I only describe them in this section.

There are different post-processing approaches such as the roll deconvolution, the reference star differential imaging (RDI), the angular differential imaging (ADI), which was first developed in the context of post-processing for space instruments, spectral differential imaging (SDI), and finally the polarimetric differential imaging (PDI).

Roll deconvolution

In 2000, Heap developed a post-processing tool to reduce an image of β Pictoris taken by the HST instrument, STIS. The method used was to use several images of the same system (planet-star) acquired during a single orbit of the instrument around the Earth. The rotation of the instrument with respect to the sky meant that the speckle field on the detector remained static in contrast to the various objects present during the observation.

Angular differential imaging

In 2004, Liu interpolated the roll deconvolution method to post-process AU-Microscopii with the NIRC2 instrument of Keck II. He uses the advantages of the alt-azimuth mount of the telescope to rotate the observed planet with respect to the optical axis without rotating the speckles. This statistical method allowed to obtain a sequence of about 100 images during one hour of observation and is based on the field subtraction of quasi-static speckles: ADI [START_REF] Marois | Angular Differential Imaging: A Powerful High-Contrast Imaging Technique[END_REF], LOCI [START_REF] Lafrenière | A New Algorithm for Point-Spread Function Subtraction in High-Contrast Imaging: A Demonstration with Angular Differential Imaging[END_REF], ANDROMEDA [START_REF] Cantalloube | Direct exoplanet detection and characterization using the ANDROMEDA method: Performance on VLT/NaCo data[END_REF][START_REF] Mugnier | Maximum likelihood-based method for angular differential imaging[END_REF], PCA [START_REF] Soummer | Detection and Characterization of Exoplanets and Disks Using Projections on Karhunen-Loève Eigenimages[END_REF]. [START_REF] Racine | Speckle Noise and the Detection of Faint Companions[END_REF] hypothesised that the spectra of planets have different absorption spectral bands from those of their host star. The method he developed consisted of simultaneously imaging the star and the planet in two neighbouring spectral bands of equal width, one of which is centred on the assumed absorption band. With spectrographs such as the SPHERE IFS, it is possible to obtain image cubes in several wavelengths. In these cubes, the image of the planet remains at the same location while the speckles move with the wavelength. By combining this method, similar to the one used for ADI (ANDROMEDA and PCA) and methods that provide information about the chromaticity of the speckles [START_REF] Ygouf | Simultaneous exoplanet detection and instrument aberration retrieval in multispectral coronagraphic imaging[END_REF], it is possible to extract the signal of the planet in the speckle field.

High contrast imaging

Simultaneous differential imaging

Polarimetric differential imaging

In 2001, Kuhn developed a method based on the polarisation difference between the planet and the reflected light from the star. When the two images are differentiated, the intensity of the speckles is reduced because they are not polarised.

Discoveries with Ground-based telescopes

In 2004, the first exoplanet has been directly observed at the Very Large Telescope (located at the top of the mountain in Paranal, Chile) with NACO (2M1207 b, [START_REF] Chauvin | A giant planet candidate near a young brown dwarf. Direct VLT/NACO observations using IR wavefront sensing[END_REF])), followed by the detection of β Pictoris b [START_REF] Lagrange | A probable giant planet imaged in the β Pictoris disk. VLT/NaCo deep L'-band imaging[END_REF]. At the Keck observatories (located at the top of Mauna Kea mountain in Hawaii, USA), four companions have been detected around the star HR 8799 by NIRC2 at 0.37 arcsec for the closest one [START_REF] Marois | Images of a fourth planet orbiting HR 8799[END_REF]. The technological development in the Adaptive Optics and coronagraphs fields paved the way for the next generations of high-contrast imagers.

High-contrast imaging combines extreme adaptive optics (ExAO, e.g., Fusco et al., 2006) to measure and compensate for the atmospheric distortion in ground-based observations, with coronagraphy to attenuate the on-axis starlight (Guyon et al., 2006;[START_REF] Mawet | Direct imaging of extra-solar planets in star forming regions. Lessons learned from a false positive around IM Lupi[END_REF]. However, the technique is mainly limited by quasi-static speckles in the focal plane (Soummer et al., 2007), which cover the planetary signal. To deal with the challenges of HCI, a new generation of instruments has been implemented on large ground-based telescopes in the last decade: VLT/SPHERE (Beuzit et al., 2019), Gemini/GPI (Macintosh et al., 2014), and Subaru/SCExAO [START_REF] Jovanovic | The subaru coronagraphic extreme adaptive optics system: enabling high-contrast imaging on solar-system scales[END_REF].

Spectroscopy

These new instruments have succeeded in discovering challenging companions such as 51 Eri b with GPI [START_REF] Macintosh | Discovery and spectroscopy of the young jovian planet 51 Eri b with the Gemini Planet Imager[END_REF], HIP 65426 b with SPHERE [START_REF] Chauvin | Discovery of a warm, dusty giant planet around HIP 65426[END_REF] and PDS 70 b [START_REF] Keppler | Discovery of a planetary-mass companion within the gap of the transition disk around PDS 70[END_REF]. Ground-based observatories offer great advantages from an operational point of view since they enable easy access to the telescope infrastructure and to the instruments. However, they need constant upgrades with new instruments to be able to outperform the limitation to the detection and characterisation of new companions.

While existing telescopes are being upgraded, others are being created with unparalleled technical challenges. This is the case of the future extremely large telescopes such as the Extremely Large Telescope by ESO [START_REF] Gilmozzi | The European Extremely Large Telescope (E-ELT)[END_REF]. The US Extremely Large Telescope Program includes the GMT [START_REF] Bernstein | Overview and status of the Giant Magellan Telescope project[END_REF] and the TMT (Sanders, 2013), which is one of the highest priorities in the ground-based frontier category. Future observations using the TMT will offer tremendous and unique opportunities for the coming scientific decades.

In order to avoid the Earth's atmosphere and these inconveniences for exoplanetary observations, space-based telescopes have been successfully launched for a few decades and have provided emblematic discoveries. Since my work is highly focused on ground-based observation, I will not present the space missions dedicated to the discoveries of exoplanets in this thesis. More detailed information regarding these missions can be found in: Lallo, 2012 for the Hubble Space Telescope (HST), [START_REF] Gardner | The james webb space telescope[END_REF] for the James Webb Space Telescope (JWST), and Dalcanton et al., 2015 for the Habitable World Observatory.

Spectroscopy 1.3.1. Historical introduction

In the first part of the 17th century, Auguste Comte summarised in one sentence the mystery regarding the composition of the stars: "We will never know how to study by any means the chemical composition (of stars), or their mineralogical structure." However, in 1814, Joseph Von Fraunhofer used a prism to diffract a ray of sun coming from a slit in his shutters, projected on a white wall. The rainbow spectrum was not surprising since it had already been characterised by Sir Isaac Newton, who published its experiments and theoretical explanations of the dispersion of light in Opticks: or, a treatise of the reflections, refractions, inflexions and colours of light, but Fraunhofer found in this spectra many dark lines. For each line, he catalogued the exact wave-1.3. Spectroscopy length and labelled the strongest ones with letters. Not understanding the origin of the dark lines, he decided to observe the light from a nearby star-Betelgeuse and noticed that the localisation of the dark lines changed. He concluded that it was probably due to the composition of the observed objects. Kirchhoff and Bunsen, in the mid-19th century, developed a spectrograph more accurate than the prism used by Fraunhofer. If we could attribute the first western spectrograph invention to Fraunhofer many other scientists had contributed to their development and understanding. Until today, they are part of central technological development by astronomers to enable more precise measurement of observed objects.

Resolving power

A spectrograph has a given line spread function (LSF), which describes the light distribution at the focal plane as a wavelength function in response to a monochromatic light source. The dominant effect in the spectrum is a broadening of the spectral features due to the finite resolution of the instrument. The model of the LSF is a Gaussian function with a FWHM of ∆ λ.

The spectral resolution of an instrument is given by its resolving power R:

R = λ ∆λ , (1.17)
with ∆λ is the smallest wavelength difference that can be resolved.

From Low to High-Resolution Spectroscopy

Our understanding of exoplanets is still limited due to the sample size across varied planet parameters such as the mass, the separation, the SNR, and the wavelength coverage. Observing targets with large telescopes will add an essential piece to the highly complex puzzle of exoplanet formation and evolution mechanisms. Spectroscopy is already used to characterise the atmosphere of mini-Neptunes, transiting giant exoplanets, super-Earth [START_REF] Sing | A continuum from clear to cloudy hot-Jupiter exoplanets without primordial water depletion[END_REF] and young giant exoplanets [START_REF] Bonnefoy | First light of the VLT planet finder SPHERE. IV. Physical and chemical properties of the planets around HR8799[END_REF][START_REF] Chauvin | Discovery of a warm, dusty giant planet around HIP 65426[END_REF][START_REF] Macintosh | Discovery and spectroscopy of the young jovian planet 51 Eri b with the Gemini Planet Imager[END_REF]. These characterisations have revealed for direct and transiting imaged exoplanets discoveries about cloud formation, which had been created by a silicates condensation process [START_REF] Kreidberg | Clouds in the atmosphere of the super-Earth exoplanet GJ1214b[END_REF]. The advantage of using direct imaging spectroscopy is that it allows probing 1.3. Spectroscopy deeper atmosphere layers, and thus, enables to detect spectral biosignature features [START_REF] Morley | Thermal Emission and Reflected Light Spectra of Super Earths with Flat Transmission Spectra[END_REF] in comparison to transmission spectrum methods used to study transiting exoplanet atmospheres such as HD 209458 b described in [START_REF] Charbonneau | Detection of an Extrasolar Planet Atmosphere[END_REF]. A more detailed review of the transit exoplanets discoveries characterised by spectroscopy can be found in Kreidberg. In order to access spectral information, IFS instruments are used in different spectral resolutions divided into three categories: low (R: 50-300), medium (R: 300-6000), and high (R > 6000) in the NIR. Complementary to spectrographs onboard space telescopes (such as STIS/HST), various ground-based imagers instruments have become available and combined high-contrast coronagraphs with IFS. For example, these instruments (P1640, SPHERE, GPI, SCExAO+CHARIS) combine AO and coronagraphs with low spectral resolution IFS, while VLT/MUSE, VLT/SINFONI and Keck/OSIRIS use ExAO HCI with medium spectral resolution IFS. SPHERE and GPI exoplanet imagers enable us to detect and characterise thanks to their IFSs, faint objects such as 51 Eri b [START_REF] Macintosh | Discovery and spectroscopy of the young jovian planet 51 Eri b with the Gemini Planet Imager[END_REF][START_REF] Samland | Spectral and atmospheric characterization of 51 Eridani b using VLT/SPHERE[END_REF] and HIP 65426b [START_REF] Chauvin | Discovery of a warm, dusty giant planet around HIP 65426[END_REF]. Even though, the low spectral resolutions of these instruments, typically R = 50 for the SPHERE IFS (Zurlo et al., 2014), are a major limitation for exoplanet characterisation, they provide key information about the composition, the structure of their atmospheres, and about the formation and evolution of planetary systems.

By studying Brown Dwarfs (BD, masses below 75M J ), we access an intrinsic understanding of the properties of young giant exoplanets since their physics and chemistry should be quite similar with the exception of the surface gravity [START_REF] Charnay | A Self-consistent Cloud Model for Brown Dwarfs and Young Giant Exoplanets: Comparison with Photometric and Spectroscopic Observations[END_REF]. Additionally, BDs offer an extended range of effective temperatures between 300 and 2500 K. Usually, stars remain at the same effective temperature for millions of years due to nuclear core fusion. However, BDs tend to cool with age because their cores are not able to reach the temperatures required to maintain hydrogen fusion [START_REF] Buenzli | Brown Dwarf Photospheres are Patchy: A Hubble Space Telescope Near-infrared Spectroscopic Survey Finds Frequent Low-level Variability[END_REF]. They go from a hot M type to an L spectral type to T spectral type. For effective temperatures between 1100-1400 K, an L-T transition occurs where L dwarfs are characterised by red color (J-K: 1-2mag) in NIR and silicate opaque clouds (Kirkpatrick, 2005) and T dwarfs are characterised by blue color (J-K: 0 mag) in NIR with methane absorption at 1.6 and 2.2 µm.

A hypothesis explaining the L-T transition, shifting the CO-CH 4 equilibrium [START_REF] Baraffe | Planetary Internal Structures[END_REF]) can be explained by the formation of silicate clouds in the photosphere of L dwarfs, which make them closer to a blackbody emission. In Fig. 1.14, we present a color-magnitude diagram covering the J-K bands with curves from a cloud model (Exo-REM) and from a blackbody. In the diagram, we notice that for T dwarfs process 1.3. Spectroscopy methane features and that cloud formation occurs deep in the atmosphere (below the photosphere). However, exoplanets appear redder than BDs in the diagram and their L-T transition occurs at a lower temperature. Marley 2012, has proposed that due to the lower gravity of giant planets, the temperature increases as we go deep in the atmosphere. At low effective temperatures, clouds condensate below the radiative line (defined in the community as "patchy clouds"), highly impact the spectra exoplanets, hence variability and limit the characterisation below these clouds. upper atmosphere submicron hazes, and causes cloud opacities to remain down to Te f f = 600 K at early ages (Bonnefoy et (Kaeufl et al., 2004). HDS in the near-infrared (NIR) for ground-based observation has provided a great deal of essential information, such as the wind speed or the rotational velocity of some transiting exoplanets (I. A. G. Snellen et al., 2010). It has also been used to characterise exoplanets by spectrally resolving molecular features of species present in the atmosphere (Brogi et al., 2013;de Kok et al., 2013). The combination of high angular resolution using AO to first spatially separate the planet from the stellar signal and the implementation of 1.3. Spectroscopy medium-to high-resolution spectroscopy to spectrally filter the stellar light from the planet's light was first successfully demonstrated by using the VLT/CRIRES instrument with a resolution of R = 100 000 in the K band. Using the MACAO AO system (Arsenault et al., 2003), CRIRES was used to detect the CO lines at 2.3 µm in β Pictoris b and to measure its orbital and rotational velocities (I. A. G. Snellen et al., 2014). However, these results were partly limited by the relatively poor high-contrast performance of the CRIRES system, which was not designed for this purpose.

State of the art of spectrographs

Integral field units (IFUs) are instruments in which the FoV is divided into several cells, commonly referred to as spaxels. They are used in astronomy to characterise objects using a technique known as Integral field spectroscopy (IFS). The signal from each spaxel of the FoV is fed to the spectrograph providing a spectrum for each spaxel. Then, all the spectra are stacked in a data cube, which includes the 2D FoV and the wavelength composition.

Many IFUs design exist, in the following paragraph, I will present the main ones used in astronomy and described in Fig. 1.16.

-Lenslet array: they are traditionally used for WFS in AO system [START_REF] Artzner | Aspherical wavefront measurements: Shack-Hartmann numerical and practical experiments[END_REF], but recently, they are used in instruments to achieve astronomy spectrography.

The technique enables to obtain a spectrum for each spaxel in a 2D FoV. The lenslet is located in the focal plane of the telescope to sample the image. Each lenslet contributes to have a small image of the telescope pupil at the entrance of the spectrograph. Then the light is dispersed and a spectrum is available for each lenslet in the focal plane. -Lenslets and fibre: They form an image at the entrance of the fibre, the 2D array is then rearranged in a 1D array slit and the light from the slit is dispersed by the spectrograph and forms a strum for each spaxel. -Image slicer: cuts the image into slices in 1D, each slice is sent in different directions thanks to a first mirror and a second one enable to align the slices onto the slit.

The use of lenslets in IFS is advantageous since the method aims to achieve continuous spatial sampling of the telescope focal plane with a fill factor > 90%, but also enables to efficiently couple light into fibres at the right F number.

High dispersion coronagraphy

High dispersion coronagraphy 1.4.1. Combining HCI and HDS

The proper combination of HCI and HDS was first proposed by (Riaud et al., 2007) to improve the sensitivity in contrast to exoplanets, and a more in-depth study was performed by (I. Snellen et al., 2015) in the framework of ELT instrumentation. In theory, for ground-based observations HCI and HDS can respectively reach a planet-star contrasts down to 10 -3 and 10 -4 , so combining the two to perform high-dispersion coronagraphy (HDC) could theoretically enable contrasts of 10 -7 or better to be reached (I. Snellen et al., 2015). More recently, the study by Wang et al. (2017a) developed a detailed model of HDC observations and analysed the trade-off between starlight suppression and spectral resolution for the characterisation of young giant exoplanets in the NIR. This framework opened the path for HDC, which is now implemented in several projects on existing telescopes: Keck/KPIC (J.-R. Delorme et al., 2021), Subaru/REACH (Kotani et al., 2020), and VLT/HiRISE (Vigan et al., 2018). The three projects mentioned above consist in coupling existing high-contrast instruments with medium-or high-resolution spectrographs. They propose sampling the planetary signal with a single-mode fibre (SMF) and feeding it to a diffraction-limited spectrograph [START_REF] Coudé Du Foresto | Very High Angular Resolution Imaging[END_REF]Jovanovic et al., 2017). The VLT/HiRISE project will be described in detail in the next chapter. KECK/KPIC aims at observing challenging exoplanets in the K and L bands. The 1.4. High dispersion coronagraphy instrument integrates a fibre injection unit (FIU) that injects the planet's PSF from the AO system into the NIRSPEC spectrograph using SMFs. Phase I has already demonstrated the system's capabilities to observe HR8799 bcde and nearly 30 objects. Phase II aims to refine the HDC concept by upgrading some of the subsystems to reach diffraction-limited, and high spectral resolution (R > 30000). Phase II aims at implementing innovative technologies, such as a high-actuator-count deformable mirror, a Phase-Induced Amplitude Apodization (PIAA) and a pupil plane vortex mask. Phase II is already on the sky and partially revalidated.

REACH/SUBARU combines the high-resolution spectrograph InfraRed Doppler (IRD) and the extreme adaptive optics instrument, SCExAO at the Subaru Telescope to realise high spectral resolution, over R = 100, 000 at extreme contrast. REACH uses a mini-IFU, which includes 7 SMFs bundle located at the SCExAO focus, a high-speed photometric camera, a beam switching and a system from the fibre bundle to IRD's 2 SMFs. On-sky demonstration of REACH has been performed and provided a spectrum of HIP 18413 A and D (results available in the presentation of the SCExAO team). Communicating information has occupied humans' minds since the beginning of time. In 1790, the Chappe brothers invented the first telegraph and thus paved the way for further advances in optical technologies. Multimode fibres were first used in the 1970s to fulfil the needs of the optical devices available at that time, which supported 1.4. High dispersion coronagraphy multiple modes. However, the 1980s, named the decade of glass by the industrials, appeared as the birth of single-mode fibres due to their telecommunication applications. It is only two decades ago that the multimode fibres resurfaced, mainly motivated by their capabilities to be used for multiplexing in communication systems. In Fig. 1.17, I display the differences between the two types of fibres, single mode fibres are defined as the dielectric waveguides for optical waves. During my thesis, I only used SMFs, so I will describe them in this thesis.

Optical fibres 1.4.2.1. Single-mode fibres vs multi-mode fibres

Light in a single mode fibre

SMFs only accept one single mode of light, with 45% of the light propagating in the fibre's cladding. The spatial intensity profile of the beam can be described by the Bessel function but can be approximated by a Gaussian beam. One key parameter to define the fibres is the mode field diameter, which is proportional to the beam waist of the Gaussian beam. Inside the fibre, the light propagates as a Gaussian beam with a constant radius, however, as soon as the light leaves the fibre, the beam becomes divergent. The output shape of the fibre is a Gaussian beam with a waist located at the tip of the fibre.

Coupling a telescope PSF into a SMF 1.4.3.1. Condition for a good coupling efficiency

For precision and stability purposes, SMFs are optimal for feeding light into spectrographs (Crepp, 2014;Jovanovic et al., 2016). They are used in the focal plane of telescopes for their spatial filtering effect (Ghasempour et al., 2012). However, efficiently coupling a point spread function (PSF) into a SMF is inherently challenging due to their intrinsic properties. A SMF is designed only to support a quasi-Gaussian fundamental mode (LP01). According to the field theory of guided waves, optimal coupling efficiency occurs when the overlap integral between the electric field of the input beam and the LP01 mode is maximised (Barrell et al., 1979;[START_REF] Jeunhomme | Single-mode Fiber Optics. Principles and Applications Jovanovic[END_REF]Neumann, 1988). It implies that the complex amplitude of the transverse component of the electric field at the telescope focal plane must match the LP01 mode of the SMF (Coudé du Foresto et al., 1993).

High dispersion coronagraphy

Coupling efficiencies applied to telescopes

In the ideal case of an unobstructed pupil, an Airy pattern is formed in the focal plane and is composed of a constant phase core surrounded by successive dark and bright concentric rings where the phase flips by π. Coupling an Airy pattern into the LP01 mode is bounded by the opposite phase of the first ring, which leads to destructive interference and reduces the coupling efficiency. The maximum coupling efficiency of an Airy pattern into a SMF occurs when only the core matches the quasi-Gaussian mode. An unobstructed circular aperture's theoretical maximum coupling efficiency into a SMF is ∼81% (Shaklan et al., 1988).

However, most ground-based telescopes have obstructed circular apertures and spiders. The presence of a central obstruction and spiders in the pupil has a significant impact on the coupling efficiency. Due to their respective pupils, the Gemini telescope offers a maximum coupling efficiency of ∼70%, the Keck and the Subaru telescopes ∼60% (Jovanovic et al., 2017) (see, Fig. 1.19), and the VLT ∼73% (see, Fig. 1.18). Groundbased observations are also limited by optical aberrations, which are classified into two categories: quasi-static aberrations caused by optical defects and misalignments e.g. N'Diaye et al., 2013 and atmospheric aberrations caused by the turbulent atmosphere. Both types of aberrations disturb the wavefront and require the use of an AO system to re-establish a wavefront that is as flat as possible, which will better couple into a SMF. An ExAO correction has proven to increase the Strehl ratio, minimise the aberrations, and therefore bring the injection efficiency closer to its theoretical maximum (Jovanovic et al., 2017).

The overall transmission of the planet's signal into the SMF connected to spectrographs drives the signal-to-noise ratio of molecule detection and abundance measurements and, thus, our understanding of the exoplanet's formation and evolution mechanisms. To achieve molecular mapping, contrast is not as critical as for exoplanet detection since HDC relies on successfully injecting the signal of a previously known exoplanet detected by an exoplanet imager into a SMF. Historically, fibre technology has been used in telecommunications where repeaters have been employed to boost the signal to compensate for injection losses, which is not applicable in astronomy.

This thesis and outline

Observing targets with large ground-based projects will add an essential piece to the highly complex puzzle of exoplanet formation and evolution mechanisms. The question of my thesis is to answer: how to blindly efficiently couple a PSF of a planet into a single mode optical fibre, given the limitations of the instruments located at ground-based observatories.

The project HiRISE, the main topic in this thesis, is a recent contribution in the context of HDC. It bases its observing strategy on the use of a few science fibres: one is dedicated to sampling the planet's signal, while the others sample the residual starlight in the speckle field. One of the challenges of HiRISE resides in blindly centring the planet's signal of a previously known exoplanet detected by SPHERE into a SMF. The fibre injection module (FIM) part plays a critical role since it will pick up the planet's PSF in SPHERE and inject it into a SMF located in the fibre bundle to feed the spectrograph. To maximise the coupling efficiency, the planet's PSF must be positioned with an accuracy better than 0.1 λ/D (4 mas in the H band for SPHERE) to minimise light losses. Therefore, defining the best possible strategy for HiRISE to centre a planet's PSF on a SMF is essential. Three centring strategies are foreseen, based on retro-injecting calibration fibres to localise the position of the science fibre, or on a dedicated centring fibre. I implemented these approaches and compared their centring accuracy using an upgraded setup of the MITHiC HCI testbed, which emulates the instrument setup used in HiRISE.

My work has allowed me to analyse the advantages and disadvantages of several methods, compare them, and show that it is applicable to each of the HDC ongoing and future projects. I studied the contributors to the centring error and proposed a quantification for the most impactful terms. In addition, I contribute to the AIT phase preparation of HiRISE at LAM to prepare the validation of the centring strategies on sky. The goal of my work is to analyse the difference between the work done on MITHiC and its implementation on HiRISE and to extrapolate them to the challenges we will meet on the sky.

My research comparing the centring methods was driven to understand the limitation of HDC and assure that HiRISE can benefit from the lessons learned during the laboratory work to reach the optimal throughput afterwards the commissioning. Although these three ongoing projects (KPIC, REACH, HiRISE) share the same HDC principle, they are unique in their design, spectral bands and advancement. They are 1.5. This thesis and outline complementary in terms of spectral band coverage for specific targets and the ongoing and future HDC projects may benefit from the answers and questions provided during this thesis.

Chapter 1: I present the introduction of exoplanets, and the methods used to detect them, I provide a brief overview of the spectroscopy state of the art and I introduce the concept of high-dispersion coronagraphy before giving a short description of the HDC on-going projects.

Chapter 2: I describe SPHERE and CRIRES+ and present an extended overview of the HiRISE implementation at the VLT. I also detail the expected science performance of HiRISE and provide information about the first targets that HiRISE aim to observe. Finally, I describe the general centring strategy principles in the case of HiRISE.

Chapter 3: I demonstrate the MITHiC testbed and its global characterisation with an emphasis on the tip-tilt mirror. I also provide details on the description of the FIM. In this chapter, I explain the limitations of the setup and the specifications required for the centring strategies. I introduce the description of the centring strategy procedures in laboratory and discuss the performance results. Finally, I conclude on the best strategy to use for HiRISE and to analyse the differences between MITHiC and its implementation on HiRISE, and to extrapolate to the challenges we will meet on the sky.

Chapter 4: I introduce the recent activity of HiRISE. The assembly, integration and tests (AIT) phase of HiRISE started at LAM, where I contribute to the Test phase preparation of HiRISE and investigate how to validate the centring strategy on the sky since some validation regarding the best centring strategy for HiRISE will come from the AIT phase, but the final decision regarding the centring strategy will be taken after the on-sky tests in spring 2023.

Chapter 5: In the last chapter, I present the conclusion of the work achieved during this thesis and I present the direct application of my work to the HARMONI project, described in Appendix B I also bring a short-and long-term perspectives for HiRISE at the VLT, not only regarding the centring strategy but also about improving the stateof-the-art of fibre injection modules. I end this thesis by providing wider perspectives for HDC from space and ground observatories.

The High-Resolution Imaging

and Spectroscopy of Exoplanets: HiRISE

High-Dispersion Coronagraphy on the VLT with HiRISE

In this chapter, I introduce a direct application of the high dispersion coronagraphy concept on the VLT. HiRISE aims to couple two existing flagship instruments located at the opposite Nasmyth platforms of the UT3/VLT -SPHERE and CRIRES+, as illustrated in Fig. 2.1. By coupling these two instruments, HiRISE will benefit from the HCI capabilities of SPHERE (ExAO) and the high spectral resolution in the NIR offered by CRIRES+. The goal will be do blindly inject a well-known directly detected exoplanet signal by SPHERE into a single mode fibre and into CRIRES+. I start by introducing SPHERE and CRIRES+, then I describe HiRISE and its implementation on sky. Finally, I conclude this chapter by introducing the centring strategy principles that I developed in the framework of my thesis to fulfil the HiRISE requirement specification.

The SPHERE high-contrast imager on the VLT

The Spectro-Polarimeter High-contrast Exoplanet REsearch (SPHERE) is a secondgeneration high-contrast imaging instrument developed by a consortium of eleven institutes in 2004 to study a large exoplanet sample. The instrument is based on the implementation of (i) an extreme adaptive optics system (ExAO) to improve the fast-evolving atmospheric turbulence and quasi-static speckles compensation, (ii) a stellar coronagraphic system and (iii) a visible high-contrast imager (ZIMPOL) and two near-infrared high-contrast imagers (IFS and IRDIS).

The scientific objective of the SPHERE instrument is to detect and characterise young giant exoplanets orbiting closely to their host stars at low resolution through the Y-, J-, H-and K bands, using the direct imaging technique. The main challenge is to overcome the high flux ratio between the planet and the star, and their small angular separation. SPHERE's objective in the near-infrared is to detect the signal of bright targets with a 15 -16 magnitudes contrast, having a magnitude below 10, as summarised in Table ??. The entire design of SPHERE was therefore driven by the need to obtain the highest contrast around the star's close environment and to obtain the highest opto-mechanical stability necessary for the calibration and coronagraphic performance.

SPHERE instrument overview

The SPHERE instrument is structured in four subsystems (see Fig. In the following, I briefly describe each of these subsystems.

The common path and infrastructure (CPI)

The CPI transfers the telescope light to the three other subsystems via a highly stabilised AO-corrected beam. Near the entrance focal plane, a pupil stabilisation mirror (PTTM) and a derotator ensure either a pupil or an image stabilisation. Three mirrors (TM1, TM2 and TM3) placed after the PTTM direct the beam to two pupil planes, the fast image tip-tilt mirror (ITTM) and the High Order Deformable Mirror (HODM).

After the fold mirror, the beam goes through a dichroic beam splitter, which separates the visible (VIS) and near-infrared (NIR) light. The visible light is transmitted through an atmospheric dispersion corrector and a wavefront sensor (WFS) to ZIMPOL. After going through the infrared-dispersion corrector and coronagraphs, the NIR beam passes through a second beam splitter dividing the light between the IFS spectrograph and the IRDIS dual-band imaging camera. The dichroic "DIC-H" sends the Y and J bands to the IFS and the H to IRDIS, while the dichroic "DIC-K" sends the Y,J, and H bands to the IFS and the K band to IRDIS. Right after the sensor wavefront path, a beam splitter allows to send a few percent of the light to the differential tip-tilt sensor (DTTS), which is then sent back to the differential tip-tilt loop (DTTP) located in the AO system to compensate for any misalignments between the coronagraph and the wavefront sensor. The ITTM and HODM are considered to be part of the first loop of SAXO, but two more loops are added to the AO system. The first one includes the DTTP, which ensures the centring of the star on the coronagraph. Few percent of the stellar light forms an image on the DTTS in the H band and the DTTP located in the WFS stage is used in anticipation to compensate for tip-tilt aberrations with a frame rate of 1 Hz and a precision < 0.5mas in the H band. The second loop ensures the stability of the VLT pupil in the system at 0.1 Hz. The PTTM is used as a corrector at the entrance of the system to stabilise the pupil image on the Lyot stop.

Coronagraphs on SPHERE

The choice of the coronagraph on SPHERE relies on the observing wavelength and inner working angle. The coronagraph wheel contains several focal-plane optics with 7 round, hard-edge focal-plane masks, 2 monochromatic four-quadrant phase masks, 2 field stops, and 4 empty positions.

SPHERE's science instruments

In the following paragraphs, I introduce a brief description of the science instruments available on SPHERE. A more detailed description of these instruments can be found in (Beuzit et al., 2019).

ZIMPOL has first been developed for polarimetric imaging of the Sun. The concept the has been used for SPHERE to reach higher transmission and a broader spectral band. To fulfil these new requirements, several cutting-edge elements have been developed and implemented, including an achromatic polarisation modulator, and stripe mask with a micro-lens array aiming to decrease photon loss. The ZIMPOL beam follows first a common optical branch, which is then separated due to a polarising beamsplitter in two optical branches for which each one of them has its own detector. The two branches allow us to simultaneously measure the polarisation modes (I ∥ , I ⊥ ) with the same, or in different filters. The detectors are placed in a common cryostat and cooled to -80 • C, while the opto-mechanical system is kept at ambient temperature. The instrument works between 500 nm and 900 nm and allows us to obtain observations at high resolution (20-30 mas) and high contrast, as well as imaging polarimetry for planets orbiting closely around bright stars (<4 arcsec); this is facilitated by the ExAO system and the VIS coronagraphs.

IRDIS [START_REF] Dohlen | The infra-red dual imaging and spectrograph for SPHERE: design and performance[END_REF]) is a versatile instrument capable of performing imaging, polarimetry and spectroscopy in a wavelength range from 0.95 to 2.4 µm. It has a field of view of 10 ′′ in a spectroscopic mode and 11 ′′ × 11 ′′ in an imaging mode with a spatial sampling of 12.25 mas/pixel consistent with Nyquist sampling at 950 nm. The instrument is divided into four distinc modes: the Dual Polarimetric mode (DPI) (Langlois et al., 2010), the Long-Slit Spectroscopy mode (LSS) [START_REF] Vigan | Exoplanet characterization with long slit spectroscopy[END_REF], the classical mode (CI) and finally, the dual-band imaging mode (DBI) [START_REF] Vigan | Photometric characterization of exoplanets using angular and spectral differential imaging[END_REF]. The latter aims to simultaneously acquire two images at two different wavelengths and then subtract these two images with the objective to minimise the differential aberrations to less than 10nm rms in order to detect a planet. The principle observing mode combines IRDIS' dual imaging in the H band with imaging spectroscopy using the IFS in the Y-J bands. This configuration permits taking advantage of the dual imaging over a large field (out to 5 ′′ radius) and spectral imaging (out to 0.7 ′′ ).

IFS is SPHERE's integral field spectrograph, which is a lenslet-based integral field unit called BIGRE [START_REF] Antichi | BIGRE: A Low Cross-Talk Integral Field Unit Tailored for Extrasolar Planets Imaging Spectroscopy[END_REF]. The IFS offers a 1.73 ′′ × 1.73 ′′ FoV (Nyquist sampled at 0.95 µm). The IFS has two modes, one for the Y and J bands with a spectral resolution of R = 50, and the other for the Y, J and H bands with a spectral resolution of R = 30 (see, Fig. 2.8. In Fig. 2.7, we notice that the IFS includes an internal calibration source and its own Lyot stop. The spectra are aligned with regards to the detector columns over a hexagonal grid. Each spectrum from a spaxel is projected on a 5.1x41 pixel area on the detector. During the data reduction, the image is transformed into a data cube, which has available spectral resolutions. Each image is resampled onto a regular square grid at (7.4 mas)/spaxel.

CRIRES+

Since 2006, the CRIRES instrument was operating at the ESO VLT UT1 (Paranal, Chile). The instrument was one of the few IR spectrographs operating at a high spectral resolution. The spectrograph operates at a resolving power of R = 10 5 (using a 0.2 ′′ slit) over the 1 to 5 µm wavelength range. CRIRES was equipped with a MACAO [START_REF] Paufique | On-sky results of the adaptive optics MACAO for the new IRspectrograph CRIRES at VLT[END_REF] adaptive optics system to increase the light within the 0.2 ′′ × 30 ′′ slit.

In 2019, the instrument was upgraded to CRIRES+ by transforming CRIRES into a cross-dispersed spectrograph and by adding new technologies [START_REF] Dorn | CRIRES + on sky at the ESO Very Large Telescope[END_REF]. The instrument has been transferred to the Nasmyth platform of the UT3. CRIRES was originally limited by its wavelength range of 0.95 -5.3 µm. Hence, by implementing a cross-dispersion element, the wavelength coverage would increase by an order of magnitude [START_REF] Follert | CRIRES+: a cross-dispersed high-resolution infrared spectrograph for the ESO VLT[END_REF].

The scientific goals of CRIRES+ are defined by the search for super-Earths and potentially habitable planets around low-mass stars; the atmospheric characterisation of warm Jupiters, super Earths and potentially habitable planets around low-mass stars; and the understanding of the formation and evolution of stellar magnetic fields.

The optical design of CRIRES+ is displayed in Fig. 2.9. The instrument itself is located in a cryostat (darker area), interfaced by a dichroic entrance window. CRIRES+ is mainly divided into two parts, the cross-dispersion unit (CDU) and the spectrograph unit. The upgraded optics are a cross-dispersion unit instead of the existing prism, three HAWAII-2RG 2k×2k IR detectors, a new spectro-polarimeter, and a wavelength calibration system to perform high-precision RV measurements using a gas-absorption cell. The AO system, the derotator, and the calibration elements are implemented in a warm part between the telescope and the spectrograph (light grey area). The wavelength calibration sources are inserted into the optical beam just after the telescope, where the absorption gas cell is located (red cylinder).

Combining SPHERE and CRIRES+ to obtain HiRISE

At the VLT, two flagship instruments are installed on the Nasmyth platforms of the unit telescope 3 (UT3) as illustrated in Fig. 2.1: the exoplanet imager SPHERE on one side, and the NIR high-resolution spectrograph CRIRES+ (Dorn et al., 2016) on the opposite side. The High-resolution imaging and spectroscopy of exoplanets (HiRISE) project involves implementing a fibre coupling between these two instruments to enable the characterisation of known directly imaged young giant exoplanets at spectral resolutions up to R = 100000 in the H band. HiRISE is composed of three independent parts: (i) the fibre injection module (FIM) that will be implemented in the IFS arm of SPHERE, (ii) the fibre bundle (FB) that will link SPHERE and CRIRES+, and (iii) the fibre extraction module (FEM) that will be installed on the calibration stage of CRIRES+. HiRISE will benefit from the SPHERE infrastructure for the HCI and from 2.1. High-Dispersion Coronagraphy on the VLT with HiRISE CRIRES+ in NIR for the HDS techniques.

Anticipated science with HiRISE

Scientifically, HiRISE will bring new knowledge on known directly imaged young giant exoplanets and brown dwarfs within 1.5 ′′ from their host star. The characterisation of these targets at high spectral resolution will offer some prospects to understand their formation mechanisms and their atmospheric compositions and dynamics.

The composition of the protoplanetary disk is not uniform since the temperature of the disk decrease with the radial distance from the host star. The first molecule to reach the snowline is H 2 O, then CO 2 followed by CO, which cause molecular abundance gradients for gas vs solid element. In the community, scientists use to associate targets formation to an observational element such as the carbone-oxygene (C/O) ratio, which includes information regarding the fractional amount of solid and gaseous elements accreted by the targets. Associated with the chemically disk models the C/O ratio can constrain the time and localisation of the planet birth in the protoplanetary disk. The presence of some molecular species using the cross-correlation function (CCF) at medium resolution has been done for HR 8799 c [START_REF] Konopacky | Detection of Carbon Monoxide and Water Absorption Lines in an Exoplanet Atmosphere[END_REF] and HR 8799 b [START_REF] Barman | Simultaneous Detection of Water, Methane, and Carbon Monoxide in the Atmosphere of Exoplanet HR8799b[END_REF] and has led to inform that the planets have been formed outside the CO and CO2 snowlines. In 2014, Snellen has suggested for bet a Pictoris b at R = 100000 a formation through core accretion (I. A. G. Snellen et al., 2014). High spectral resolution will enable to improve the constraints on the C/O ratio. In recent years, significant results have been obtained with GRAVITY. There are several results in the ExoGRAVITY program that have addressed these CO measurements at a resolution of a few hundred.

The more lines that a high resolution spectrograph can detect, the stronger the constraint on the planet's atmospheric composition. The line contrast is obtained by taking the depth of the lower planet lines with respect to the continuum and dividing it by the stellar flux. The line contrast points out the differences between the line cores in the planet's spectrum and the continuum that led to constrain the temperaturepressure (T-P) profile and abundances in the planet's atmosphere. In 2017, Brogi has shown that a multi-resolution approach by combining the power of low and high spectral resolution highly constrained the T-P profiles and abundances by deleting degeneracies with the atmospheric compositions [START_REF] Brogi | A Framework to Combine Low-and High-resolution Spectroscopy for the Atmospheres of Transiting Exoplanets[END_REF]. In the framework of this approach, it will be useful to combine HiRISE and IFS data to probe different depths in the planet's atmospheres.

Measuring the planet's spin and estimate its angular momentum via the formula 2.1. High-Dispersion Coronagraphy on the VLT with HiRISE v r ot .sin(i) is a key to understand planetary formation. This technique is also sensitive to small velocity shifts, which contains information on atmospheric dynamics (winds).

The measure of RV via the formula v or b .sin(i) led to knowing the orbital motion of the planet with respect to its host star. Combined with the relative astrometry, this can provide constraint on the mass and the detection of variations in the RV signal. In the near future, GAIA/ESA might provide absolute astrometry that combined with HiRISE RV measurements would enable more accurate estimations of the planet's masses of young giant exoplanets.

HiRISE instrument description 2.1.4.1. Instrument overview

Conceptually, HiRISE diverts the SPHERE/IFS beam downstream of the ExAO and coronagraph and injects the light of a known exoplanet into a SMF. This fibre is connected to the NIR spectrograph CRIRES+ on the opposite Nasmyth platform, which is used to disperse the planet's light at high spectral resolution. The practical implementation requires three inter-connected elements: the FIM implemented inside of SPHERE that takes care of properly injecting the planetary signal into the science fibre, the FB around the telescope that routes the science fibre and additional fibres between the two Nasmyth platforms, and the FEM implemented inside of CRIRES+ that reimages the science fibre's output at the entrance of the spectrograph with the right optical properties. Since the current work focuses on the strategies to best inject the planet's signal into the science fibre, we describe in greater detail the FIM, and refer the reader to other works for the descriptions of the other elements (Otten et al., 2021;Vigan et al., 2018).

Fibre Injection Module

The FIM, represented in Fig. 2.10, is implemented as a vertical bench immediately downstream of the Lyot stop wheel in the IFS arm of SPHERE (Beuzit et al., 2019). Fig. 2.12 shows that the FIM includes a pick-off mirror that can be inserted into the IFS beam to send the light towards the FIM instead of the IFS. The SPHERE pupil is reimaged onto a mirror mounted on an S335 piezo tip-tilt platform from Physik Instrumente1 . The beam is then recollimated using a custom achromatic doublet and goes through a dichroic filter that reflects the short wavelengths (0.95-1.3 µm; YJ bands) into the "tracking branch" and transmits the longer ones (1.4-1.8 µm; H band) to the "injection branch". In the tracking branch, a focal plane image is formed at F/40 on a C-RED 2 camera from First Light Imaging [START_REF] Gibson | [END_REF], and we refer to it as the tracking camera in this section. This image is sampled at 12.25 mas/pix, corresponding to Nyquist sampling at 0.95 µm. Although the images from the tracking camera are not expected to be used for any astrophysical interpretation, they will nonetheless be of sufficiently high quality to enable basic processing. In the injection branch, the beam is refocused with a very fast doublet at F/3.5, which has been designed to match the numerical aperture (N A = 0.16) of the science fibres used in the bundle. The optical system is designed to be telecentric in the injection branch to maximise the injection efficiency even when considering fibres located off-axis. Although the science fibre will be located on-axis to maximise the wavefront quality and, therefore the injection efficiency (Jovanovic et al., 2017), three additional fibres will be located off-axis to sample the stellar light in the speckle field. In practice, the FB remains static after the alignment of the system, and the focal plane image is moved with respect to the science fibre using the tip-tilt mirror, so as to place the PSF of a known companion onto the fibre. The strategies to centre the PSF accurately on the science fibre are detailed in the following section.

High-Dispersion Coronagraphy on the VLT with HiRISE

In addition to the fibres dedicated to science, the bundle will also include 'feedback fibres', which are connected to a calibration source at ∼1.3 µm and used to retro-inject signal into the system. Because of the orientation of the dichroic filter, the retroinjected signal is reflected on the dichroic, then on a dedicated corner cube, and then transmitted through the dichroic into the tracking branch. The outputs of the feedback fibres are finally reimaged on the tracking camera superimposed on the focal plane coronagraphic image. The position of the feedback fibres with respect to the science fibre is calibrated, giving the possibility to use them for accurate centring on the science fibre. This solution was previously proposed to optimise the centring on the science fibre in a situation where the planet's signal remains undetectable in short exposures [START_REF] Mawet | [END_REF]. The wavelength of the feedback fibres was selected to be in the transition zone of the dichroic filter because the retro-injected beam has to go through that filter twice. At 1.3 µm, the transmission of the dichroic is ∼50%, which means that only 25% of the photons will ultimately reach the tracking camera.

The fibre injection module has been designed regarding (i) the space available inside the SPHERE enclosure and (ii) the best position to totally benefit from SPHERE in the NIR arm. To efficiently inject a planet's PSF into a SMF, it is necessary to have the best wavefront and a highly stable PSF, so placing the FIM downstream of the AO, the DTTS stabilisation and the coronagraph was the best choice to fulfil these requirements. As an independent module, the FIM must respect the basic requirement to not damage SPHERE (be the most robust, with no heating, no cooling, and no creating extra vibrations). Its mechanical design has been developed to match the environmental variation at Paranal, by optimising the tolerancing analysis of the optical design (OD). The volume has also been optimised to be more compact, with an approximate volume of 530 (l) x210 (w) x 810 (h) mm3. The FIM will be pre-aligned in the laboratory with a SPHERE simulator and then implemented vertically in SPHERE. The SPHERE/CPI offers threaded holes to mount an interface plate. These holes have been used during the SPHERE integration in Europe (Grenoble). The plate is installed on the interface plate and in the centre of it a custom pick-off mirror assembly based on a Thorlabs rails that hold an OWIS translation stage, which is compatible with the VLT software. It is used to insert a pick-off mirror into the IFS arm and redirect the light towards HiRISE instead of the IFS. The 25mm coated pick-off mirror is from Edmund and is glued on a Thorlabs Polaris mount. The main board includes all the opto-mechanical devices, including the one-inch Thorlabs relay lens and the folding mirror from Edmund. The tracking camera is placed at 45°with regard to the vertical to isolate the camera from the core optic bench. Since the camera will use an air/liquid-cooling system and thus expel warm air, a cover will be implemented on the core optics bench to prevent any turbulences on the fibre injection branch. This FIM will be shut down when HiRISE is not used to avoid any impact on SPHERE. The core optics bench is an independent bench, it holds sensitive elements crucial for the fibre injection, centring strategies and tracking. The majority of the elements are customs optics and are described The tip-tilt platform is from Physik Instrumente (PI), the description of this element is detailed in Sec. 3.1.2.2 of Chap. 3.

The collimating doublet is a custom doublet used to collimate the beam after the tip-tilt mirror. The dichroic filter, manufactured by Institut Fresnel, splits the YJ bands for the tracking camera branch and the H band to the injection branch. The dichroic is a 1-inch diameter with an anti-reflective coating. A custom air-gap doublet is used for the injection in the science fibre mount, which holds the SPHERE-FIM bundle section. In the retro back branch, a lens is placed to correct the defocus when this procedure is used for the planet's acquisition on the tracking camera. The lens is a custom one held by a Polaris mount. Additionally to the correction lens, an off-the-shelf corner cube is used to reflect the light to the tracking branch.

In the FIM, three devices emit heat inside the enclosure. In this section, we only cover the pick-off mirror translation stage and the tracking camera contributions. A more detailed description of the thermal budget of the tip-tilt platform is described in Chap. 3. For clarity purposes, in the summary thermal budget table (Table 2.2), the tip-tilt contribution is considered. The C-RED 2 contains a top-of-the-art sensor able to cover wavelength ranges between 0.9 and 1.7 µm with more than 70% Quantum Efficiency (QE). The tracking camera integrates a 40×512 InGaAs PIN photodiode detector with 15 µm pixel pitch for high resolution. It has three key regions: the "air cold intake" area in blue, "the hot air exhausts" in red and the "liquid cooling connectors area" in green. To estimate the thermal budget allocated to the tracking camera, a test has been realised in the laboratory by acquiring thermal imaging using an infrared camera. During the test, the camera operated in an air-cooled mode, and the images were acquired at a higher cadence than what will be used during HiRISE operations. The test demonstrated that the temperature increased when the camera was powered on. Fig. 2.13 shows that the temperature increase by 15 degrees (numbers 3, 4) on the top surface and by 12 degrees on the side (number 5). This significant increase in the heat created by the camera could create turbulence inside the SPHERE enclosure and affect the performance of the FIM. So instead of using air cooling, the best option would be the use of a liquid cooling system for the tracking camera similar by principle to the one used for the SAXO WFS camera. The risk of leaking inside the SPHERE enclosure in the case of the tracking camera is not higher than the one already implemented on SPHERE, however, the installation of the cooling system must be done carefully. The pick-off translation stage is an OWIS LTM 60P-100-HiDS 2 , with a motor using a maximum 45W. It will be briefly powered on (less than 10s) when inserting the FIM into the IFS branch or when returning to standard SPHERE configurations. The thermal contribution of the motor of the pick-off mirror translation stage is therefore considered to be negligible. No thermal tests have been performed in the laboratory since no translation stage was acquired when we performed a thermal study for the devices.

The installation of the FIM is extremely sensitive since it consists of implementing an additional sub-system inside SPHERE. The FIM will be inserted inside the SPHERE enclosure by using the NIR bench door, which has a dimension of 800×800 mm. During the installation of the FIM, SPHERE will be maintained in an intervention state. The FIM comprises four independent parts that will be installed sequentially into SPHERE. Each of the four FIM's parts fits the door size facilitating the implementation. The FIM installation steps are described as follows:

1. Opening the door and adapting the air system in SPHERE.

2. Unplugging the IFS Lyot stop motor cable to avoid any shock with the FIM while the installation.

3. Installing the interface plate using the existing threaded holes in SPHERE.

4. Installing the support structure (very sensitive step regarding SPHERE). After the installation of the FIM, some verification will be necessary. Regarding the daytime verification for HiRISE, the tests will be described in the subsection HiRISE operations. For SPHERE, the first verification will consist to adjust the pneumatic system to filter the vibrations from the telescope. During the implementation of the FIM, the IFS Lyot stop motor cable will be connected and disconnected. One of the tests will consist of checking the motor. For the IFS imaging test, the FIM pick-off mirror will be outside the IFS beam. Two images will be acquired, the first one will be a pupil image by inserting a pupil lens in the IFS beam, and the second will be an image of the PSF using a calibration source.

When we do not operate in a HiRISE configuration, the FIM will remain in the SPHERE enclosure, eventually shutting down the tracking camera. If it is necessary to dismount HiRISE, a removal procedure for the FIM is settled and considered to restore the previous pneumatic system configuration.

Fibre Extraction Module

The fibre extraction module (FEM) will be located at the calibration stage of CRIRES+ (warm part). The goal of the FEM is to image the science fibre at the entrance of the CRIRES+ slit. Compared with the FIM, the FEM is more compact and has to fit the space allocated in the visitor gas cell on the CRIRES+ carrier stage unit (CSU). The FEM includes a holder to the fibre bundle's end to ensure high repeatability while plugging-unplugging the bundle's end. A key requirement consists of positioning the FEM along the optical axis defined by the telescope. This position has to be adjustable to accurately focus the fibre's image in the telescope focal plane.

The FEM operates in two configurations, between 0.1 and 1 µm for the MACAO AO system. The MACAO system is described in the section CRIRES+. For the science light, the FEM works from 1.5 to 1.8 µm. The optical design is represented in Fig. 2.14. The bundle output is not represented in the FEM 3D layout, the vertical part length (L1, L2, L3, folding mirror) is 36.86 mm, and the horizontal part (folding mirror, L4, focal plane) is 86.45 mm.

High-Dispersion Coronagraphy on the VLT with HiRISE

The FEM mechanical implementation in CRIRES+ is illustrated in Fig. 2.15. We will use existing holes to accurately position the FEM. The FEM is composed of four custom lenses and a folding mirror mounted by custom mechanics offering tip-tilt motions for the mirror and a rotation for the entire module. The fibre bundle will arrive from the top and to preserve the FEM from any parasite light and dust, a cover will be added.

High-Dispersion Coronagraphy on the VLT with HiRISE

The FEM will reimage the output of the fibres in the VLT focal plane, although there is no atmospheric turbulence to compensate, it is not suitable to perform HiRISE observation while MACAO is in an open loop. The reason is due to the shape of the MACAO DM that will drift with time, degrade the shape of the PSF and decrease the science throughput because some of the light will not be going through the spectrograph slit. In order to stabilise the light going through the slit during the exposure, we implemented an off-axis fibre that will be located near to the science fibre but outside of the slit. This fibre will be used with visible light by MACAO WFS to maintain the DM flat during HiRISE observation. By closing the MACAO loop on an off-axis fibre, we wanted to be confident that it will not affect the wavefront on the on-axis science fibre so a FEM closed-loop analysis has been realised based on an optical design from Jérôme Paufique. The metric used to verify the test is the image quality (spot diagram) for different positions in the FoV; ie; the fibres located at different separations from the optical axis. As a conclusion of this test, we noticed as closing the loop on the off-axis fibre a small degradation in the spot diagram and that the encircled energy is within 50 µm for both open and closed loop, so the off-axis fibre will not highly impact the quality of the wavefront for the on-axis fibre.

The installation of the FEM steps is described as follows:

1. Opening the panel closest to the gas cell.

2. Positioning the FEM.

3. Insert the fibre bundle and guide it to the gas cell side.

4. Connect the bundle to the FEM connector.

Close back the panel.

After the installation of the FEM, some verification will be necessary. As for the FIM, regarding the daytime verification for HiRISE, the tests will be described in the subsection HiRISE operations. For the CRIRES+, two verifications have been targeted. The first one consists of checking that the FEM and the FB do not impact the function of the CSU. The second verification aims to perform daytime and nighttime calibrations to ensure the integrity of CRIRES+ while the FEM and the FB are implemented.

If the FEM must be uninstalled from the gas cell, the bundle will remain in place and will be secured to not cause any damage to CRIRES+.

Fibre Bundle

The fibre bundle (FB) is part of the four parts of HiRISE and aims to connect SPHERE and CRIRES+ instruments. The role of the FB is to route the planet's photon to CRIRES+ with the highest optical efficiency since one of the main requirements for HiRISE is to maximise the H-band overall transmission in the science and reference fibres. The bundle end geometries have been designed to satisfy SPHERE and CRIRES+ requirements. To maximise the transmission, the bundle is composed of a single cable without any connectors in the central part.

The bundle is divided into three sections A, B, and C, as illustrated in Fig. 2.16, with different lengths and bend radii. The bundle is composed of one science fibre in yellow, three reference fibres in blue, and several ancillary fibres in green, purple and pink. The bundle will be complete with dummy fibres for input and output symmetry (white). The science fibre transmits the planet's signal to CRIRES+, the science fibre goes through the entire bundle length (section A, section C and section C) and the science signal is extracted by the FEM on the CRIRES+ side. The reference fibres sample the speckle field close to the science fibre. The signals obtained by the reference fibres will be used in the data science analysis to subtract the stellar contribution and estimate the noise level. On the SPHERE side (Section A), the bundle includes four feedback fibres (green) and one centring fibre (green). The feedback fibres are retro-injected using calibration sources located in the HiRISE cabinet (HiCab), and the feedback fibres are reimaged on the tracking camera. The centring fibre is connected to a power meter (not represented in the general description) also located in the HiCab. The aim of these ancillary fibres is to guarantee accurate injection of the planet's PSF into the science fibre. On the CRIRES+ side (section C), the FB includes AO-calibrations fibres (purple), and one of them (pink) will be connected to the CRIRES+ integrated sphere. Section A of the bundle is between 2.5 and 3m long, with a bending radius smaller than 5cm. The bundle's input has a hexagonal geometry. The fibres are positioned cladding to cladding into a hexagonal pattern with the science fibre in the centre of the bundle. The tolerances on the localisation of the fibres regarding each other are 10µm. However, the fibres are supposed to be stable in time at better than 1µm. The SPHERE side input should be compatible with the Newport FPR2-C1A fibre optic positioner, which provides six degrees of precision in position and enhances long-term stability, reducing drift over both time and temperature. The device should be located within ± 50µm of the centre of the science fibre. The planet's signal is expected to be faint, so the FB input entrance must be AR coated between 1200 and 1850 nm (average transmission > 98% to minimise science and reference signal losses. The ancillary fibres have FC connectors and do not need an AR coating. Section A will share space inside and outside SPHERE to reach the HiCab to connect the ancillary fibres to the calibration sources. The fibre connectors must be protected since one single dust particle on the core of a fibre can cause a loss of flux, resulting in a degradation of transmission performance. For HiRISE, an adequate protective cap is foreseen not to damage the fibres or the coating during the installation.

In the context of HDC, fibre bundles are used to connect imagers and exoplanet spectrographs on ground-based telescopes. However, an extended cable length is usually needed to achieve this, the routing of the bundle is sometimes complex, and it is, therefore, sometimes necessary to split the length of the bundle into different sections. For HiRISE, the choice to privilege the overall throughput instead of the ease to route the FB around the telescope has led to not dividing section B of the FB. This section is the longest part of the FB, with a length between 75 and 80m with a bending radius not larger than 20cm.

Section B includes the science, the reference fibres and four ancillary fibres. Since this section will be routed from SPHERE to CRIRES+, it will be exposed to high risks, so consequent protection will be necessary during the installation.

Section C of the bundle is the one corresponds to the CRIRES+ side. The length is between 3.0 and 3.5m with a radius not larger than 5cm. On this side, the bundle's output has a linear geometry. The fibres are positioned as close as possible following a linear pattern with two rows. All the cores must be aligned within an envelope of 8µm. The mechanical centre should be located within ± 50µm of the centre of the science fibre. To minimise the signal losses, the FB exit is AR coated between 800 and 1850 nm. This section will share two environments, inside and outside CRIRES+, so protection similar to the one used for the section is foreseen.

All single-mode fibres selected are the 1310M-HP fibres from Nufern, which offer small attenuation in the H-band regarding the length of the bundle and have a NA compatible with the HiRISE optical system. A matching NA is necessary to achieve the highest coupling efficiency into the fibres. All the fibres are acquired from Nufern and sent to FTO to manufacture the fibre bundle.

HiRISE electronics -HiCab

The electronics box ( see Fig. 2.17) used for HiRISE is from Rittal with the dimension size 800×600×300 mm (L, H, D). The cabinet's content is listed in Tab. 2.2, the total power consumption is approximately 400W at maximum. This peak power would be reached if all the devices were used simultaneously at the full cadence. This will not be the case on HiRISE since the tracking camera and the TTM platform will be used at a slow cadence. The pick-off mirror translation stage will be used only when inserting in and out of the mirror. The values mentioned as "measured" in the table are detailed in Sec. 2.1.4.2. As for the cabinet, it will be screwed into a support structure that will be attached to the base frame of SPHERE (close to IRDIS).

HiRISE operations

The foreseen science operations for HiRISE are divided into three parts. The first one consists of the target acquisition performed by SPHERE, followed by the planet acquisition achieved by the FIM and finally the science data acquisition done by CRIRES+.

Regarding the target acquisition, the telescope and SPHERE are controlled by OBs, which are made up of templates. They are divided into three categories: acquisition, observation and calibration. HiRISE aims to use the template "SPHERE-irdifs-acq" in which we could select the derotator mode (field or pupil tracking), the AO parameters, the NIR coronagraph if any and the position angle (PA) offset.

HiRISE will use the observing mode template "SPHERE-irdifs-ext-obs" to send the YJH bands to SPHERE IFS and the K band to IRDIS. The observation will be performed in a field-tracking mode since this mode is suitable in the non-coronagraphic configuration. In the field tracking mode, the pupil rotates in time while the target PSF remains at the same localisation during the observation. The TTM in the FIM will remain static during the observation and HiRISE will rely on the SPHERE AO system to maintain the focal plane image stable.

The FIM operation includes several steps, such as the calibrations and the target acquisition. At the beginning of the night, the calibration required for the FIM is the calibration of the image scale in the focal plane. This calibration is crucial for HiRISE and relies on an accurate calibration between the image on the tracking camera and the position of the science fibre in the fibre bundle.

Once the target acquisition has been performed by SPHERE, the FIM receive a stable AO corrected light and no more communication is required with SPHERE. The planet acquisition in the FIM relies on several centring strategies developed during the PhD, which consist of the centring of the planetary PSF on the science fibre. Mostly, the planet's PSF will not be visible in the focal plane image of the tracking camera, so the planet acquisition will have to be performed blindly, relying on the known astrometry of the planet and on the calibrations performed in the daytime in the laboratory and on sky. The centring strategy principles are described in the following section of this chapter and their laboratory investigations are described in detail in the following chapter.

CRIRES+ observation will perform the acquisition of a calibration source with MACAO, closing the AO loop, centring and offsetting the light with respect to the 2.1. High-Dispersion Coronagraphy on the VLT with HiRISE slit. When the CSU in CRIRES+ will operate in a HiRISE/FEM mode, the derotator will be configured to be static and orientated in one direction, which will be calibrated during the on sky installation of the FEM.

Expected performance of HiRISE

The first simulation of the expected performance for HiRISE in the H band was based on an end-to-end model of the instrument and described in detail in (Otten et al., 2021). These performances were then compared to the expected performance of CRIRES+ standalone for the same targets. The HiRISE end-to-end simulation includes the properties of stellar and target sources, the atmosphere, the telescope, SPHERE, CRIRES+ and the fibre coupling system. For CRIRES+ in standalone mode, the simulation do not include the effect of SPHERE and HiRISE. In this section, I will summarise the end-to-end simulation performed by (Otten et al., 2021) and provide the HiRISE transmission budget, which has later been updated based on the final optical components and AR coatings.

To simulate the stellar source, we used the Phoenix model, which includes the effective temperature, surface gravity, the metallicity (similar to the solar metallicity).

For the planetary source, we used a 1D radiative transfer code ATMO2020 at high resolution with a classical cross-correlation function (CCF) approach. The Earth's atmosphere transmits and emits light, so to model its behaviour, we used ESO Sky Calc model3 that includes water vapour (2.5 mm) and a seeing of 0.8 ′′ emulating the atmospheric conditions in Paranal.

The contribution of the telescope and SPHERE has been considerate separately. For the telescope measures, we considered the reflections on the total mirrors M1, M2 and M3 with a total reflectance of 80%. Added to that contribution we estimate a flat 86% on M1 due to the dust. For SPHERE, we used the transmission values for the dichroic measured and provided by the manufacturer Cilas in the YJH bands. The average CPI transmission for the dichroic DICH-K in the H band is 47.3%.

For HiRISE, the optics (6 lenses, 1 mirror, 1 dichroic) in the FIM contribute to reduce 2.1. High-Dispersion Coronagraphy on the VLT with HiRISE the transmission mainly due to the Fresnel reflection on the surfaces. In his paper, Otten assumed a 2% loss per optical surface for the lenses and 5% loss per optical surface for the dichroic due to the coating for a total transmission of 71%.

To estimate the fibre injection efficiency, we used a coronographs Python toolkit (N'Diaye, private communication), which simulate the SPHERE instrument based on the VLT pupil, the NCPA, the coronagraph masks and the wavefront errors inherent to the FIM optics. The calculation of the coupling efficiency for SPHERE was done in three configurations (APLC, CLC, and no coronagraph). Due to the oversized spiders, the coupling efficiency is lower in the case of the APLC and the CLC, in the case of no coronagraph, the transmission is estimated to 66.7%.

Injection into single mode fibres (SMF) can quickly lead to significant flux losses if the centring is not accurate, which is why this parameter is critical. The simulations by (Otten et al., 2021) and illustrated in Fig. 2.18, show that a centring accuracy of 0.1 λ/D is a necessary requirement for HiRISE. With this accuracy we expect a maximum peak coupling efficiency loss of five percentage points compared to a case with perfect centring of the PSF on the science fibre. The stellar contamination in the SMF is not extremely dramatic since the performance of the HiRISE instrument is essentially driven by the overall transmission of the system. The planetary signal is several orders of magnitude fainter than the star, so the final signal can easily become limited by either photon noise (ideal case) or instrumental noise sources such as the background or readout noise (worst case). The fibre transmission was calculated based on the attenuation values provided at the time from le Verre Fluoré. The first fibre bundle design included several connectors, for each of these connectors, we estimated a loss of 0.15 dB and we also assumed a 2%

2.1. High-Dispersion Coronagraphy on the VLT with HiRISE loss on the input and output surface of the fibre to reach a total fibre transmission of 78.2%. The FEM integrates four lenses with a transmission calculated of 80%.

CRIRES+ transmission has been measured during the AIT in Europe, although the slit transmission value was not available, the total transmission (including the quantum efficiency) is 20% in the H band. For a 0.2 ′′ slit, we presumed, based on the FEM optical design that 93% of the incoming light goes through the slit. We notice that for CRIRES+ standalone, the slit efficiency drops drastically with the increase of the seeing. This effect is due because the slit losses are much higher with the seeing low order AO system MACAO.

Recently, I worked with Dr Arthur Vigan to upgrade the end-to-end simulation of HiRISE based on the final optical components, the AR coatings and the optical design of the fibre bundle. For SPHERE and CRIRES+ we rely on values that have been measured either during AIT in Europe or during on-sky operations. For the lenses in the FIM and the FEM, we use the AR coatings measurements provided by the optics manufacturers (Fichou, Institut Fresnel). For the mirrors from Edmund, we use a value of 0.98 for the reflectance at all wavelengths. Regarding the fused silica fibre, we use the attenuation values provided in the literature (Zblan fibres) and interpolate to the attenuation provided at 1300 and 1500 nm for the 1310M-HP fibre. For the coupling efficiency, we use the HiRISE simulation model (N'Diaye, private communication) to compute the overlap integrals between the planet's PSF electric field and the field transmitted by the science fibre. We included ExAO residuals for a 0.8 ′′ seeing, a SPHERE NCPA measured with ZELDA and the wavefront errors of the FIM based on the HiRISE Zemax model. We also include a centring error of approximately 8 mas (equivalent to 0.2 λ/D at 1.6 µm) on the science fibre, which corresponds to a pointing error after centring the planet on the science fibre. This pointing error value has been implemented in the final end-to-end simulations based on the research achieved in the framework of this PhD (El Morsy et al., 2022).

The updated transmission budget, illustrated in Fig. 2.19, shows a gain of 20% at 1.6 µm compared to the values previously reported in (Otten et al., 2021). We notice that the gains are due to the quality of the custom optics AR coating, the quality of the coatings for the FIM dichroic manufactured by Institut Fresnel, and the use of highly transmissible fused silica fibres from Nufern. The current model does not take into account the transmittance of the glasses used for the custom lenses because it is negligible. These values include a centring error of 0.2 λ/D of the PSF into a SMF. We, therefore, have better performance than estimated in (Otten et

First targets objective of HiRISE

HiRISE aims to achieve detailed characterisation of exoplanets at high-spectral resolution. The first immediate objective of HiRISE is focused on characterising six directly imaged exoplanets and brown dwarfs. All these targets, already characterised in low spectral resolution will be available for HiRISE and be visible for the Paranal observations (Period 111, from April 1 2023 to September 2023).

High-Dispersion Coronagraphy on the VLT with HiRISE

We estimate the expected performance of HiRISE in the signal-to-noise-ratio (SNR) of the CCF for the detection of atmospheric features in these targets. We then compare the expected performance between HiRISE (SPHERE and CRIRES+) and CRIRES+ standalone, by exploring the contrast vs the angular separation for given stars (mag, distance, age) and targets (T e f f ). The expected performance on the science targets is illustrated in Fig. 2.20. We can illustrate with two examples the unique spot for high spectral resolution characterisation with HiRISE. The first case is for targets similar to HD 4113. In Fig. 2.21 the expected detection limit for a target around a moderately bright star (H=6.5) similar to HD 4113 is represented for one hour of integration time with CRIRES+ and HiRISE in H band as a function of contrast and separation.

In Fig. 2.21, the expected SNR of the CCF for one hour integration in normal seeing conditions and with a rotational velocity of 15 km/s illustrates that HiRISE offers a unique window of contrast and separation not accessible to CRIRES+. It is mainly due to CRIRES+ limitation in contrast and because of the performance of the MACAO system. The second HiRISE simulation is for a target around 51 Eri, which is the faintest companion detected by the direct imaging technique. We see in Fig. 2.22 that 51 Eri is out of reach for CRIRES+ and that HiRISE should be capable of detecting the companion signal. The largest gain for HiRISE is expected for the highest contrast (> 12mag) and smallest separation (<1000 mas). HiRISE will offer a gain of a factor > 3 in SNR. In the nearby future, JWST will offer a more precise estimation of the targets T e f f , which combined with HiRISE performance will provide more information regarding molecular features and abundances within their atmospheres (Carter et al., 2022).

Centring strategies for HiRISE

One of the challenges of coupling SPHERE and CRIRES+ resides in successfully injecting the signal of a previously known exoplanet detected by SPHERE into a SMF with a centring accuracy of 0.1 λ/D.

In this section, I present the three different strategies developed during my PhD to fulfil the required centring specification for HiRISE. Two configurations are described, with and without a coronagraph.

Centring strategies in a non-coronagraphic configuration

Immediately after the FIM receives the ExAO-corrected beam from SPHERE it becomes entirely independent from SPHERE and the planet acquisition relies only on the FIM. It consists in centring the planet's PSF on the science fibre with the required accuracy mentioned previously. Since the planet's PSF will not usually be visible on the tracking camera image because of the S/N, the planet acquisition will be performed blindly based on its known relative astrometry with respect to the star and on calibrations performed during the day. Three strategies are foreseen for centring the planet's PSF on the science fibre, and for each strategy, two configurations are possible depending on the presence (or absence) of a coronagraph. For the practical implementation of the centring strategies, a certain number of key calibrations are necessary and are detailed below.

The first strategy (Fig. 2.23, top row) relies only on a dedicated centring fibre located close to the science fibre. In the non-coronagraphic configuration, the first step consists in placing the stellar PSF on top of the centring fibre to refine the position with an optimisation algorithm that maximises the coupling efficiency of the star into the centring fibre (Fig. 2.23, panel 2). Then, by using the offset pre-calibrated during the laboratory validation of the instrument (Fig. 2.23, panel 1), we place the star onto the science fibre (Fig. 2.23, panel 4). And finally, by using the interaction matrix and using the known right ascension and declination (RA and DEC) offsets, we apply an offset to the tip-tilt mirror to move the planet on the science fibre (Fig. 2.23, panel 5).

The second strategy (Fig. 2.23, middle row), also in the same non-coronagraphic configuration, uses the science fibre and four feedback fibres that retro-inject light into the system via the dichroic and the corner cube. The four fibres are re-imaged 2.2. Centring strategies for HiRISE on the tracking camera on top of the stellar PSF. Their diagonal intersection (I ) in theory provides the position of the science fibre with respect to the focal plane image. Consequently, the first step of the procedure consists in switching on the four feedback fibres to acquire an image with the tracking camera, find the centre of the feedback spots and then determine the position of the science fibre (Fig. 2.23, panel 2). However, an offset may occur between I and the position of the science fibre. It is due to an alignment mismatch between the science branch and the retro-injection branch, and would need to be calibrated beforehand during the laboratory validation of the instrument (Fig. 2.23, panel 1). Then we position the stellar PSF onto the science fibre by moving the tip-tilt mirror (Fig. 2.23, panel 4) and, as described for the first strategy, we apply an offset to move the planet into the science fibre (Fig. 2.23, panel 5).

The third strategy (Fig. 2.23, bottom row) combines the first and the second strategies using the four feedback fibres, the centring, and the science fibre. The first step consists in switching on the feedback fibres to find the centre of the four spots and the intersection I (Fig. 2.23, panel 2). We use the tip-tilt mirror to place the star on the centring fibre (Fig. 2.23, panel 3). By using the offset pre-calibrated during the laboratory validation of the instrument (Fig. 2.23, panel 1), we place the star onto the science fibre (Fig. 2.23, panel 4). Then we apply an offset to place the planet onto the science fibre (Fig. 2.23, panel 5).

Centring strategies for HiRISE

The challenge to accurately inject the planet's PSF into the science fibre relies on the high calibration accuracy performed at each procedure step. In the first strategy, the critical first step is to accurately inject the stellar PSF into the centring fibre, while for the second strategy, the crucial first step consists of accurately placing the stellar PSF on the intersection I . All the following steps to inject the planet's PSF into the science fibre will be performed blindly, relying only on the high accuracy of the calibrations computed in the laboratory and the known astrometry of the planet. In HiRISE, the science fibre S will be connected to CRIRES+ preventing any verification of the planet's PSF injection in the science fibre during the acquisition. Therefore, it is essential to define the best possible strategy to centre the planet's PSF on a SMF.

Centring strategies in a coronagraphic configuration

In a coronagraphic configuration, the centring strategies are slightly different. Due to the presence of the occulting mask of the coronagraph, the star is not directly visible on the tracking camera. Therefore, to monitor the localisation of the star behind the mask, we use 'satellite spots' artificially created by the deformable mirror in the system. These spots are routinely used in VLT/SPHERE and provide an accuracy of 1.2 mas (0.03 λ/D) for the centring of coronagraphic images (Vigan et al., 2016;Zurlo et al., 2016). The satellite spots, which are replicas of the stellar PSF, are created at a known angular separation by applying two orthogonal sinusoidal modulations on the high-order deformable mirror (HODM). In a coronagraphic context, the centring strategies presented above are modified by the necessity of first accurately locating the stellar PSF using the satellite spots. This can be achieved by injecting each spot into the centring fibre. The diagonal intersection of these spots allows the star's PSF position to be retrieved. Then, we place the planet on top of the centring fibre by using the calibrated interaction matrix. Finally, we apply the pre-calibrated centring-science fibre (C -S ) offset to place the planet into the science fibre.

Prototyping of a centring procedure on MITHiC

In the previous chapter, I introduced the HiRISE project, its technical and scientific challenges and its specification requirements. I ended that chapter by describing the principle of several centring strategies to accurately inject the planet's PSF into a SMF, which connects SPHERE and HiRISE.

In this chapter, I present the results of laboratory experiments I conducted to explore the centring strategies described in the previous chapter. The testbed I used for these activities was the upgraded version of the Marseille Imaging Testbed for High-Contrast (MITHiC) -I describe it in the first section. I also describe the characterisation of the bench and explain the limitations of the setup and the specifications required for the centring strategies. I introduce the description of the centring strategy procedures in the laboratory, and I discuss the performance results. Finally, I conclude and propose some perspectives regarding the best strategy for HiRISE.

Ongoing projects such as Keck/KPIC, Subaru/REACH, and VLT/HiRISE base their observing strategy on the use of a few science fibres, one of which is dedicated to sampling the planet's signal, while the others sample the residual starlight in the speckle field. The main challenge in this approach is to blindly centre the planet's point spread function (PSF) accurately on the science fibre, with an accuracy of less than 0.1 λ/D to maximise the coupling efficiency. In the context of the HiRISE project, three possible centring strategies are foreseen, either based on retro-injecting calibration fibres to localise the position of the science fibre or based on a dedicated centring fibre. We implemented these three approaches, and we compared their centring accuracy using an upgraded setup of the MITHiC high-contrast imaging testbed, which is similar to the setup that will be adopted in HiRISE.

Implementation of the centring strategies on MITHiC

Our results demonstrate that reaching a specification accuracy of 0.1 λ/D is extremely challenging regardless of the chosen centring strategy. It requires a high level of accuracy at every step of the centring procedure, which can be reached with very stable instruments. In this chapter, we present the MITHiC testbed and detail the description of the FIM. We also explain the limitations of the setup and the specifications required for the centring strategies. We introduce the description of the centring strategy procedures in the laboratory, and we discuss the performance results. Finally, we conclude and propose some perspectives.

Implementation of the centring strategies on MITHiC

MITHiC is a HCI testbed located in the optics laboratory at the Laboratoire d'Astrophysique de Marseille (France). The development of the testbed started in 2010 and has been used to develop and test various methods for HCI, such as COFFEE ( MITHiC is composed of a telescope simulator (TS), a wavefront sensor (WFS) to measure the static aberrations, and a classical Lyot coronagraph (CLC) (Lyot, 1933), as shown in Fig. 3.2. A detailed description of the testbench is explained below with an emphasis put on the key components of the telescope simulator and on the FIM.

General description of the MITHiC testbed

MITHiC characterisation

Description of the key elements

The telescope simulator is represented as an orange box in Fig. 3.2 and is composed of a monochromatic laser source, a phase screen, a second stage AO and a coronagraphic setup. The lenses on the bench are 2-inch diameter achromatic doublets from Thorlabs with a coating covering the visible and NIR, in addition, three 1-inch beam splitters from Thorlabs are implemented, one following the spatial light modulator (SLM), one at the intersection with the wavefront sensing branch (ZELDA), and one in the FIM part represented as a blue box. The point source emitted by the laser source illuminates the pupil entrance, which its design is a simple clear annulus rather than 3.1. Implementation of the centring strategies on MITHiC a padded replica of the telescope aperture. Then, a phase screen is placed to simulate different types of aberrations shape emulating the ones presumably encountered during ground based observations. The phase screen is manufactured by SILIOS technologies following the specification requirements. In the context of the thesis, the phase screen has not been used for the centring tests.

❖ Laser source

The TS generates a PSF with a polarised monochromatic fibre-coupled super-luminescent diode (SLD) at a wavelength of 670.7 nm (the chromatism of MITHiC will be ignored in the manuscript). The source emits non polarised light, but one device on MITHiC work with polarised light, such as the SLM, so it is necessary to polarise the source light. In that perspective, the source is connected to a setup composed of a polariser and a half-wave plate. The polariser aims at selecting the direction for which the light is maximised and the quarter-wave plate enables to turn the polarisation direction to match the one required by the SLM. Finally, the home build setup (Fig. 3.1, purple inset) is connected via a polarisation-maintaining fibre to a six degrees of freedom optic mount allowing to obtain a point source at the entrance of MITHiC.

In the context of the injection of the light into a fibre, the stability of the source is important. On MITHiC, the typical stability of the SLD output power after 3 hours of warm-up at T = 25˚C + 0.2 is less than 500 ppm, which corresponds to a flux variation of 0.005%.

❖ Spatial Light Modulator

The Spatial Light Modulator (SLM) is composed of liquid crystals (LC), which are organic materials sharing properties between solid and liquid states. The principle of the SLM relies on the LCs orientation, which is a preferential direction (nematic mesophase) defined by a director vector. An external electric signal applied to the LCs leads to the reorientation of the crystals in the direction of the electric field. Therefore, the spatial control of an applied electric signal to the LCs offers the possibility to modulate the phase of an incident optical wave. Nowadays, old commercial SLMs are addressed through digital video interface (DVI) with each grey level corresponding to a given voltage. They can be employed either in transmission or in reflection.

Implementation of the centring strategies on MITHiC

The technology principle of SLM located on MITHiC is named Liquid Crystal on Silicium (LCoS) and its principle is shown in Fig. 3.3. SLM-LCoS are composed of several layers such as a glass substrate, a transparent electrode, alignment films, a parallel aligned LCs layer, a dielectric mirror and a silicon substrate. On the silicon substrate, an active matrix circuit is formed to apply voltages to pixel electrodes. The parallel aligned LCs layer allows to module the phase and the quantity of phase modulation varies depending on the applied voltage. The proper functioning of the SLM-LCoS lies in the polarisation efficiency of the incident beam on the SLM display. The incident electric field is composed of two components, S and P.

The S component is linearly polarised in the orthogonal direction with regard to the SLM's plane of incidence, and the P component is parallel to the same plane of incidence. The SLM can vary the phase of the P component, so to make full use of the SLM, the S component must be minimised. The properties of the SLM could diverge from the one provided by the manufacturer due to a lack of spatial homogeneity on the SLM display, which creates phase modulation variations between the centre and the edges of the SLM display. It can result in a wavefront distortion in the optical path. Therefore, the characterisation of an SLM is an essential step before using it. On MITHiC, the SLM-LCoS from Hamamatsu operates in reflection, which enables to fold the optical system. The SLM, which acts as a deformable mirror (DM) in the pupil plane allows a phase correction to be applied in closed-loop to flatten the wavefront to be modulated for particular needs, such as creating the satellite spots or introducing known aberrations. After the light cross the LCs layer and the first beam splitter, only 25% of the light is transmitted to the AO branch. The SLM is composed of a matrix of 792 x 600 pixels with a pitch of 20 µm. 274 pixels across the pupil diameter D (D=5,5 mm) aim to control the high spatial frequency of the phase. The wavefront error induced by the SLM is 0.76 nm root mean square (rms) at a wavelength of 670.7 nm. In the context of my thesis, the SLM was used based on the previous characterisation performed by Baptiste Paul. For those tests, the SLM 3.1. Implementation of the centring strategies on MITHiC was installed on a dedicated test bench to evaluate its performance. The test bench includes a commercial Shack-Hartmann and a camera for focal plane imaging. The main characterisation results are presented below.

1. Regarding the stability of the SLM, it is absolutely necessary that the aberrations introduced by the SLM remain stable over time. The first test has consisted in applying an aberration map to the SLM and measuring 10 wavefronts by an HASO (Shack-Hartmann) within a 5 minute interval. The result of this test showed that the phase variations calculated for the 10 wavefront measurements is 0.38 nm RMS in averaged, which demonstrates the stability of the SLM. 2. Another key test concerns the linearity of the SLM, which plays an important role during its operation. To evaluate the linearity of the SLM, a test has consisted in applying a defocus ramp from -1000 to 1000 nm RMS and measuring the amplitudes with the HASO. The SLM shows a high linearity and a good fit with the data provided by Hamamatsu. The overriding limitation of the SLM is the polarisation efficiency as mentioned above. Thus, with the combination of the polariser and quarter-wave plate, the S component has been minimised so that the light is predominantly linearly polarised in the parallel direction. SLM-LCoS combines the advantages of the highest resolution with the small pixel size and the highest fill factor (FF), which is the active area of the display surface. On MITHiC, the SLM resolution is 2.64 nm in equivalent optical path difference (OPD) and the FF is 98%. However, the limitation of SLM-LCOS is its slowness (the settling time limits the correction speed to a few Hz) and chromatism. In the context of the work carried out on MITHiC, these two aspects have not been identified as a limitation. Indeed, the SLM is used for the calibration of quasi-static aberrations that do not require high-speed correction.

❖ Zernike wavefront sensor

The WFS on MITHiC is a Zernike wavefront sensor called ZELDA (N'Diaye et al., 2013; Pourcelot et al., 2021). It emulates the phase-contrast method of Zernike (1934) applied to direct exoplanet imaging. The ZELDA formalism is described in more detail in N'Diaye 2013, and its concept is given in Fig. 3.4. In the entrance pupil plane A, the residual wavefront errors are encoded in the electric field's complex amplitude. Then, the mask placed in the focal plane B where the star's image is formed. It introduces a phase change of the image going through the mask. The interference in the pupil plane C, between the electric fields going in and outside the phase mask displays an 3.1. Implementation of the centring strategies on MITHiC intensity shape associated to the wavefront aberrations.

The ZELDA phase mask on MITHiC located at an F/90 focal plane consists of a circular shape of fused silica manufactured by SILIOS using photolithography. The mask, shown in Fig. 3.4 has a depth of 350 nm, corresponding to λ/4 in optical depth at 670.7 nm, and a diameter of 64 µm, equivalent to 1λ/D (N'Diaye et al., 2013). As shown in Fig. 3.5, the phase mask is mounted on a three-axis motorised mount with the actuators having a 1 µm position accuracy. Following the phase mask, there is a pupil plane, where a Hamamatsu ORCA-Flash 4.0V3 CMOS camera is located to image the pupil of a diameter D W F S = 2.75mm (418 pixels on the detector).

Due to the aberrations in the MITHiC setup, if no corrections are applied on the SLM, the optical aberrations of the MITHIC bench are quantified to ∼33 nm RMS, and can be decreased to 20 nm rms or better with a correction based on a ZELDA measurement (Pourcelot et al., 2021), as seen in Fig. 3.6. -ZELDA Wavefront map in a unit of Optical Path Difference (OPD). We notice that there are no remaining wrinkles in the pupil. These wrinkles are generated from a slight offset between the SLM and the beam. These offsets explain the difficulty to achieve a correction below 20 nm.

❖ Classical Lyot Coronagraph

The last part of the telescope simulator is the coronagraph, which its principle is described in Sect. 1.2.4 in Chap. 1. Initially, the coronagraph implemented on MITHiC was a Roddier and Roddier [START_REF] Roddier | Stellar Coronograph with Phase Mask[END_REF]. In theory, this mask allows obtaining high-contrast thanks to its performance at small separation angles. However, its main limitation is its sensitivity to optical aberrations and vibrations. Thus, to increase the performance of MITHiC, a Classical Lyot Coronagraph (CLC) has replaced the Roddier and Roddier focal plane mask (FPM). A focal plane at F/90 followed by the pupil plane allows the implementation of a focal-plane mask and a Lyot stop. The diameters of the mask and the Lyot stop have been optimised by a simulation shown in Fig. 3.7 to maximise the average contrast between 5 and 10 λ/D. For a separation between 5 and 10 λ/D, the diameter of the mask is 5.382 λ/D and 0.77D for the Lyot stop. The mask has been manufactured by OPTIMASK using a circular chromium 3.1. Implementation of the centring strategies on MITHiC deposit on an N-BK7 substrate, and four aids have been implemented for centring purposes. The specifications of the mask are shown in Fig. 3.8. The Lyot stop, whose specifications are represented in Fig. 3.9, has been manufactured by STEEC using highly accurate laser-cutting technology. The mask is mounted on three motorised axes, which allows it to be offset from the optical axis when desired. The Lyot stop is mounted on a standard Thorlabs mount and is manually removable, however, the Lyot stop has not been dismounted from MITHiC in the framework of the thesis.

Fibre Injection module (FIM)

To reproduce the setup that will be implemented in HiRISE, I modified MITHiC by adding an implementation of the FIM (Fig. 3.2). The first modification was to re-image the pupil of the bench on a mirror glued on a piezo tip-tilt mount (PI-S335) and located after the coronagraph stage. The mirror is oriented at 45˚with respect to the optical axis to also fold the beam and make the whole setup more compact. Then, the beam is recollimated and split into two to implement the branches of the FIM. We use a 50/50 beam-splitter cube and not a dichroic because MITHiC is fully monochromatic, unlike HiRISE. The description of the tip-tilt mirror is presented in more detail in the following subsection.

❖ Injection branch

In the injection branch, the beam is refocused using a Thorlabs F810SMA-635 collimator (output 1/e 2 beam diameter: 6.7 µm; wavelength: 635 nm) to create a focal plane image at the tip of a FB.

The FB is a custom bundle manufactured by Thorlabs, as shown in Fig. 3.11. It is composed of seven 4.5/125 SMF fibres, 2 m in length, mounted with a unique SMA connector in the collimator. A picture of the tip of the bundle is provided Fig. 3.11. The fibres are labelled S for the science fibre, C for the centring fibre, and F 1 to F 4 for the feedback fibres. There is one spare fibre that is not used in the setup. The seven fibres are separated from each other at the centre of the FB and the end connectors on the other side are individual FC connectors. During the alignment of the FIM described in Sect. 2.2.1, the science fibre is aligned with respect to the optical axis, while the others remain off-axis. Since MITHiC is monochromatic and does not have a dedicated spectrograph, we connect the S and C fibres to two different Thorlabs PM101 power meters with S150C cells (Fig. 3.11, S power meter and C power meter) to measure the injected flux in watts.

❖ Retro-injection branch

For the second and third centring strategy, the F 1-4 fibres are retro-fed into the system through a home-built system (Fig. 3.12, calibration sources) based on four LEDs controlled by an Arduino micro-controller, whose circuit diagram is illustrated in Fig. 3.13. The LEDs emit light into the SMF through the collimator, which also acts as an injector in this configuration. The retro-fed light goes through the beam-splitter cube and is reflected to the system by a plane mirror placed closely behind the cube to avoid significant differential defocus between the tracking branch and the retroinjection. The four retro-fed fibres are finally re-imaged on the tracking camera on top of the science image. in Fig. 3.12. We soldered to the circuit several electronic components such as a LED, resistors, and MOSFETs.

❖ Tracking branch

In the tracking branch, the stellar PSF is imaged using a doublet on a Coolsnap HQ2 CCD camera manufactured by Teledyne Photometrics located in a focal plane with a 4.26 pixel/(λ/D) sampling. Fig. 3.14 shows the modulation transfer function (MTF) describing the response of the imaging system as a function of spatial frequency.

The MTF has been calculated as the Fourier transform of the PSF1 . The MTF cutoff frequency for a detector of dimension d is f d et = 1/d and to avoid aliasing, we need to operate at Nyquist frequency, f N = f d et /2 = 1/2d . The sampling and linearity informations establish the equivalence for the different units, so 1λ/D = 4.26pi xel s.

In the rest of the paper, the Coolsnap camera will be referred to as the tracking camera.

The Tip-Tilt mirror

Introduction to high precision piezoelectric devices

The term "piezo" is derived from the Greek word "piezeinfor" meaning pressure.

The piezoelectric effect was discovered in 1880 by the Curie brothers, Jacques and Pierre. They demonstrated in the laboratory the first piezoelectric effect by using crystals of tourmaline, quartz, topaz, cane sugar, and Rochelle salt. Their experiment showed that quartz and Rochelle salt showed the most piezoelectricity ability at the time. Decades later, piezoelectricity remained in the laboratory to be further explored. World War I initiated the first practical application for piezoelectric devices using the sonar device. This use of piezoelectricity in sonar created intense worldwide developmental interest in piezoelectric devices. Over the next decades, new piezoelectric materials and applications for the materials were developed. The piezoelectric effect is the conversion of electrical energy to mechanical energy using natural materials, such as crystals. However, polycrystalline ferroelectric ceramic materials, such as Lead Zirconate Titanate (PZT), have proven to achieve more gain and they are used in actuator or sensor applications.

Piezo drives are common nowadays in high-precision motion control systems. They provide the highest symbiosis between stability, accuracy, responsiveness and res-3.1. Implementation of the centring strategies on MITHiC olution. In most ultra-precision applications, piezo positioners are used with a position feedback sensor and closed-loop control, which principle is described below. With suitable controllers, closed-loop operation enables reproducibilities in the subnanometer range and reduces the hysteresis effect.

The piezo TTM used on MITHiC is from Physic Instrument (PI-S335), it is ideal for dynamic applications such as scanning and tracking. PI's piezo flexure nanopositioning systems employ patented PICMA piezo actuators, the only polymer-free actuators with co-fired ceramic encapsulation. The monolithic PICMA actuators are space qualified and were submitted to 100 billion cycles of life testing at NASA's JPL. Co-fired multilayer piezo actuators are similar to ceramic capacitors and are not affected by wear and tear. The systems are designed to be driven at lower voltages than most other piezo systems. In addition, the monolithic ceramic-encapsulated design provides better humidity protection than conventional polymer-film insulation. Humidity is the main influence on the long-term reliability in low-dynamics or quasi-static operation modes, where the piezo actuator is supplied with a DC voltage to maintain a position for a long time. One of the advantages of piezo ceramics is their high force generation and extremely fast response capabilities. Piezo actuators are mostly used to replace solenoids or other classical actuators in fast valve applications, micro-dispensers or pumps. The meander-shaped design of the strips ensures stable electrical contact with all inner electrodes.

The design of the TTM on MITHiC is based on two piezo actuators that allow to push/pull the platform. The platform, which handles a mirror is displaced around one centre of rotation that provides great advantages for angular stability.

Closed loop controlled system

Control systems in which the output impacts the input in a way that the input will adjust itself based on the output generated are called closed-loop control systems, which are described in Fig. 3.17. The controller receives a command (IN: commanded position). It sends the command to the piezo via the amplifier (bottom path with arrows to the left). The sensor measures the actual position of the piezo and returns it to the signal processor, which calculates the error and deduces a new command to apply to the controller (top path with arrows to the right). Finally, the corrected piezo command is sent to the user (OUT: exact position). The command is a low-voltage electronic signal (typically between 0 and 5V). It converts the signal to a voltage applied to the piezo (several tens of volts). For any electronic system, there is always an amplifier stage between the command and the system itself (piezo, motor or other) to adapt the signal (shaping and amplification).

Metrology study for the tip-tilt mirror

Before the gluing step, the mirror with the best optical quality must be selected. Thus, three Edmund silver-coated mirrors were tested at LAM in order to determine which one would be used first on MITHiC and then implemented on HiRISE. Once glued, the mirror cannot be removed, hence it is important to choose the best one from the beginning. A metrology study using a Fizeau interferometer allowed to control the wavefront of each of these mirrors. Fizeau interferometers are eminently suitable in optics quality control. They are used for a wide variety of applications such as testing the wavefront distortion of optical systems. Since the test and reference beams travel through the same optics, the wavefront errors from the instrument are minimised involving the maximum accuracy. Furthermore, Fizeau interferometers are scalable via beam expanders to very large apertures. And finally, they are capable of using either flats or spheres reference surfaces, allowing the testing of concave and convex optics.

Regarding the measurement errors of the Edmunds mirrors, the interferometric phase map acquisitions are handled by a Moller-Wedel V-100 interferometer in an ISO 5 clean room. The Fizeau-type interferometer is using a fibre-coupled HeNe-Laser (λ = 632.8nm) to send the beam to the tested surface, in our case the Edmund mirror. In a phase-shifting interferometer (Fig. 3.18), the reference surface is moved with regard to the test surface. The interferometer acquires one frame of data for each reference position, then, all the frames are combined to calculate the wavefront error. The final phase map results for each mirror relies on an acquisition of 5 measurement frames, using a flat reference surface. The challenge with phase-shifting relies on the vibration and turbulence during the measurement data, which can degrade the quality of the frames. Thus, we operate these metrology measurements in an environment isolated as possible from vibration as seen in Fig. 3

.19

The chosen mirror presented in (Fig. 3 -Laboratory setup used to perform the metrology study of the mirror that is to be glued on the tip-tilt platform. The Fizeau Phase-shifting laser interferometer is on the left on the picture with the reference surface directly implemented in the device (black ring). On the right side of the picture, we see the tested mirror on its mount. The mirror has been tilted only when the picture has been taken.

Gluing procedure

The mirror gluing on the tip-tilt mount is critical since any excessive force would increase the risk to damage the piezo actuators. Thus, a method performed by Dr Floriot at LAM consisted of using fish wires to apply the exact amount of glue to not damage the piezo and to perfectly flatten the mirror on the platform. We used an automatic glue dispensing to provide the exact amount of epoxy bicombo to apply on the wires.

The first step described in the top row, the second panel of Fig. 3.21 has consisted of 3D printing centring aid made of thermoplastic resin (ABS) and then can be used for gluing a mirror onto the S-335 TTM. One of the challenges remains in the fact that the piezo platform is smaller than the mirror surface. Thus, the centring aid has been divided into two pieces, secured by screws, which aim to hold the mirror at the desired position during gluing procedure and to easily remove it when the gluing phase is achieved.

The glue used for the procedure has typically a thickness between 100-200 µm and the thickness of the wire is the same. The quantity of glue to apply has been established by the formula:

ρ = π.R 2 .e
with R the radius of the wire and e the average diameter of the dot of glue. The amount of glue applied for the three points is 1 µl.

In the bottom row, the first panel of Fig. 3.21, we applied weight to the mirror for 24 hours to secure the gluing process and we cut the wires sticking out as shown in the following panel of Fig. 3.21. Finally, the TTM has been placed back on MITHiC. Several tests have been achieved to verify the functional integrity of the TTM. One of them is described in more detail in Sect. 3.1.2.3. By the end of the gluing procedure, we noticed that the TTM functionality has been preserved.

Thermal behaviour study

A thermal behaviour study of the tip-tilt system was performed on MITHiC.The system includes the tip-tilt platform, the tip-tilt controller and its power supply. This study has been performed to understand the heat power contribution of each element since they either will be part of the HiCab (the controller and power supply) or inside SPHERE (the tip-tilt platform). For the HiCab, a liquid cooling system will be employed for heat dissipation. As for the tip-tilt platform, it will be placed on the FIM located inside SPHERE. Hence, a power consumption budget has been established for the HiCab. In this section, we focus on describing only the heat dissipation test made for the tip-tilt system.

Implementation of the centring strategies on MITHiC

For this test, we used an infrared camera and two temperature sensors to crossvalidate the results recorded with the camera. The infrared camera was directed towards the entire system located outside of the bench, for that purpose, we opened the lateral panel on MITHiC. On (Fig. 3.23), we see that one temperature sensor has been placed close to the tip-tilt platform and the other ones on the controller of the TTM and the power supply themselves. The sensors are in contact with the power supply surface of the TTM controller thanks to an alternative layer of Teflon and aluminium foil tapes to isolate the tip of the sensors from the ambient air and to ensure heat transfer between the controller and the temperature sensor. The second temperature sensor, attached to the Thorlabs stand, is placed just in front of the mirror preventing any surface damage. Even though the probe tip is in the ambient air, we used the results of the infrared camera to cross-validate the temperature variations when the TTM is used in regular conditions. On MITHiC, the test performed shows an image displayed in (Fig. 3.23) that corresponds to a differential measurement between an acquisition taken with the infrared camera when the TTM had been shut down for a few hours and one taken after two hours with the TTM powered on. The increase is approximately 0.37°C over two hours. In parallel, the temperature sensor located right next to the tip-tilt stage (point n°5) addresses that the room temperature elevated from 22.45°C to 22.77°C over 2 hours, which corresponds to an increase of 0.32°C. This increase in temperature corresponds to the increase in the ambient temperature. We can conclude that the TTM under normal conditions has a thermal dissipation that is negligible. We used the infrared camera to study the heat dissipation of the controller and power supply after 2 hours of standard use of the TTM. For both the controller and power supply, we noticed in (Fig. 3.22) an increase in the temperature with respect to the ambient air of 17°C. The temperature sensor positioned on the controller shows an increase of 15.2°C, which corroborates with the results from the infrared camera.

On HiRISE, the TTM will be used only in specific procedures such as for the centring of the planet's PSF on the science fibre and for the calibrations. During the science observations, the tip-tilt mirror remains static for the entire duration of the exposure. This study has enabled to investigate the best thermal management strategy for the HiCab. Temperature elevation with respect to the ambient air for the tip-tilt stage controller and its power supply. The black rectangle on top of the controller is the aluminium tape that holds the temperature sensor, which has a different emissivity than the rest of the controller surface.

Implementation of the centring strategies on MITHiC

Laboratory characterisation of the tip-tilt mirror

Despite their robustness, piezo tip-tilt systems are sensitive precision technology. PI sets high standards for the reliability and quality of its piezo tip-tilt system. However, SMF injection applications are demanding fields requiring precise knowledge of key component performance such as the tip-tilt mirrors. For active components such as 3.1. Implementation of the centring strategies on MITHiC piezo actuators, such knowledge includes linearity, resolution, and repeatability. These parameters are necessary to be defined with precision to understand the limitation of this component.

MITHiC is located in a grey room at ambient temperature and acceptable humidity. It is enclosed with aluminium panels, two temperature probes are located in the centre of the bench and on the external side of the table, another dedicated probe records the variation of the humidity in the room. MITHiC is not controlled in temperature or humidity.

Quality specifications have been provided by PI regarding the piezo component. For operating the TTM on MITHiC, there has been set no specific requirement for the resonance frequency, only that the resonance frequency must not be greater than 0.7 kHz so the TTM mechanism will not be affected by system dynamics. The resolution in closed-loop provided by PI is 1.0 µrad typically and the repeatability of the TTM is estimated in both directions at 1.0 µrad typically. On MITHiC, the TTM repositioning accuracy has been tested but is mainly impacted by the PSF stability described in Sect. 3.1.3.3.

Ideally, the linearity of the TTM should be perfect, however, in practice, the linearity of the actuators (PICMA P-885) can be affected by several factors such as the load capacitance, stiffness, and parasitic motions. In the first approximation, the PICMA actuators behave as a spring and mass system. The elasticity module of the ceramic, which is 25% steel affects the stiffness of the actuators. Typically, the actuator's stiffness is between 1 and 2,000 N/µm so precautionary measures must be applied to protect the piezo from bending forces. In order to know the actual motion of the TTM stage, a displacement curve of the actuators has been characterised on MITHiC. Fig. 3.24 displays the tip-tilt linearity test results. For each position of the tip or tilt range, a PSF image is acquired on the tracking camera. A 2D Gaussian fit provides the position of the PSF in the focal plane of the tracking camera in pixels. Then, a linear fit model is applied to the data for each tip and tilt axis and the residuals between the model and the data are shown in the bottom panel of Fig. 3.24, where we notice that the residuals amplitudes are within -5 and 5 pixels and that the non-linearity regime is more pronounced at the edges of the TTM. This linearity test includes the optical aberrations of the system, the field distortions and not only the proper linearity of the TTM.

The response behaviour of the TTM has been characterised after the gluing phase. The TTM is able to reach the tip edge range value and if no time delay is provided to the TTM command, the target position is reached almost instantly within a few ms. A rapid change of the operating voltages can cause a rapid change in the position of 3.1. Implementation of the centring strategies on MITHiC the actuators thus leading to a strong overshoot of the target position. In the context of the centring strategy tests achieved in the laboratory, it has been ensured to wait at least 10 ms before sending another command to TTM and to apply no time delay while asking the TTM to reach any required target position within overshooting.

In HiRISE, the TTM should not be used in its full range, but will only be used in a so-called useful range. This range is defined by the targets that HiRISE aims to characterise, and the size of the pupil on the tip-tilt mirror (12 mm). Initially, this would be targeted with an angular separation up to 1000 mas. In the case where there is no misalignment between the FIM and SPHERE, the useful region of the TTM would be defined to be: ± 3.5 mr ad around the reference position, with the reference position defined at the tip-tilt position that allows placing the on-axis star at the centre of the science fibre. In Fig. 3.24, if we look at the area of the useful range of the tip-tilt, we notice that the residuals, which include the distortion of the FIM, the optical aberrations and the limitation of the bench, are at worst 0.7 λ/D in tilt and 0.4 λ/D in tip. The residuals on MITHiC are way more significant than what we would have when the FIM will be implemented on SPHERE, mainly because of the distortion of the laboratory setup.

Limitation of MITHiC

One of the main challenges when injecting a signal into a SMF is the stability of the system used to perform that objective. As mentioned in the introduction, HiRISE will benefit from the high stability of SPHERE (< 0.2mas in H band), so in order to understand the system used in the laboratory, we performed a global study of MITHiC. The first study consisted to understand its behaviour in time, regarding the temperature and humidity. The aim was to identify any major contributors that would impact significantly the performance of the centring strategies. The other tests have been made to (i) improve the stability of MITHiC and (ii) to study the contributors to the centring error in the case of MITHiC and to propose a quantification for some of the most impacting terms. To study the influence of temperature and humidity on the PSF drift, a 3D data representation (Fig. 3.26) has been produced to study the correlation between the PSF position, the temperature, and the humidity. It was followed by a 2D plane model fit to achieve a detrending, which removes systematics from the PSF position data by correlating it with other parameters, such as temperature and humidity. For the 2D plane fit, the method consists to solve A * x +B * y +C = Z in a matrix form by applying an inverse method. A, B and C are the parameters of the 2D plane fit, thus, for 1°C 3.1. Implementation of the centring strategies on MITHiC corresponds the parameter A and for 1% humidity corresponds the parameter B. The results of the PSF drift as a function of the temperature and humidity are summarised in the table Fig. 3.1.

Implementation of the centring strategies on MITHiC

Environmental study of MITHiC stability

In the investigation of the cause of the PSF drift, the 3D data acquired during the week-end has been subtracted to the 2D fit to display the residual as a function of time. The drift is approximately 1 pixel in X and Y directions and showed two jumps that seems to be in a diagonal direction. I produced an histogram of the PSF motion values and I identified preferential directions. From further investigations, I noticed that the motions were in two preferential directions: +45°and -145°. After eliminating the TTM as the source of the vibrations. I could not conclude on the localisation of the mechanical vibrations on the MITHiC. Therefore, a new test was carried out and has consisted in establishing a vibration study of the entire bench. The vibration analysis paragraph below provides the solution to estimate, localise and reduce the vibration.

Vibration analysis

The MITHiC testbed is enclosed by aluminium protective panels and is subject to daily variations since it is not controlled either in temperature and humidity. Some active devices located on the testbed contribute to heating it, creating turbulence and frequency vibrations. We noticed a vibration at approximately 56 Hz in fast sampled focal plane images using a Hamamatsu ORCA FLASH V2.0 camera and that was traced to the acoustic coupling of a DC power supply near the bench. After moving the DC power supply, the 56 Hz signal fell to the background level as shown in Fig. 3.27. We note that the other peaks in the PSD plots are at levels between 20 and 30 dB below the vibration at 56 Hz. However, even if these disturbances have been attenuated some effects remain and contribute to the limitation of the testbed.

Jitter

Several phenomena are major contributors to the limitation of the bench for the fibre injection, such as the jitter, the drift of the PSF, and, to a much lesser extent, the quasi-static aberrations. Firstly, the jitter of the PSF is intrinsic to the turbulence or the vibration inside of the enclosure. To measure the PSF's jitter, we acquired data of 200 frames of 1 ms exposure time and measured the PSF's position with a 2D Gaussian fit in every frame. Based on the measurements shown in Fig. 3.28, we estimate the standard deviation at 0.04 λ/D for the PSF's jitter. The typical timescale of the jitter is of the order of a few milliseconds. The jitter estimated at 0.04 λ/D is intrinsic to MITHiC. However, on HiRISE, the vibrations are estimated to be approximately equal to 0.01 λ/D in the H band and at 1 Hz. The high stability of SPHERE would be similar to the jitter contribution on MITHiC.

Implementation of the centring strategies on MITHiC

Drift

For the estimation of the PSF's drift, I acquired an image of the stellar PSF every 0.5 s for 30 min using the tracking camera. Then, the centre of the PSF was estimated in every frame with a 2D Gaussian fit. The PSF's drift value is computed from the standard deviation and is estimated for both X and Y to 0.02 λ/D over 30 min.

NCPA

Finally, the variation of static aberrations measured with ZELDA are estimated at 7 nm rms in two weeks if the bench remains in the same configuration (no opening of 3.2. Centring strategies for MITHiC the panels). Since the timescale of the variations of the static aberrations is very long, this is not considered as a significant error term for our tests that take at most a few hours.

Centring strategies for MITHiC

Centring accuracy specification

Strategy 1

The centring procedure starts by measuring an injection map to coarsely position the star's PSF on the C fibre, then an injection optimisation is performed to accurately centre the star on the C fibre. The pre-calibrated C -S offset is applied to the tip-tilt command to position the star on the science fibre as an intermediate step. Then, I use the pre-calibrated interpolation function to measure the offset command to switch between the stellar PSF and the planetary PSF on the science fibre, based on the relative astrometry computed on the tracking camera images. Finally, a verification optimisation (VO) is performed to evaluate the ϵ error.

Strategy 2

The second strategy starts by switching on the four feedback fibres and taking an image on the tracking camera. In the focal plane, the position of the four feedback fibres is determined by a 2D Gaussian fit. The positions are used to compute the intersection I and compare its position to the stellar PSF. Then, by applying a tip-tilt command retrieved by the interpolation function, the stellar PSF is placed into the science fibre by using the previous I -S calibration. The offset command in tip-tilt to move the planet into the science fibre is calculated using the same method described previously. Finally, the VO is performed to estimate the final ϵ error.

Strategy 3

The third strategy combines the first and the second strategies. The initial step is to scan the mirror in tip-tilt to coarsely position the star on the C fibre and perform an injection optimisation to refine the centring. Then, I use the same steps described for the second strategy to place the star into the centring fibre based on its relative position with respect to I . The calibration is now not performed between I and S but between I and C . After the star is positioned on the C fibre, we apply the corresponding tip-tilt offset command to place the planet on the C fibre and we apply the pre-calibrated offset to switch from the centring fibre to the science fibre. Finally, a VO is performed to check if the planet is accurately injected into the science fibre and to measure the error ϵ. The first necessary calibration is the ability to locate the S and C fibres in the tip-tilt command's space, so I compute a coarse injection map. The performance of HDC instruments is essentially driven by the overall transmission of the system. The planetary signal is several orders of magnitude fainter than the star, so the final signal can easily become limited by either photon noise (ideal case) or instrumental noise sources such as the background or readout noise (worst case).

Calibration

Injection map

Injection into SMF can quickly lead to significant flux losses if the centring is not accurate, which is why this parameter is critical. The simulations by (Otten et al., 2021) show that a centring accuracy of 0.1 λ/D is a necessary requirement for HiRISE. With this accuracy, we expect a maximum peak coupling efficiency loss of five percentage points compared to a case with perfect centring of the PSF on the science fibre. This is a tight requirement that is illustrated in Fig. 3.29, which shows a normalised injection map of the star's PSF into the centring fibre on MITHiC, with two circles delimiting the 0.1 λ/D and 1 λ/D regions around the centre. The injection map represents the flux injected into the S and C fibres, as measured by the corresponding power meters. Each point of the injection map corresponds to a tip-tilt mirror position and a PSF position in the focal plane of the tracking camera. The radial profile of the injection map shown in Fig. 3.30 demonstrates that at 0.1 λ/D the loss is estimated to 2.6 percentage points on MITHiC. Although VLT/HiRISE and MITHiC have slightly different optical parameters, this value is consistent with the values obtained by simulation for HiRISE. A slightly lower accuracy of 0.2 λ/D could be acceptable for HiRISE, but at the cost of a loss of approximately ten percentage points compared to the perfectly centred case.

Minimisation algorithm

For a more accurate determination of the centre of the fibres, I used the tip-tilt mirror position associated with the maximum of the injection map as input to a gradient descent algorithm based on the Nelder-Meade approach, which maximises the flux injection into the fibres. Because the core of the PSF is a convex envelope, the convergence is highly repeatable and I did not encounter problems related to local minimums. From here on, this optimisation of the injection based on the gradient descent algorithm is referred to as an injection optimisation.

Interpolation function

An alternative approach would be to use a classical AO-like interaction matrix, where the relationship between the focal plane position and the tip-tilt commands is calibrated by introducing a single known offset in tip and tilt. However, this approach assumes that the offset value does not matter because there is a strictly linear relationship. This is not the case in our system because of optical distortions introduced between the tip-tilt mirror and the tracking camera, which is why an interpolation grid was adopted.

A final calibration is required to be able to accurately position the stellar PSF at any coordinate on the tracking camera. I use a non-linear approach with an interpolation function based on a full 2D calibration of the response of the tip-tilt mirror [START_REF] Service | A New Distortion Solution for NIRC2 on the Keck II Telescope[END_REF]Yelda et al., 2010), as seen by the tracking camera. To create the interpolation function, I build a calibration grid by scanning a 12.5×12.5 mrad area in tip-tilt, with a pitch of 2 mrad Fig. 3.31. For each tip-tilt position, the stellar PSF is imaged on the tracking camera and a 2D Gaussian fit is used to compute the PSF's centre in pixels. The Gaussian fit accuracy has been estimated to ∼0.01 pix, which corresponds to 0.03 λ/D. The calibration grid is then provided as input data to the LinearNDInterpolator function from the scipy library [START_REF] Virtanen | [END_REF], which uses the Delaunay triangulation method to perform interpolations in N dimensions. Using the resulting interpolation function, it is possible to obtain the tip-tilt command to place the stellar PSF at any position in the camera's FoV. I estimated the accuracy of the positioning by using the interpolation function to place the PSF on a test grid of 48×48 points interleaved with the original calibration grid. For each target position, the position of the PSF was estimated on the tracking camera image and compared to the target position to compute the residuals. I find that 6% of the outliers are located at more than 20σ from the sample data mean. I reject all outliers located beyond three standard deviations from the sample data mean. The histogram of the residuals for the full test grid is displayed in Fig. 3.32. The residuals are quasi-Gaussian with a standard deviation of 0.03 λ/D, which is well Even though the accuracy for most positions is well within our specification of 0.1 λ/D, the presence of outliers can potentially have a negative impact. In Fig. 3.33 we plot the measured position on the tracking camera of all points in the test grid, colour-coded with the position error with respect to the requested target position. The positions of the C and S fibres are indicated with crosses. I note an area of particularly poor accuracy located close to the position of the C fibre, in the direction that corresponds to the planet's position angles (in tip-tilt space) between ∼45˚and ∼100˚. For those tip-tilt commands, the beam starts hitting the edge of one of the lenses, which impacts significantly the PSF's image quality on the camera. A combination of aberrations is noticed in the PSF's shape, the coma being the main contributor, which affects significantly the shape of the PSF. As a result, the 2D Gaussian fit of the PSF is less accurate, which is problematic since the PSF's centroid is used to create the interpolation calibration grid. The presence of the outliers could explain the loss of accuracy. The calibration grid used to build the interpolation function is based on the acquisition of the stellar PSF on the tracking camera; consequently, its stability relies on the bench limitation. The calibration grid takes approximately 6 minutes to be computed and is stable over approximately 30 minutes in optimal conditions due to the PSF's drift estimated at 0.02 λ/D. The second important calibration is the accurate C -S distance, which is required to be able to apply a tip-tilt offset to switch between fibres in the first and third centring strategies. To calibrate this offset, we performed 100 measurements (50 measurements on each fibre) based on the following steps. First, the PSF is centred on the S fibre using the injection optimisation; then a coarse tip-tilt offset is applied to switch to the C fibre; and finally, the PSF is accurately centred using the injection optimisation. This provided 100 measurements of the accurate distance between the two fibres, and the final adopted value corresponds to their average. The calibration accuracy of the C -S distance is illustrated in Fig. 3.34, where each point represents the displacement position in tip-tilt before and after the optimisation. I find that 99% of the points are within the accuracy requirement of 0.1 λ/D with a mean estimated at -4.416 mrad in tip and -2.183 mrad in tilt and a standard deviation of 0.007 mrad (0.04 λ/D) in both tip and tilt. We conclude that the C -S distance calibration matches our accuracy requirement since the standard deviation is below the requirement. Finally, I note that the standard deviation estimation is approximately equal to the PSF's jitter uncertainty, so the C -S distance calibration precision and accuracy are certainly limited by the jitter of the PSF. In the second and third strategies, the calibration fibres F 1-4 are retro-fed at the same time with a LED signal and re-imaged on the tracking camera superimposed on the science image. This is illustrated in Fig. 3.35, where the stellar PSF is visible close to the centre with the four images of the retro-injection fibres. In this image, the PSF was previously centred on the science fibre using the method described above. In theory, the diagonal intersection (I ) of the four spots, retrieved by a 2D Gaussian fit, should determine the position of the science fibre on the tracking camera with respect to the retro-injection fibres. However, the mirror positioned behind the beam splitter is slightly skewed with respect to the optical axis and introduces an offset between the tracking branch and the retro-injected beam. Although the PSF is centred on the S fibre in Fig. 3.35, this is why its image on the tracking camera shows a significant offset with respect to I . The I-S offset is accurately measured during a dedicated calibration procedure and used for the second strategy. For the third strategy, the calibration follows the same steps, but measures the I -C offset.

Distance C-S

Offset between the retro-injection and tracking branches

ZELDA calibration

The overall optical quality of the bench would normally allow the centring strategies to be investigated without requiring a dedicated optimisation of the wavefront. However, the standard operations of the MITHiC testbed include a calibration of the aberrations of the bench using the ZELDA wavefront sensor (Pourcelot et al., 2021). I maintain this calibration at the beginning of each test as a sanity check and to benefit from the best possible PSF quality. A wavefront quality better than 20 nm rms is typically obtained. In the paper of (Pourcelot et al., 2021), the wavefront quality was better than 20 nm rms. In our case, the decrease in the wavefront quality is mainly due to imperfect alignment, especially of the SLM.

Performance study on MITHiC

Data acquisition

In this section, I test the centring strategies and quantify their respective accuracy. I recall that the goal, in the context of HiRISE, is to place the planet's PSF as close as possible to the centre of the S fibre so as to maximise the injection efficiency and therefore the planetary flux that will be transmitted to a high-resolution spectrograph.

On MITHiC I do not have the capability to create a true off-axis point source that would simulate a planet. To create the planet's PSF, I introduce a sinusoidal modulation on the SLM that creates two symmetric satellite spots and take one of these spots as the planet's PSF. The spatial frequency and orientation of the sine wave enable choosing the angular separation and position angle of the planet. Contrary to an actual planet for which the astrometry will be known beforehand based on previous direct imaging measurements, in our tests I measure the relative star-planet astrometry on a tracking camera image just after the planet has been introduced with the SLM. The amplitude of the sine wave is set to 100 nm rms, which results in a star-planet contrast ratio of a factor of 3.48. The contrast is modest but does not impact the final performance results because on-sky the system is blind to the planet's signal during the centring procedure. However, having a modest contrast ratio in the laboratory is necessary to check the final accuracy.

At the end of each centring procedure (regardless of the strategy), a verification optimisation (VO) is performed to evaluate how close the planet's PSF is to the centre

Performance study on MITHiC

of the S fibre. The displacement in tip and tilt between the position before the VO and after the VO, ϵ, provides a direct measurement of the distance to the centre. This ϵ is the error that defines the success or failure status of the performance test by comparing it to the specification accuracy of 0.1 λ/D. However, the VO is performed only in the laboratory and cannot be used on-sky to test if the planet is accurately injected into the science fibre. The science fibre will be connected to the CRIRES+ spectrograph and in any case the planet's signal will be several orders of magnitude fainter than that of the star.

For the performance study, I performed five series of 20 centring tests for planets introduced at 12 different position angles around the star. The star-planet angular separation was set to 10 λ/D for all tests, which corresponds to the average separation where known companions have recently been imaged with HCI. I had to take into consideration the drift of the PSF and its impact on the temporal stability of the calibration grid. This is why between each series I recompute the calibration grid used as input to the interpolation function. For each position angle, all the ϵ values are combined to compute an overall success rate when compared to centring accuracy specifications of 0.1, 0.2, and 0.3 λ/D. This repeatability test is decisive to achieve the performance study since it highlights the accuracy of each strategy. for the first, second, and third strategies are plotted in the upper, middle, and lower panels, respectively. The grey area represents the region where an emphasised trend is found. The black dashed lines at 90˚and 210˚represent the angles for which additional tests are performed and demonstrated in Fig. 3.39.

Our results for a planet located at different position angles around the star and with an angular separation of 10 λ/D are summarised in Fig. 3.36. The figure shows the success rate of each strategy for three specification accuracies of 0.1, 0.2, and 0.3 λ/D. I note a correlated trend between all strategies, particularly emphasised in the plot's 40-150˚region (Fig. 3.36, grey region). In this region all the strategies show a clear decrease in the success rate. This region roughly corresponds to the range of angles where a significant number of outliers have been identified in the calibration of the 3.4. Performance study on MITHiC interpolation function This is very likely correlated to the poor results now obtained in this region. Since this is an issue related to our specific setup, I do not consider the results in the 40-150˚range as representative of the final expected performance.

For the first strategy (Fig. 3.36, top panel), I never reach a success rate of 1.0 for a specification accuracy of 0.1 λ/D or 0.2 λ/D for all position angles, while a success rate of 1.0 is reached for all position angles when considering a specification accuracy of 0.3 λ/D. For a specification of 0.1 λ/D the success rate goes as low as 0.2, but is on average around 0.7. For a specification of 0.2 λ/D the success rate is significantly improved, with a value of 1.0 for most position angles and a drop at 0.8 for only a single point in our measurements.

For the second strategy (Fig. 3.36, middle panel), the success rate for a specification of 0.1 λ/D never falls below 0.3, but is on average slightly lower than for the first strategy (∼0.6). The success rates for specification accuracies of 0.2 and 0.3 λ/D are above 0.95 for all position angles.

Finally, the results of the third strategy (Fig. 3.36, bottom panel) show a more or less equal performance as the first strategy for a specification of 0.1 λ/D, but the results for a specification of 0.2 λ/D appear worse than for the other two strategies. For a specification of 0.1 λ/D, the average success rate is around 0.5, with less extreme variations inside and outside of the grey area. However, the success rate values are clearly lower in the grey area for this third strategy. Since the third strategy is a combination of the first and second strategies, the fact that I do not find a significant increase of the success rate for the 0.1 λ/D specification is not surprising.

Performance study on MITHiC

For the first strategy (Fig. 3.37, top panel) the angle 90˚shows the lowest success rate since it drops drastically as a function of the angular separation. It reaches 0.0 at worst with the specification of 0.1 λ/D and 0.2 λ/D, and it drops below 0.4 for the 0.3 λ/D specifications for planets at 20 λ/D. In contrast, for the two other position angles, the success rate is higher than 0.4 at all separations for the 0.1 λ/D specification, and better than 0.95 at all angles for 0.2 λ/D and 0.3 λ/D.

The second strategy (Fig. 3.37, middle panel) shows a success rate higher than 0.9 with an accuracy of 0.2 λ/D and 0.3 λ/D at all position angles and all angular separations. For a specification of 0.1 λ/D the success rate is on average below 0.8 and shows a decrease with angular separation. There is no apparent strong correlation with the position angle for the 0.1 λ/D specification.

For the third strategy (Fig. 3.37, bottom panel), the results are consistent with the ones previously seen in Fig. 3.36: the success rates for the different specifications at position angles of 90˚and 210˚are worse than for the first or second strategy, and at 330˚they are similar. The drop in performance for the three specifications at a position angle of 90˚is even sharper than for the first strategy, confirming that whatever limits the performance of the first strategy has an even stronger impact in the case of the third strategy. The results above demonstrate that reaching a specification accuracy of 0.1 λ/D is extremely challenging, whatever the centring strategy. In the case of the first and third strategies I hypothesise that the loss of accuracy in the centring of the planet likely occurs at the level of the switch between the C fibre and the S fibre, although the C -S distance is accurately pre-calibrated using the tip-tilt mirror to inject the light, alternating between the two fibres.

Understanding the limitations

To validate this assumption, I conduct a series of additional tests. In the first I follow the process of the first centring strategy with the goal of simply centring the stellar PSF on the S fibre. The results for 100 independent tests are presented in Fig. 3.38 and show a success rate of 0.94 for a 0.1 λ/D specification and 1.0 for a specification of 0.2 λ/D on the S fibre. I see that on the science fibre most points are well centred, although there is a visible scatter. Nonetheless, the success rate is very high and the test demonstrates that I are able to accurately place the stellar PSF on the science fibre.

The second test is similar, but this time it is performed on planets located at a sepa-3.4. Performance study on MITHiC ration of 10 λ/D and position angles of 90˚and 210˚. The results for 100 independent tests are shown in Fig. 3.39. At both position angles the centring is both relatively precise and accurate on the centring fibre, but the accuracy is lost when switching on the science fibre, especially for the 90˚position angle. At this position angle, the success rate is almost zero with the 0.1 λ/D specification and >0.9 with the 0.2 λ/D specification. The PSF's jitter uncertainty appears compatible with the scatter of the points for the 100 tests; however, it cannot explain the loss of accuracy so there must be another limitation in the system.

The interpolation function, which is used in all three strategies to place the stellar PSF at any position in the FoV, is potentially the limiting factor. I show in the previous section that a significant part of the tip-tilt space close to the centring fibre C in the range of position angles 45-110˚shows a reduced accuracy that is likely due to optical aberrations on the testbed. Interestingly, this range closely corresponds to the range of position angles in Fig. 3.36 where the success rates significantly decrease. Figure 3.33 also shows that the accuracy is worse when going away from the C fibre's position (i.e. for planets injected at larger angular separations). This is highly consistent with the drop in performance observed with angular separation in Fig. 3.37. I conclude that for planets in the 45-110˚range of position angles, the centring on the C fibre is biased because of the limited accuracy of the interpolation function and the error gets amplified when switching to the S fibre.

For the second strategy, the C -S offset is not involved since I use the I -S distance to place the planet's PSF into the science fibre. However, the low success rate as a function of the angle positions for a specification accuracy of 0.1 λ/D could be explained by the defocus of the four retro-injected spots imaged on the camera. It impacts the accuracy of the 2D Gaussian fit and consequently the accuracy of the I position determined on the camera. The loss of accuracy with angular separation is actually less pronounced than for the other two strategies, so it could be that several error factors add up and limit our accuracy to only 0.2 λ/D.

Discussion and conclusion

HiRISE proposes to implement a coupling between SPHERE and CRIRES+ at the VLT. One of the main constraints in the project is the ability to inject a known planet's PSF on the science fibre to transmit it to the spectrograph with the highest possible throughput. Previous studies for HiRISE have determined that a specification of 0.1 λ/D would be the best choice to maximise the transmission (Otten et al., 2021).

Performance study on MITHiC

To study the best centring approach, I used the MITHiC testbed at LAM, which has been upgraded to closely emulate the setup used in HiRISE. The FIM part is divided into three branches: the science branch that images the focal plane on the tracking camera, the injection branch that injects the light into a small bundle of fibres using a collimator, and the retro-injecting branch following the reverse injection branch and images feedback fibres on the tracking camera. With this setup, three strategies were implemented and tested on MITHiC to assess the feasibility of reaching a specification of 0.1 λ/D.

I conducted a performance study to verify the planet's PSF centring on the science fibre S for several angular separations and for several position angles around the star. Regardless of the strategy, I conclude that reaching an accuracy of 0.1 λ/D is extremely challenging. It requires a high level of accuracy at every calibration step, which is difficult to reach, especially in a non-optimised system built from off-theshelf components. In our case the final performance over a range of planet position angles (or conversely a range of tip-tilt positions) can be explained by a lower accuracy in the calibrations used to performed the first and third centring strategies. Some aspects related to performance can be explained by limitations in the system, such as the PSF jitter and the accuracy of the interpolation function. The interpolation function is used in all three strategies to place the stellar PSF at any position in the FoV. Even though most of the interpolation function's uncertainty distribution is within the accuracy specification of ±0.1 λ/D, the presence of outliers negatively impacts the interpolation function in certain areas. These outliers originate from hardware limitations inherent to the MITHiC testbed, which hopefully will not be present for HiRISE.

The FIM implemented in SPHERE will benefit from the complete instrument's infrastructure (stability, high-quality optics, ExAO, coronagraph). As in the MITHiC testbed implementation, I will have an optimised system with a dedicated C fibre connected to a power meter in HiRISE, which will allow the stellar PSF injection to be verified during the centring procedure. However, a major difference between the laboratory environment and the final implementation is that the S fibre will be connected to the CRIRES+ spectrograph. This will prevent the output flux from being measured directly, which will affect the centring of the stellar or planetary PSF on the science fibre.

From the operational point of view there are important differences between the three centring strategies. The first strategy mainly relies on an accurate determination of the C -S distance, which will have been calibrated in the laboratory during the assembly integration test phase (AIT). The main advantage of this strategy is that no flux measurement is theoretically necessary at the output of the bundle on a daily basis.

Performance study on MITHiC

On the other hand, I see on MITHiC that issues related to the differential distortion between the injection and science branches, or to the accurate calibration of the interpolation matrix, can significantly impact the accuracy when injecting an off-axis point into the fibre instead of the star. At this stage it is still uncertain if the same problems will arise on HiRISE, where I have an optimised system. Fortunately, SPHERE includes a distortion calibration grid (Wildi et al., 2010) that could be extremely useful to fully characterise the differential distortion in the final system.

The second strategy is inspired by the first calibration step used on KPIC phase I (J.-R. Delorme et al., 2021), so it has the advantage of already being demonstrated on-sky. They report that they are able to place the planet's PSF on the science fibre with a precision of less than a 0.2 λ/D (<10 mas) in K band, which is similar to the values that I obtained on MITHiC. For HiRISE, the retro-injection takes into account the differential distortion between the two branches. On the other hand, it requires calibrating the I position when the star has been perfectly centred on the science fibre. This calibration could be completed in the laboratory during the AIT. Even so, the temporal stability of the opto-mechanical elements between the retro-injection and the science branches are uncertain, so there is a risk that the calibration needs to be redone regularly. Once the bundle is installed at the telescope, it will not be possible to disconnect it easily to perform any calibration directly at the output of the science fibre. The recalibration of the exact position of the S fibre with respect to I will therefore require using data directly acquired with the spectrograph, which may be less straightforward than in the laboratory where a simple photometer can be used. This is nonetheless a possibility that will be carefully considered during commissioning.

The third strategy will hopefully combine the advantages of the first and the second strategies. It includes by design the compensation of the differential distortion using the retro injection and the C fibre, and I will have a direct measurement of the flux injected into the C fibre. On the other hand, the switch from the C to the S fibres for an off-axis object seems to be the limiting point in the first strategy. In the light of the performance study on MITHiC and considering the operational point of view, the first strategy is considered for HiRISE. However, it will be necessary to wait for the AIT to verify the strategy feasibility in the case of HiRISE.

Lessons learned for HiRISE from the centring strategies developed on MITHiC

The aim of the research work on MITHiC was to develop, implement and test accurate centring strategies. To establish these strategies, I integrated a fibre injection module on MITHiC to reproduce the final setup on sky. Then, I characterised the bench in its environment, according to temperature and humidity. I paid particular attention to the identification of the limiting terms for the centring strategies and their estimation. Once the performance study was completed, the goal was to analyse the differences between the work achieved on MITHiC and to extrapolate to the challenges I will meet on sky with HiRISE.

The error budgets for centring a PSF into a SMF are shown in Tab. 3.2 and are divided into two parts: MITHiC and HiRISE, the latter including SPHERE and FIM. The error budget for MITHiC has been estimated following the results described in Sect. 3.1.3. Some values, described below, have not been measured but estimated by making hypotheses. In the calibration section, the jitter and drift were set to 0.04 and 0.02 λ/D, respectively.

The values for the error of the centring strategies in particular are detailed in Tab. 3.3. In this sub-budget, the value of the distortion has been estimated from a distortion map made during preliminary tests on MITHiC. For the calibration accuracy, I took the average value (excluding outliers) from the residual of the interpolation function (Fig. 3.33). The repeatability of the centring strategies was found to be high under the conditions where the bench remains baffled.

For the high-order values, the static residuals were measured by the WFS and estimated at 20 nm RMS in the worst case. To obtain the λ/D equivalence, I divided this value by the wavelength used on MITHiC. The quasi-static residuals were not measured during this thesis but I assumed the same residual values like on SPHERE. The tests performed on MITHiC did not include the use of the phase screen mask to simulate atmospheric turbulence.

The estimated error budget for HiRISE includes the PSF and jitter values, for which I referred to the data established in (Beuzit et al., 2019). In the literature, the jitter is estimated at 2.5 mas, and to obtain the correspondence in λ/D, I divided by 40 (on the VLT, one element of resolution corresponds to 40 mas). For the drift of the PSF, I assumed a perfect DTTS loop and thus estimated it as zero.

Lessons learned for HiRISE from the centring strategies developed on MITHiC

As with MITHiC, the error budget for centring a PSF in a, SMF is detailed in Tab. 3.3. Regarding the distortion on the IFS arm of SPHERE, I note that it is small but existing in the form of anamorphism. To estimate its values, I assumed that it is 1/20 of those estimated for IRDIS [START_REF] Maire | Lessons learned from SPHERE for the astrometric strategy of the next generation of exoplanet imaging instruments[END_REF]. For the accuracy of the calibration, I assumed that this value would be identical on the sky. For repeatability, I assumed that SPHERE is less stable than MITHiC by a factor of 5.

For the high-order values, I took the values found in the literature (Beuzit et al. (2019), Jean-François Sauvage (private communication)). I summed the error terms quadratically and added a margin of 20% for the uncertainty on the estimations. I notice that there is a significant gain on HiRISE of a factor of 2 compared to MITHiC. However, although these are encouraging results for HiRISE, it is necessary to be conservative and wait for AIT tests and the first tests on SPHERE, and estimate their errors for the centring strategy.

Assembly, integration and testing process of the HiRISE instrument

In this section, I describe the assembly, integration and tests (AIT) phase of the HiRISE instrument (started in the summer of 2022). The AIT of Hirise will first take place at LAM in an ISO8 room, with the support of the mechanical workshop to perform a blank assembling of the FIM and the FEM. The second location is at the UT3/VLT, where the AITV will take place in the integrating hall and at the telescope.

The AIT at LAM will be divided into several stages and will consist to implement, test and validate the different sub-systems that comprise HiRISE. A block diagram, describes in Fig. 4.1 the main stages of the AIT at LAM. The implementation of the SPHERE simulator, the FIM and FEM as well as their assembly and alignment have been carried out independently. Once each of these sub-systems has been validated, they come to merge to form HiRISE. We note that for the first part of the AIT, the FB cannot be tested as it has not yet been received. In this chapter, I describe the different stages of the mechanical assemblies, the tests carried out and those to come at the LAM and then during the AIT at the VLT. Then, I will analyse the risks and challenges within the AIT of HiRISE.

HiRISE AIT

aspect, the radius of curvature, and the thickness at the centre of the optics. This quality analysis demonstrated that the optics were at the required specification. The gluing of the optics (made by Michel Marcos) in their Polaris mount from Thorlabs was achieved by putting 3 points of Structural Epoxy Adhesive EC-9323-2 B/A glue at 120 degrees from each other.

The pre-assembly was done in the mechanical workshop in order to anticipate any problem with the assembly in the clean room. The reworking of some mechanical parts (lapping, rectifications) was necessary to correct small design and manufacturing errors. In order to practice the optics mounting/dismounting, we had 3D lens replicas of the real lenses made by Phillipe Ballard. A large part of the pre-assembly consisted in putting the helicoils on the mechanical plates of the FIM and FEM, which allow the reinforcement and repair of thread holes. Left: the FIM as it will be inserted in SPHERE. The cover (on the table) will be used to baffle the core optics bench. Middle: we can see the core optics bench, the fibre mount and the helicoils implemented in their holes. Right: we see the position of the pick-off mirror and the bottom part of the FIM.

A home build mechanical system has been implemented for the pre-alignment of the optical cube (see next section), which is the most sensitive part to align, as we need to align the doublet with an accuracy better than 5 µm. As part of the project quality approach, the FIM and FEM elements were dismantled, and cleaned in two 4.1. HiRISE AIT stages using an acetone and alcohol bath, before being sealed and taken to the clean room to be integrated.

The FEM, which is more compact than the FIM, should not be as challenging as the FIM regarding its assembly and alignment. However, it will require a careful assembly procedure, as the lenses are small and difficult to handle. The most challenging part of the integration will be to pile up the lenses, and spacer rings in the mount (see Appendix C) without skewing them on the FEM ferrule mount. One foreseen solution consists of using a screw, which has the appropriate height and flat end area. By placing the optics on top of the end of the screw and by gently lifting the mount off the table, it is possible to insert the lenses without getting them stuck in the threads of the mount. This test was carried out using the 3D printed lenses but this method will need to be adapted and improved so as not to damage the real optics.

Integration and alignment of the FIM SPHERE Simulator

The alignment of the system will be based on a simplified SPHERE simulator, represented in Fig. 4.3 that will reproduce the main characteristics of the SPHERE IFS beam using off-the-shelf components (Thorlabs S4FC1550 source at 1.55 um coupled with SMF (N A =0.14), lenses, and a pupil stop). The assembly and the alignment of the FIM were carried out in LAM clean room by the mechanical engineer (José Garcia), the research engineer (Dr Maxime Lopez) and the PI (Dr Arthur Vigan).

The elements of the SPHERE simulator have been positioned in the rail at their near nominal position, defined by the Zemax optical design and using the Faro's arm. The first and second lenses mounted in the Thorlabs mount create a converging beam where the 5 mm diaphragm is placed. Following the diaphragm, the third lens is positioned to re-collimate the beam and image the exit pupil. The pupil diameter and the axis height have been verified to validate the alignment of the SPHERE simulator. They have been respectively measured at 10.087 mm for the pupil size and 250 mm for the height. The final F/39 will also be checked during the alignment procedure by placing a camera in the pupil plane.

The SPHERE simulator is used to align the bench and verify the image and wavefront quality. However, the simulator is highly chromatic, which means that the system is aligned with a monochromatic source at 1.55 µm. The alignment will be simply checked at other wavelengths if time permits. This implies that the centring strategies 4.1. HiRISE AIT may not be fully testable during the AIT phase. To test the centring strategies (e.g. the first strategy), at least two fibres are required. While waiting for the FB to arrive, a SMF connected to a power meter can be used to perform an injection map and an optimisation verification on the fibre.

Optical cube

The optical cube is one of the trickiest elements of the FIM to align so it has been decided to proceed with its assembly and alignment independently of the FIM bench. The details of the optical cube assembly procedure will not be detailed in this manuscript. To illustrate the elements that compose the optical cube, pictures are shown in Fig. 4.4. The optical cube is composed of two lenses, one of which is an air-gap doublet (L2) and the other is a cemented lens (L1) and dichroic filter lens manufactured by the Fresnel Institute. The alignment of the optical cube depends on the alignment sensitivity of three crucial elements used to send the beam into the fibres. T One requirement for the cube alignment is to centre L2 with regard to L1 at better than 5 µm. Any misalignment of the injection doublet will introduce coma, which will decrease the injection efficiency of the planetary PSF in the science fibre.

Core Optics Bench

Once the optical cube had been assembled, the next step consists of mounting the optical cube on the core optics bench (COB), as illustrated in Fig. 4.6. To keep it in a vertical configuration to perform the alignment of the entire COB (optic cube included), a home-built mount has been implemented to tie them. To verify the optical quality, a Phasics WFS1 (infrared WFS, which allows direct measurement of wavefront quality) has been placed in a post-focus configuration, at the level of the divergent beam, so that the beam has the right size. The value of the Zernike coefficients for the measurement is represented in Fig. 4.7, where the main Zemax model aberrations of the optical system and the one reached after aligning the COB with respect to the telescope simulator (TS) are displayed. The experimental results are in accordance with the ones provided by the model 'as built'. The remaining aberrations in the system at LAM are mostly driven by astigmatism (0 and 45deg) and spherical aberrations, which are the ones expected for the FIM at the VLT. However, we notice that we have more astigmatism than expected and a future refinement of the COB alignment is foreseen in the near future.

It is important to point out the dimensions and localisation of the optical cube and the tip-tilt piezo. As you notice in Fig. 4.5, the two elements are extremely close to each other. Therefore, it will be important to have at least 100 µm margin between the edge of the tip-tilt mirror and optic cube. It will be necessary to test the tip-tilt in its full range to ensure that no collision with the backside of the optical cube occurs. This test also requires that the tip-tilt is fully functional. A s ti g . 0 °As ti g .

FIM assembly beyond this thesis

The final assembly of the FIM and the FEM and their respective alignment have not yet started but will be the subject of the next activities. I present here a brief description of the assembly plans and the main tests that will be carried out to validate the two sub-systems.

The FIM main bench, illustrated in Fig. 4.8 will be assembled in a horizontal configuration, where the tracking camera, the core optics bench, the lens blocks and the tip-tilt mirror will be implemented at their nominal positions thanks to the mechanical reference planes (pins) in the main bench structure and thanks to an alignment laser used to define the optical axis going through the centre of the optics. Then the CPI 4.1. HiRISE AIT interface plate will be placed with respect to the SPHERE simulator by using the Faro arm 2 . At this point, we will install the support structure on the CPI Interface plate, then the FIM main bench on the support structure and finally the pick-off mirror. A blank test will also be carried out to see if the optics move when switching from a horizontal to a vertical configuration.

HiRISE AIT

After the FIM will be placed vertically at the right position regarding the SPHERE simulator, the alignment of the FIM will be achieved by verifying the image quality on the tracking branch using the Phasics and the focal plane camera. The installation and alignment of the pupil imaging lens are also foreseen to verify if the Tip-Tilt mirror is in the pupil plane. To verify that the tip-tilt is conjugated with the entrance pupil, we could replicate the method I used on MiTHIC to place the Tip-Tilt in the pupil plane, i.e. using a microscope to see the dust of the mirror and verify that there are in the same plane than the pupil mask. However, this method is not plausible during the AIT, a proper procedure will be determined but a foreseen solution would be to use a pupil plane mask.

For the injection branch verification, the F-number will be measured with the tracking camera and the image quality (WFE) with the Phasics WFS. Injection maps would be performed using a power meter to optimise the bundle focus. The alignment of the retro-injection branch could be adjusted with the plane corrector so that the image of the feedback fibres is focused on the tracking camera. At the time of writing the thesis, the fibre bundle has not been delivered yet, thus, the first tests will be carried out using only a SMF.

Integration and alignment of the FEM

The pre-assembly of the FEM has been done recently (see Fig. 4.11) with some mechanical parts that have been corrected by José Garcia. The assembly of the FEM has just started, as shown in Fig. 4.12. Although no difficulties have been identified yet, in the initial assembly of the FEM, there is still a sensitive assembly aspect regarding the stacking of the optics in the ferrule mount. A robust solution will be determined in the following weeks. In order to test the FEM, a foreseen test consists of inserting a single fibre into the ferrule, as shown in Fig. 4.13. The possibility of inserting the fibre into the ferrule was made possible thanks to a 3D-printed mount (made by Philippe Balard) that will be interfaced with the SMF. It will allow the fibre to slide inside the FEM ferrule and be sufficiently stabilised to prevent any movements during the tests. As with the FIM, the FEM verification involves testing the image quality using a focal plane camera and the WFE using a Phasics.

HiRISE test phase at LAM

Additionally, to the tests mentioned above, several tests will be carried out to verify the centring strategies developed during my thesis. The first tests will not include the fibre bundle as it has not yet been delivered.

However, when it will be available, we will first verify the image of the fibres under the microscope, plug it into the FIM side and in order to test the FB integrity, we will perform injection maps in the centring fibre using a power meter, followed by an optimisation. Regarding the calibration, the C-S distance will also have to be performed as a function of time and temperature. Although the temperature of the clean room will not be similar to the one at the VLT, the verification of the C-S distance as a function of time is required to prevent any unexpected surprises at the VLT.

First tests using a monochromatic source and one SMF:

-Find the wavelength to obtain the flux in the injection branch and in the tracking branch. -Perform injection maps into the fibre using a power meter, followed by an optimisation. -Characterise the tip-tilt mirror and perform a calibration map to test the interpolation function.

Tests using a polychromatic source and one SMF:

HiRISE will be tested in NIR and might be also tested at several wavelengths. To fulfil the polychromatic tests, we will be using the NKT Photonics SuperK Compact Supercontinuum source connected to the NKT SELECT NIR Acousto-optical tunable filtre (AOTF) with one of the power meters used on MITHiC to monitor the flux in the setup. From the AOTF, the light is injected into a distribution fibre. This fibre can be connected with an FC/PC connector to the SPHERE simulator. The calibration of this laser source at different wavelengths would be the subject of the next AIT activities.

-Adapt the Telescope Simulator setup to be able to focus the beam for each required wavelength. -Perform injection maps into the fibre using a power meter, followed by an optimisation. -Characterise the tip-tilt mirror and perform a calibration map to test the interpolation function.

Tests using a monochromatic source and the entire Fibre Bundle:

-Check the fibre bundle terminations under a microscope to characterise the fibre geometry "as-built". -Perform injection maps into the fibres using a power meter, followed by an optimisation. -Perform a calibration map to test the interpolation function.

-Test of the C-S distance as a function of time and temperature. Although the temperature of the clean room will not be similar to the one at the VLT, the verification of the C-S distance as a function of time is required to prevent any unexpected surprises at the VLT. -Test the centring strategies and provide an estimation of their errors to compare them to the ones (asterisk) mentioned in the error budget in Chap. 3.

Commissioning plan for HiRISE

Regarding the commissioning of HiRISE, two types of verifications are foreseen. To verify the functional validation of the entire system including SPHERE and CRIRES+, we aim to perform daytime verifications. The on-sky verifications will be dedicated to the validation of HiRISE performance on real targets. In this section, I will provide a global overview of the tests that we will carry out at the VLT.

Daytime verifications FIM sub-system verification:

Daytime verifications are estimated to last at least 5 days, with margin included with the goal to ensure the preparation for night-time verification.

The first verification relies on the control system tests aiming to verify the network connections and the control interface. In order to achieve these tests, we will connect the HiRISE workstation and switch on and off all the elements. An important verification lies on the pick-off mirror since it is a crucial element of the FIM. The tests are divided between functional validation and calibration. It is necessary to verify if the IFS beam is properly sent to the FIM and calibrate the translation stage position of HiRISE. To perform this test, we will use SPHERE internal source and SAXO in a closed loop. The first step will be to acquire an image with the IFS, then insert the pick-off mirror in the IFS beam, acquire an image with HiRISE, and finally move out the pick-off mirror and acquire an image with the IFS.

To perform this test, we will use SPHERE internal point source, SAXO in a closed loop, and we will insert the pick-off inside the IFS beam. To verify that the tracking camera is able to image the SPHERE internal source, we will set the tip-tilt stage to its central range position, and acquire a PSF image with the tracking camera. Then, for a set of tip-tilt range positions, we will move the tip-tilt to the asked position and acquire a PSF image with the tracking camera. It will also enable to verify the available tip-tilt stage range for HiRISE.

The centring strategies developed on MITHiC might not be entirely tested during the AIT in Europe, however, during the daytime verification, we will verify that the feedback fibres are properly re-imaged on the tracking camera. The advantage of the 4.2. HiRISE AIT at the VLT SPHERE calibration source is that it is polychromatic, so we can test the complete strategies on the internal source. The test procedure will follow the one used during the tests on MITHiC (see centring strategy 2). All three strategies will be tested to verify their respective centring accuracies. To inject off-axis planets, we can introduce a waffle mode on the SPHERE HODM. The performance accuracy achieved during this test provides a baseline to compare the on-sky performance with the one performed on MITHiC. The tests of the centring strategies also include calibration of the distortion of the tracking camera through the interpolation function. Additionally, the orientation and plate scale will be determined to establish the correspondence between the milliradians of the tip-tilt mirror and the pixel grid of the tracking camera.

FEM sub-system verification:

The purpose of testing the FEM alignment with CRIRES+ resides on calibrating the translation stage position required for HiRISE. To achieve this test, we will use CRIRES+ in Slit Viewer (SV) mode. We will perform a MACAO calibration on CRIRES+, scan the position of the CSU until it matches the reference calibration position and redo the process with performing a MACAO calibration on the FEM science fibre.

In order to calibrate the derotator orientation for HiRISE, CRIRES+ must be in SV mode, MACAO in open-loop and we also need to inject light into the FEM calibration fibres. To achieve the orientation calibration, we have to turn the CRIRES+ derotator and for each position acquire an image with SV. In the end, we should record the position for which the calibration fibres are aligned with the science fibre.

The last test for the FEM will consist in verifying that the MACAO and SV control loops can be closed on the calibration fibres.

HiRISE AIT at the VLT

HiRISE system verification:

We aim to verify our ability to measure the flux from the fibres on the CRIRES+ detectors and to calibrate the fibre's position on the CRIRES+ detectors. In order to carry out these tests, we will use SPHERE internal point source and SAXO in closed-loop. We will operate in a HiRISE mode, i.e., the pick-off mirror will be inserted into the IFS beam. Regarding, CRIRES+, its calibration stage, as well as its derotator, will be set at the pre-calibrated HiRISE positions and the spectrograph will be set to operate in the H band. MACAO and the SV will be used in a closed loop on one calibration fibre. To perform the verification, we will centre SPHERE PSF on the science fibre using one strategy and acquire a short sequence of data on CRIRES+ science detectors and the analysis will be performed offline.

On-sky verifications FIM sub-system verification:

During the on-sky verifications, we aim to verify the full acquisition procedure with SPHERE and HiRISE by targeting, first, bright single star (H<4). As described in chapters 2 and 3, the target acquisition will be performed by SPHERE with SAXO in closed-loop and in a no coronagraph configuration, as for HiRISE, the pick-off mirror will be inserted in the IFS beam. The tests consist in acquiring an image on the tracking camera. We must also verify that the image contains no saturation by measuring the ADU levels. Another test is foreseen and aims to verify the image quality (computing the Strehl Ratio of an image acquired on the tracking camera).

Three additional tests will consist to verify the centring strategy accuracy described in Fig. 2.23.

HiRISE system verification:

It is essential to verify the acquisition of CRIRES+ data after SPHERE and HiRISE target acquisitions are performed by FIM. The objective is to acquire a long sequence of data on the CRIRES+ science detectors.

Stability tests should also be carried out, testing the stability of the fibres as a function of time and temperature. For this verification, we will use the centring fibre as it is connected to a power meter and we will test the repeatability of the centring strategies with (i) a bright star (H > 4) and (ii) a binary system.

Risk of laboratory and on-sky AIT activities

The potential challenges that we could face on the sky should be anticipated. In this section, I expressed several risks and the foreseen solution to overcome them. An example concerning the optimisation, which is performed in the centring strategies, and which will be carried out only on the centring fibre in the case of HiRISE. This optimisation follows an injection mapping step, but the concern is that the optimisation may not work due to the low flux injected into the fibre. Three solutions are foreseen:

-Perform an injection map with the centring fibre and instead of the optimisation verification, perform a Gaussian fit. -Retro-inject light through a calibration source into the centring fibre and reimage the fibre on the tracking camera, perform a Gaussian fit to find the best position of the tip-tilt to inject the star into the centring fibre and compare the retro-injected position with the value found with the combination of injection map and Gaussian fit. -Refrain from using the centring fibre and thus verify the star flux injection using a power meter, but use the second strategy instead with the four retro-injection fibres.

Another concern is that the FIM aberrations could have been underestimated during the AIT and could decrease the coupling efficiency between the planet's PSF and the SMF. Although we do not wish to use the SPHERE HODM, it would be possible to use it to compensate for the FIM aberrations. However, one would encounter difficulty in measuring these aberrations. A technique developed by the KPIC team Echeverri et al., 2022 consists in scanning the amplitude of some Zernike modes while recording the flux with the power meter. Then for each mode, plot the peak flux for each pair of injection maps as a function of the applied Zernike amplitude. A Gaussian fit is then applied to the data to find the optimum aberration amplitude to apply to the DM to maximise the coupling efficiency.

The verifications on one (or more) scientific targets to determine the full performance of the system will be performed. This will be the baseline for future observations with HiRISE.

Conclusion

The assembly, integration and testing of HiRISE are currently implemented at LAM. We aim to assemble all the sub-systems (FIM, FEM and FB (when it will be delivered)) in order to perform all the required functional tests on HiRISE before sending the instrument to the VLT. In the coming months, HiRISE will be tested on the sky and we will decide which centring strategy is best suited for verification, functional and calibration tests and also during observations.

Conclusions and perspectives

In the last decade, exoplanet science has experienced a revolution. The exoplanet boom is driven by technological development, which allows us not only to detect but also to retrieve their physical properties. Among all indirect and direct methods, direct imaging holds a particular advantage as this is the only method which spatially separates the planetary signal from the star. Direct spectroscopic characterisation is, therefore, possible and it allows us to measure the abundance of the molecules in their atmosphere, without the potential biases of transmission spectroscopy. These and other physical properties such as their mass, semi-major axis, and orbital characteristics like eccentricity, can inform the formation and evolution pathways of these bodies. High-contrast imaging (HCI) focuses on the direct detection of young (<M Jup ), giant (>1 M Jup ) exoplanets orbiting at relatively large orbital separation (>10 au) from their host star, which translates to less than 1 ′′ in angular separation. It is clear that the intrinsic faintness of the planet, the contrast level at a small angular separation and quasi-static speckles (or the atmospheric turbulence) limit the performance of HCI observations. On large, ground-based telescopes, the merging of HCI with high-dispersion spectroscopy (HDS), sometimes referred to as high-dispersion coronagraphy (HDC), is a groundbreaking technique for the direct characterisation of giant exoplanets. HDS in the near-infrared (NIR) for ground-based observations has already provided critical information such as the rotational velocity and the wind speed of some transiting exoplanets, and the RVs and spins of directly imaged exoplanets. It also allowed us to spectrally resolve molecular features of species in the atmosphere of exoplanets. HDS not only brings a significant gain in terms of accessible spectral features but also enables better separation of the stellar and planetary signals. Single-mode fibres (SMFs) are advantageous for feeding light into spectrographs due to their precision and stability properties. However, efficiently coupling a point-spread function (PSF) into a SMF is challenging, mainly due to their limitation to only accept a quasi-Gaussian fundamental mode.

At the Very Large Telescope (VLT), two flagship instruments for exoplanet science are currently installed on the Nasmyth platforms of the unit telescope 3 (UT3): the exoplanet imager SPHERE and the NIR high-resolution spectrograph CRIRES+. The

Conclusions and perspectives

HiRISE instrument project involves the implementation of fibre coupling between these two instruments to enable a new era of HDS. Its goal is to characterise known, directly imaged, young, giant exoplanets at spectral resolutions up to R = 100 000 in the H band. HiRISE is composed of three independent parts: (i) the fibre injection module (FIM) that will be implemented in the IFS arm of SPHERE, (ii) the fibre bundle (FB) that will link SPHERE and CRIRES+, and (iii) the fibre extraction module (FEM) that will be installed on the calibration stage of CRIRES+. One of the challenges of coupling SPHERE and CRIRES+ resides in successfully injecting the signal of a previously known exoplanet detected by SPHERE into an SMF. The FIM will play a critical role during observations since it will pick up the planet's PSF in SPHERE and inject it into an SMF located in the FB. To maximise the coupling efficiency, the planet's PSF must ideally be positioned with an accuracy better than 0.1 λ/D on the fibre (which corresponds to 4 mas in the H band for SPHERE) to minimise light losses (Otten et al., 2021).

The overall transmission of the planet's signal into the SMF connected to a spectrograph drives the signal-to-noise ratio of molecule detection and abundance measurements. To achieve molecular mapping, contrast is not as critical as for exoplanet detection since HDC relies on successfully injecting the signal of a previously known exoplanet detected by a direct imager into a SMF. Therefore, defining the best possible strategy to centre the planet's PSF on an SMF is essential. The core of my thesis focused on the experimental validation of exoplanet centring strategies for high-dispersion coronagraphy in the case of HiRISE, using a high-contrast imaging testbed that I upgraded by implementing a fibre injection module (FIM) to emulate HiRISE. My work involved establishing the contributors to the centring error in the case of MITHiC and HiRISE by quantifying some of the most important error terms. Moreover, I created the tools to develop and incorporate three centring strategies on MiTHIC, I carried out the performance study, and I compared the centring strategies to select the optimal one for HiRISE.

In Chapter 3, I describe the performance study conducted to verify the planet's PSF centring on the science fibre S for several angular separations and for several position angles around the star. I demonstrated one centring strategy that reaches the anticipated goal: for several planet position angles with a separation angle of 10 λ/D, it shows an average success rate of 0.7 for the specification accuracy of 0.1 λ/D, and 0.95 or higher for accuracies greater than 0.2 λ/D. However, regardless of the strategy, I concluded that reaching an accuracy of 0.1 λ/D is highly challenging since it requires a high level of accuracy at every calibration step, which is difficult to reach, especially on MiTHIC. Some aspects related to performance can be explained by limitations of the system, such as the PSF jitter and the accuracy of the interpolation function. However, in the framework of the work achieved in the laboratory, I estimated an error budget regarding the centring strategies in the case of MiTHIC and HiRISE based on the information available from SPHERE. At this stage, I concluded that it is still uncertain if the same limitations will arise on HiRISE, where we anticipate having an 5. Conclusions and perspectives optimised system.

In Chapter 4, I describe the Assembly Integration Test (AIT) phase of HiRISE in Europe, which started in the summer of 2022. The alignment of the system is based on a SPHERE simulator that reproduces the main characteristics of the SPHERE IFS beam using off-the-shelf components (LED source, lenses, and a pupil stop). This simulator is used to align the bench and verify the image and wavefront quality. However, the simulator will be highly chromatic, because the system will be aligned with a monochromatic source at 1.5 µm and only cross-checked at other wavelengths. This implies that the centring strategies may not be fully testable during the AIT phase. Contrary to the MITHiC setup, HiRISE uses a dichroic filter to transmit all the science photons in the H band, and it uses shorter wavelengths for the centring and calibrations. Some conclusions regarding the best centring strategy for HiRISE might come from the AIT phase in Europe, but the final decision will have to wait for the first on-sky tests.

HiRISE will demonstrate the capabilities of characterising the atmospheres of directly imaged young giant planets at high spectral resolution with CRIRES+. The preliminary results of the on-sky commissioning will be performed in the spring of 2023. Once the commissioning is complete, the first set of observations will be analysed to improve HiRISE for future improvements, in order to maximise the science throughput in the science fibre in the H band. In the close future, HiRISE would benefit to extend its band coverage to the L and K bands. Since the overlap target observations in the K, L and H bands will bring a unique opportunity to complete the planetary survey, this would allow us to cross-validate our knowledge on already observed, challenging exoplanets. It will be possible to extend the spectral coverage first to the K-band and to couple the FIM with a compact spectrograph (VIPA; [START_REF] Bourdarot | Nano-VIPA: a miniaturized high-resolution echelle spectrometer, for the monitoring of young stars from a 6u cubesat[END_REF][START_REF] Bourdarot | Experimental test of a 40 cm-long R=100 000 spectrometer for exoplanet characterisation[END_REF], which operates at a higher spectral resolution than CRIRES+ (R > 100 000). The K band contains many molecular signatures in the atmospheres of young, giant exoplanets such as CO, H 2 O, CH 4 , and CO 2 . These are necessary, for example, to constrain temperature profiles, which is the prime focus for the astrochemical study of atmospheres. However, this coupling of light implies a decrease in coupling efficiency, which is intrinsic to the properties of the specific fibres used in the K band (ZBLAN). So far, the coupling between the FIM and the very high spectral resolution spectrograph has only been considered theoretically. However, it would be possible to manufacture a shorter infrared fibre bundle to couple HiRISE/FIM with VIPA, which could be placed on the SPHERE Nasmyth platform. In this way, we would prevent any costly and technical challenges to its manufacturing.

On a larger time scale, HiRISE could be upgraded by implementing cutting-edge technologies to the FIM to increase the PSF coupling efficiency into the SMFs. Among these technologies, there is Phase-Induced Amplitude Apodization (PIAA), successfully 5. Conclusions and perspectives used as a coronagraph and recently. In the context of HDC, it could be employed to modify the shape of a light beam to maximise the coupling efficiency into an SMF. A significant limitation of the PIAA technology is that the wavefront remapping depends on the localisation of the source with respect to the optical axis. When the PIAA is aligned with an off-axis object, like in the case of a planet, the wavefront becomes highly aberrated, and the coma aberration deteriorates the PSF. In the context of HiRISE and future instruments aiming to implement PIAA to enhance the coupling efficiency to SMFs and thus increase the end-to-end planetary signal transmission to high-resolution spectrographs, it is crucial to develop a proper method to combine the implementation of an off-axis PIAA and the best PSF shape to be coupled to SMFs. Other concerns are based on the PIAA lenses, which create aberrations and need compensation with a deformable mirror. The PIAA requires specific Non-Common Path Aberration (NCPA) compensation, which is challenging to calibrate. In order to improve the coupling efficiency into SMFs, it would be compelling to investigate couplings between photonics integrated circuits (PICs) and an IFS. The advantage of the PIC is that it would act as a second-stage wavefront sensor after SAXO, which will measure and correct the entrance wavefront. At the end of the process, it allows to obtain a Gaussian output beam, which in the HDC field would enable to efficiently feed an IFS with an SMF. There are other technologies in the R&D phase that aim to increase the capabilities of HDC (e.g., micro-mirror arrays as an adaptive apodizer for HCI (Alexis Carlotti)).

As mentioned above, several directions exist to push the understanding of HDC forward. They constitute a baseline to increase the coupling efficiency of a PSF into SMFs to maximise the science throughput. In the framework of my thesis, I developed experimental solutions to optimise the coupling efficiency between the PSF and SMFs, which feed a high spectral resolution spectrograph. Due to the strong dependence of the performance on the global transmission of the system (Otten et al., 2021), the centring procedures are crucial for HiRISE. In this particular case, we work with existing systems, which introduce strong constraints on the specifications in order to maximise the transmitted flux. These constraints will undoubtedly be relaxed for future instruments optimised for HDC.

As an example, The Planetary Camera and Spectrograph (PCS) (Kasper et al., 2021) will aim to detect and characterise nearby exoplanets with sizes ranging from sub-Neptunes to Earth size. It will potentially observe habitable planets around nearby stars, which would provide information regarding molecular fingerprints in the atmosphere. One of the most prominent biosignatures in the NIR is the O 2 A-band around 765 nm (Kasper et al., 2021). However, this band consists of several narrow lines, and a high spectral resolution would help to resolve the lines of the directly imaged exoearths orbiting around M dwarfs. To achieve its goals, PCS must provide a contrast of 10 -8 at 15 mas and 10 -9 at 100 mas, as well as high spectral capabilities in order to resolve molecular features. Thus, the best approach would be to use HDC and 5. Conclusions and perspectives push the limit of both HCI and HDS. PCS will include a fibre injection module that will feed two (High: R, I bands, and Low-med: J, H bands) spectrographs. One asset of the ELT is the telescope diameter that will enable the collection of a consequent amount of photons to inject into the fibres. The research achieved during this thesis and the results of HiRISE might guide the ESO decision while building the FIM/PCS (using a similar strategy, choice of the position of the fibres in the bundle, the limitation to be aware of, ...).

In the context of HDC, fibre bundles are used to connect imagers and exoplanet spectrographs on ground-based telescopes. However, an extended cable length is needed to achieve this, the routing of the bundle is sometimes complex, and it is, therefore, necessary to split the length of the bundle into different sections. These different sections are then joined together by connectors. In addition to the transmission loss, which is intrinsic to the connectors, it is essential from an operational point of view to be able to perfectly repeat a connection/disconnection between two connectors. During operations, the connection/disconnection directly impacts the instrument's successful functioning. On the one hand, the repeatability of this procedure must be as reliable as possible. On the other hand, the process must be as fast as possible since one single dust particle on the core of a fibre can cause a loss of flux, resulting in a degradation of transmission performance. One possibility would be to involve a robotic connection/disconnection process to ensure that this crucial step is highly successful. Robotic switchers have not been investigated during my thesis but are already in the baseline for other future HDC projects such as the High-resolution Infrared Spectrograph for Exoplanet Characterization (HISPEC) [START_REF] Mawet | Fiber-fed high-resolution infrared spectroscopy at the diffraction limit with Keck-HISPEC and TMT-MODHIS: status update[END_REF] and Multi-Objective Diffraction-limited High-Resolution Infrared Spectrograph (MODHIS) [START_REF] Mawet | High-resolution infrared spectrograph for exoplanet characterization with the Keck and Thirty Meter Telescopes[END_REF]. The knowledge that the field will gain from future tests would allow us to increase the transmission in a SMF.

To maximise K band transmission, custom infrared fibres have to be used, typically with small lengths and a more detailed characterisation to understand any losses due to the increased length and any bending related to instrument operations. HISPEC will be located in the basement of Keck, which requires a fibre run of 60 meters. For MODHIS, it is even more problematic since the fibre run will be 120 meters. A trade-off analysis is foreseen to evaluate if this fibre length could be sustained in both projects. It would be necessary to establish a thorough characterisation of infrared fibres by studying the flux losses against the wavelength, and their sensitivities during any bending process. For this last point, laboratory development procedures to control the bending and characterise its impact on the performance would be important.

Implementing HDC on board a space observatory would have many advantages (no effect on the Earth's atmosphere, or stability). The onboard instruments will have to be fairly compact and therefore contain fewer optics, which would increase the 5. Conclusions and perspectives end-to-end transmission. The disadvantages are the smaller diameter size of the telescope compared to ground-based observatories, the angular separation between the host star and the exo-Earth (2.2 -7.3 λ/D in H band (Wang et al., 2017b)) and no possible operational intervention to improve the setup in case of low throughput. Going further than the H band with future space-based missions would require the use of a cryogenic telescope and instrument. Thus the need to study the behaviour of a FIM in extremely low temperatures in the laboratory is a necessity.

To my knowledge, only the PICSAT nanosatellite [START_REF] Nowak | Short life and abrupt death of PicSat, a small 3U Cube-Sat dreaming of exoplanet detection[END_REF] has embedded a single-mode fibre for high-precision photometry on bright stars such as β Pictoris. After four years of radio silence, the satellite is once again transmitting signal and telemetry in 2022, however, the absence of any science signal makes the understanding of how fibres work in space uncertain. In the future, space telescopes would have the capability to directly image and characterise rocky planets orbiting M dwarfs and have access to Earth-like planets in the habitable zone of sun-like stars. For a 12 m space-based telescope, (Wang et al., 2017b) had determined from simulations in the case of the space-based observations that an Earth-like planet can be detected at low to high spectral resolutions for a contrast of 2 x 10 -9 . These telescopes can operate at low resolution since they are not impacted by the Earth's atmosphere, however, to switch to higher-spectral resolution the detector noise (readout noise and dark current) and the speckle chromatic noise should be minimised.

Developing IFS instruments offering very high spectral resolution is challenging and costly, so it is likely that HDC will remain largely based on fibre-fed spectrographs in the foreseeable future. My study, therefore, prepares the ground for instruments like RISTRETTO on the VLT [START_REF] Lovis | [END_REF] and, in the long term, PCS on the ELT (Kasper et al., 2021), HISPEC on Keck [START_REF] Mawet | Fiber-fed high-resolution infrared spectroscopy at the diffraction limit with Keck-HISPEC and TMT-MODHIS: status update[END_REF], MODHIS on TMT [START_REF] Mawet | High-resolution infrared spectrograph for exoplanet characterization with the Keck and Thirty Meter Telescopes[END_REF] -or post-JWST flagship missions such as the Astro2020-recommended IROUV concept, recently renamed the "Habitable World Observatory".

Introduction

Over the past decades, numerous exoplanets have been detected beyond the Solar System by indirect or direct methods allowing us to target different populations and retrieving physical key properties (Mayor & Queloz 1995). One of the main advantages of directly imaging exoplanets is that it allows quantifying the chemical compositions and abundances of their atmospheres (Snellen et al. 2014;Brogi & Line 2019), and establishing their formation and evolution mechanisms (Crepp et al. 2012;Piso et al. 2016). High-contrast imaging (HCI) focuses on the direct detection of young (<300 Myr) giant (>1 M Jup ) exoplanets orbiting at relatively large orbital separation (>10 ua) from their host star. The high contrast (>10 mag) and small angular separation (<1 ) of these planets with respect to their host star are a severe limitation to their detection, but especially to their atmospheric characterisation.

High-contrast imaging combines extreme adaptive optics (ExAO, e.g., Fusco et al. 2006) to measure and compensate for the atmospheric distortion in ground-based observations, with coronagraphy to attenuate the on-axis starlight (Guyon et al. 2006;Mawet et al. 2012). However, the technique is mainly limited by quasi-static speckles in the focal plane (Soummer et al. 2007), which cover the planetary signal. To deal with the challenges of HCI, a new generation of instruments has been implemented on large ground-based telescopes in the last decade: VLT/SPHERE (Beuzit et al. 2019), Gemini/GPI (Macintosh et al. 2014), and Subaru/SCExAO [START_REF] Jovanovic | The subaru coronagraphic extreme adaptive optics system: enabling high-contrast imaging on solar-system scales[END_REF]. However, the low spectral resolutions of these instruments, typically R = 50 for the SPHERE IFS (Zurlo et al. 2014), are a major limitation for exoplanet characterisation.

Simultaneously to HCI, high-dispersion spectroscopy (HDS) has proven to be a powerful technique to characterise the atmosphere of exoplanets using infrared spectrographs such as Keck/NIRSPEC (McLean et al. 1998) or VLT/CRIRES (Kaeufl et al. 2004). HDS in the near-infrared (NIR) for ground-based observation has provided a great deal of essential information, such as the wind speed or the rotational velocity of some transiting exoplanets (Snellen et al. 2010). It has also been used to characterise exoplanets by spectrally resolving molecular features of species present in the atmosphere (Brogi et al. 2013;de Kok et al. 2013). The combination of high angular resolution using AO to first spatially separate the planet from the stellar signal and the implementation of medium-to high-resolution spectroscopy to spectrally filter the stellar light from the planet's light was first successfully demonstrated by using the VLT/CRIRES instrument with a resolution of R = 100 000 in the K band. Using the MACAO AO system (Arsenault et al. 2003), CRIRES was used to detect the CO lines at 2.3 µm in β Pictoris b and to measure its orbital and rotational velocities (Snellen et al. 2014). However, these results were partly limited by the relatively poor high-contrast performance of the CRIRES system, which was not designed for this purpose.

The proper combination of HCI and HDS was first proposed by Riaud & Schneider (2007) to improve the sensitivity in contrast to exoplanets, and a more in-depth study was performed by Snellen et al. (2015) in the framework of ELT instrumentation. In theory, for ground-based observations HCI and HDS can respectively reach a planet-star contrast down to 10 -3 and 10 -4 , so combining the two to perform high-dispersion coronagraphy (HDC) could theoretically enable contrasts of 10 -7 or better to be reached (Snellen et al. 2015). More recently, the study by Wang et The three projects mentioned above consist in coupling existing high-contrast instruments with medium-or high-resolution spectrographs. They propose sampling the planetary signal with a single-mode fibre (SMF) and feeding it to a diffraction-limited spectrograph [START_REF] Coudé Du Foresto | Very High Angular Resolution Imaging[END_REF]Jovanovic et al. 2017). For precision and stability purposes, SMFs are optimal for feeding light into spectrographs (Crepp 2014;Jovanovic et al. 2016). They are used in the focal plane of telescopes for their spatial filtering effect (Ghasempour et al. 2012). However, efficiently coupling a point spread function (PSF) into a SMF is inherently challenging due to their intrinsic properties. A SMF is designated only to support a quasi-Gaussian fundamental mode (LP01). According to the field theory of guided waves, optimal coupling efficiency occurs when the overlap integral between the electric field of the input beam and the LP01 mode is maximised [START_REF] Jeunhomme | Single-mode Fiber Optics. Principles and Applications Jovanovic[END_REF]Neumann 1988;Barrell & Pask 1979). It implies that the complex amplitude of the transverse component of the electric field at the telescope focal plane must match the LP01 mode of the SMF (Coudé du Foresto et al. 1993). In the ideal case of an unobstructed pupil, an Airy pattern is formed in the focal plane and is composed of a constant phase core surrounded by successive dark and bright concentric rings where the phase flips by π. Coupling an Airy pattern into the LP01 mode is bounded by the opposite phase of the first ring, which leads to destructive interference and reduces the coupling efficiency. The maximum coupling efficiency of an Airy pattern into a SMF occurs when only the core matches the quasi-Gaussian mode. An unobstructed circular aperture's theoretical maximum coupling efficiency into a SMF is ∼81% (Shaklan & Roddier 1988).

However, most ground-based telescopes have obstructed circular apertures and spiders. The presence of a central obstruction and spiders in the pupil have a significant impact on the coupling efficiency. Due to their respective pupils, the Gemini telescopes offers a maximum coupling efficiency of ∼70%, the Keck and the Subaru telescopes ∼60% (Jovanovic et al. 2017), and the VLT ∼73% (Otten et al. 2021). Ground-based observations are also limited by optical aberrations, which are classified into two categories: quasi-static aberrations caused by optical defects and misalignments (e.g. N'Diaye et al. 2013) and atmospheric aberrations caused by the turbulent atmosphere. Both types of aberrations disturb the wavefront and require the use of an AO system to re-establish a wavefront that is as flat as possible, which will better couple into a SMF. An ExAO correction has proven to increase the Strehl ratio, minimise the aberrations, and therefore bring the injection efficiency closer to its theoretical maximum (Jovanovic et al. 2017).

Finally, in order to maximise the coupling efficiency into a SMF, the telescope PSF must be centred on the fibre. Any offset affects the coupling. Otten et al. (2021) demonstrate the need for HiRISE to achieve a coupling efficiency >95% (according to Sect. 3.3, paragraph 2 of the present paper) of the maximum possible to spectrally characterise exoplanets. To reach this goal, the PSF must be centred with the core of the fibre within 0.1 λ/D. We can tolerate a coupling efficiency as low as 59% of the maximum, which corresponds to a misalignment between the PSF and the fibre of 0.2 λ/D. In this scenario, we will not be able to characterise our most challenging targets and will need more telescope time to spectrally characterise the others.

At the VLT, two flagship instruments are installed on the Nasmyth platforms of the unit telescope 3 (UT3): the exoplanet imager SPHERE on one side, and the NIR high-resolution spectrograph CRIRES+ (Dorn et al. 2016) on the opposite side. The High-resolution imaging and spectroscopy of exoplanets (HiRISE) project involves implementing a fibre coupling between these two instruments to enable the characterisation of known directly imaged young giant exoplanets at spectral resolutions up to R = 100 000 in the H band. HiRISE is composed of three independent parts: (i) the fibre injection module (FIM) that will be implemented in the IFS arm of SPHERE, (ii) the fibre bundle (FB) that will link SPHERE and CRIRES+, and (iii) the fibre extraction module (FEM) that will be installed on the calibration stage of CRIRES+. HiRISE will benefit from the SPHERE infrastructure for the HCI and from CRIRES+ in NIR for the HDS techniques.

One of the challenges of coupling SPHERE and CRIRES+ resides in successfully injecting the signal of a previously known exoplanet detected by SPHERE into a SMF. The FIM will play a critical role during observations since it will pick up the planet's PSF in SPHERE and inject it into a SMF located in the FB. To maximise the coupling efficiency, the planet's PSF must ideally be positioned with an accuracy better than 0.1 λ/D (which corresponds to 4 mas in the H band for SPHERE) to minimise the coupling efficiency losses (Otten et al. 2021). Therefore, it is essential to define the best possible strategy to centre the planet's PSF on a SMF.

In this paper, three different strategies are investigated to fulfil the required centring specification for HiRISE. To explore these strategies we used an upgraded version of the Marseille Imaging Testbed for High-Contrast (MITHiC) (Pourcelot et al. 2021). In Sect. 2 we present a brief overview of HiRISE implementation on the VLT and we describe the PSF centring strategy principles. In Sect. 3, we present the MITHiC testbed and detail the description of the FIM. We also explain the limitations of the setup and the specifications required for the centring strategies. In Sect. 4, we introduce the description of the centring strategy procedures in laboratory, and we discuss the performance results. Finally, in Sect. 5 we conclude and propose some perspectives. The FIM is implemented as a vertical bench immediately downstream the Lyot stop wheel in the IFS arm of SPHERE (Beuzit et al. 2019). It includes a pick-off mirror that can be inserted into the IFS beam to send the light towards the FIM instead of the IFS. The SPHERE pupil is reimaged onto a mirror mounted on a S335 piezo tip-tilt platform from Physik Instrumente. The beam is then recollimated using a custom achromatic doublet and goes through a dichroic filter that reflects the short wavelengths (0.95-1.3 µm; Y J bands) into the 'tracking branch' and transmits the longer ones (1.4-1.8 µm; H band) to the 'injection branch'.

Centring strategies for HDC

In the tracking branch, a focal plane image is formed at F/40 on a C-RED 2 camera from First Light Imaging [START_REF] Gibson | [END_REF]), and we refer to it as the tracking camera in this section. This image is sampled at 12.25 mas pix -1 , which corresponds to Nyquist-sampling at 0.95 µm. Although the images from the tracking camera are not expected to be used for any astrophysical interpretation, they will nonetheless be of sufficiently high quality to enable basic processing. In the injection branch, the beam is refocused with a very fast doublet at F/3.5, which has been designed to match the numerical aperture (NA = 0.16) of the science fibres used in the bundle. The optical system is designed to be telecentric in the injection branch to maximise the injection efficiency even when considering fibres located off-axis. Although the science fibre will be located on-axis to maximise the wavefront quality and therefore the injection efficiency (Jovanovic et al. 2017), three additional fibres will be located off-axis to sample the stellar light in the speckle field. In practice, the FB remains static after the alignment of the system, and the focal plane image is moved with respect to the science fibre using the tip-tilt mirror, so as to place the PSF of a known companion onto the fibre. The strategies to centre the PSF accurately on the science fibre are detailed in the following section.

In addition to the fibres dedicated to science, the bundle will also include 'feedback fibres', which are connected to a calibration source at ∼1.3 µm and used to retro-inject signal into the system. Because of the orientation of the dichroic filter, the retroinjected signal is reflected on the dichroic, then on a dedicated corner cube, and then transmitted through the dichroic into the tracking branch. The outputs of the feedback fibres are finally reimaged on the tracking camera superimposed on the focal plane coronagraphic image. The position of the feedback fibres with respect to the science fibre are calibrated, giving the possibility to use them for accurate centring on the science fibre. This solution was previously proposed to optimise the centring on the science fibre in a situation where the planet's signal remains undetectable in short exposures [START_REF] Mawet | [END_REF]). The wavelength of the feedback fibres was selected to be in the transition zone of the dichroic filter because the retro-injected beam has to go through that filter twice. At 1.3 µm, the transmission of the dichroic is ∼50%, which means that only 25% of the photons will ultimately reach the tracking camera.

PSF centring strategies on the science fibre

Immediately after the FIM receives the ExAO-corrected beam from SPHERE it becomes entirely independent from SPHERE and the planet acquisition relies only on the FIM. It consists in centring the planet's PSF on the science fibre with the required accuracy mentioned previously. Since the planet's PSF will not usually be visible on the tracking camera image because of the S/N, the planet acquisition will be performed blindly based on its known relative astrometry with respect to the star and on calibrations performed during the day. Three strategies are foreseen for centring the planet's PSF on the science fibre, and for each strategy, two configurations are possible depending on the presence (or lack) of a coronagraph. For the practical implementation of the centring strategies, a certain number of key calibrations are necessary and are detailed below.

Several aspects have driven the choice to only investigate these three centring strategies and select the best one to implement for HiRISE. First, they are relatively simple to implement and require only a limited amount of dedicated hardware (either fibres or dedicated sensors). They are then usable from the operational point of view at the telescope. One of the important aspects of HiRISE is that once the system is installed, it should be operable remotely like any VLT instrument. It will not be possible to change or plug any calibration hardware either during A171, page 3 of 14 Fig. 2. Centring strategy schemes. Each row represents a strategy. The blue frames represent the calibration procedure for each strategy, while the black frames are assigned to the centring procedure. The panels labelled 1-5 show the steps followed to place the planet's PSF into the science fibre.

the day or the night. And finally, at least one of them has already been demonstrated to work on-sky, which is an important aspect. The first strategy (Fig. 2, top row) relies only on a dedicated centring fibre located close to the science fibre. In the non-coronagraphic configuration the first step consists in placing the stellar PSF on top of the centring fibre to refine the position with an optimisation algorithm that maximises the coupling efficiency of the star into the centring fibre (Fig. 2, panel 2). Then, by using the offset pre-calibrated during the laboratory validation of the instrument (Fig. 2, panel 1), we place the star onto the science fibre (Fig. 2, panel 4). And finally, by using the interaction matrix and using the known right ascension and declination (RA and Dec) offsets, we apply an offset to the tip-tilt mirror to move the planet on the science fibre (Fig. 2, panel 5).

The second strategy (Fig. 2, middle row), also in the same non-coronagraphic configuration, uses the science fibre and four feedback fibres that retro-inject light into the system via the dichroic and the corner cube. The four fibres are re-imaged on the tracking camera on top of the stellar PSF. Their diagonal intersection (I) in theory provides the position of the science fibre with respect to the focal plane image. Consequently, the first step of the procedure consists in switching on the four feedback fibres to acquire an image with the tracking camera, find the centre of the feedback spots and then determine the position of the science fibre (Fig. 2, panel 2). However, an offset may occur between I and the position of the science fibre. It is due to an alignment mismatch between the science branch and the retro-injection branch, and would need to be calibrated beforehand during the laboratory validation of the instrument (Fig. 2, panel 1). Then we position the stellar PSF onto the science fibre by moving the tip-tilt mirror (Fig. 2, panel 4) and, as described for the first strategy, we apply an offset to move the planet into the science fibre (Fig. 2, panel 5).

The third strategy (Fig. 2, bottom row) combines the first and the second strategies using the four feedback fibres, the centring, and the science fibre. The first step consists in switching on the feedback fibres to find the centre of the four spots and the intersection I (Fig. 2, panel 2). We use the tip-tilt mirror to place the star on the centring fibre (Fig. 2, panel 3). By using the offset pre-calibrated during the laboratory validation of the instrument (Fig. 2, panel 1), we place the star onto the science fibre (Fig. 2, panel 4). Then we apply an offset to place the planet onto the science fibre (Fig. 2, panel 5).

The challenge to accurately inject the planet's PSF into the science fibre relies on the high calibration accuracy performed at each procedure step. In the first strategy the critical first step is to accurately inject the stellar PSF into the centring fibre, while for the second strategy the crucial first step consists of accurately placing the stellar PSF on the intersection I. All the following steps to inject the planet's PSF into the science fibre will be performed blindly, relying only on the high accuracy of the calibrations computed in the laboratory and the known astrometry of the planet. In HiRISE, the science fibre S will be connected to CRIRES+ preventing any verification of the planet's PSF injection in the science fibre during the acquisition.

In a coronagraphic configuration, the centring strategies are slightly different. Due to the presence of the occulting mask of the coronagraph, the star is not directly visible on the tracking camera. Therefore, to monitor the localisation of the star behind the mask, we use 'satellite spots' artificially created by the deformable mirror in the system. These spots are routinely used in VLT/SPHERE and provide an accuracy of A171, page 4 of 14 1.2 mas (0.03 λ/D) for the centring of coronagraphic images (Vigan et al. 2016;Zurlo et al. 2016). The satellite spots, which are replicas of the stellar PSF, are created at a known angular separation by applying two orthogonal sinusoidal modulations on the high-order deformable mirror (HODM). In a coronagraphic context, the centring strategies presented above are modified by the necessity of first accurately locating the stellar PSF using the satellite spots. This can be achieved by injecting each spot into the centring fibre. The diagonal intersection of these spots allows the star's PSF position to be retrieved. Then, we place the planet on top of the centring fibre by using the calibrated interaction matrix. Finally, we apply the pre-calibrated centring-science fibre (C-S) offset to place the planet into the science fibre.

In the present work, we only investigate the noncoronagraphic configuration for the three strategies. The baseline coronagraph in SPHERE is an apodised-pupil Lyot coronagraph, which is based on a pupil amplitude apodiser that causes a 50% photon loss. The simulations of Otten et al. (2021) have demonstrated that although the apodisation slightly improves the injection efficiency into the science fibre, the loss of photons that it induces completely outbalances this gain in the final S/N of the science signal. Moreover, to benefit from the full attenuation of the diffraction, SPHERE should be operated in the pupil-tracking mode (Beuzit et al. 2019). This enables using an optimised Lyot stop, which masks the diffraction of the telescope spider vanes, but it induces a rotation of the field of view (FoV) that would need to be compensated in the FIM. For these reasons, HiRISE will initially be operated in field-tracking without a coronagraph, so we focus on this scenario in the following sections. MITHiC is composed of a telescope simulator (TS), a wavefront sensor (WFS) to measure the static aberrations, and a classical Lyot coronagraph (CLC) (Lyot 1933), as shown in Fig. 3. The TS generates a PSF with a polarised monochromatic fibre-coupled super-luminescent diode at a wavelength of 670.7 nm. The spatial light modulator (SLM), which acts as a deformable mirror (DM) in the pupil plane (274 pixels across the pupil diameter), allows a phase correction to be applied in closed-loop to flatten the wavefront and the wavefront to be modulated for particular needs, such as creating the satellite spots or introducing known aberrations. The WFS on MITHiC is a Zernike wavefront sensor called ZELDA (Pourcelot et al. 2021;N'Diaye et al. 2013). Due to the aberrations in the MITHiC setup, if no corrections are applied on the SLM, the optical aberrations of the MITHIC bench are quantified to ∼33 nm root mean square (rms), and can be decreased to 20 nm rms or better with a correction based on a ZELDA measurement.

Fibre injection on the MITHiC testbed

To reproduce the setup that will be implemented in HiRISE, we modified MITHiC by adding an implementation of the FIM (Fig. 3). The first modification was to re-image the pupil of the bench on a mirror glued on a piezo tip-tilt mount (PI-S335) and located after the WFS stage. The mirror is oriented at 45°with respect to the optical axis to also fold the beam and make the whole setup more compact. Then, the beam is recollimated and split into two to implement the branches of the FIM. We use a 50/50 beam-splitter cube and not a dichroic because MITHiC is fully monochromatic. In the tracking branch, the stellar PSF is imaged using a doublet on a Coolsnap HQ2 CCD camera manufactured by Teledyne located in a focal plane with a 4.26 pixel (λ/D) -1 sampling. In the rest of the paper, the Coolsnap camera will be referred to as the tracking camera. In the injection branch, the beam is refocused using a Thorlabs F810SMA-635 collimator (output 1/e 2 beam diameter: 6.7 µm; wavelength: 635 nm) to create a focal plane image at the tip of a FB.

The FB is a custom bundle manufactured by Thorlabs. It is composed of seven 4.5/125 SMF fibres, 2 m in length, mounted with a unique SMA connector in the collimator. A picture of the tip of the bundle is provided Fig. 4. The fibres are labelled S for the science fibre, C for the centring fibre, and F 1 to F 4 for the feedback fibres. There is one spare fibre that is not used in the setup. The seven fibres are separated from each other at the centre of the FB and the end connectors on the other side are individual FC connectors. During the alignment of the FIM, the science fibre is aligned with respect to the optical axis, while the others remain off-axis. Since MITHiC is monochromatic and does not have a dedicated spectrograph, we connect the S and C fibres to two different Thorlabs PM101 power meters with S150C cells (Fig. 4, S power meter and C power meter) to measure the injected flux in watts.

For the second and third centring strategy, the F 1-4 fibres are retro-fed into the system through a home-built system (Fig. 4, calibration sources) based on four LEDs controlled by an Arduino micro-controller. The LEDs emit light into the SMF through the collimator, which also acts as an injector in this configuration. The retro-fed light goes through the beam-splitter cube and is reflected to the system by a plane mirror placed closely behind the cube to avoid significant differential defocus between the tracking branch and the retro-injection. The four retro-fed fibres are finally re-imaged on the tracking camera on top of the science image.

Limitations of the testbed

Although the MITHiC bench is within an aluminium protective enclosure, it is subject to daily variations since it is not in a temperature-and hygrometry-controlled environment. Moreover, some active components placed on the bench contribute to heating it and creating turbulence and frequency vibrations below 56 Hz. These disturbances have been attenuated as much as possible, but some effects remain.

Several phenomena are major contributors to the limitation of the bench, such as the jitter, the drift of the PSF, and, to a much lesser extent, the quasi-static aberrations. Firstly, the jitter of the PSF is intrinsic to the turbulence or the vibration inside of the enclosure. To measure the PSF's jitter, we acquired a data of 200 frames of 1 ms exposure time and measured the PSF's position with a 2D Gaussian fit in every frame. Based on the measurements, we estimate the standard deviation at 0.04 λ/D for the PSF's jitter. The typical timescale of the jitter is of the order of a few milliseconds.

For the estimation of the PSF's drift, we acquired an image of the stellar PSF every 0.5 s during 30 min using the tracking camera. Then, the centre of the PSF was estimated in every frame A171, page 5 of 14 with a 2D Gaussian fit. The PSF's drift value computed from the standard deviation and is estimated for both X and Y to 0.02 λ/D over 30 min.

Finally, the variation of static aberrations measured with ZELDA are estimated at 7 nm rms in two weeks if the bench remains in the same configuration (no opening of the panels). Since the timescale of the variations of the static aberrations is very long, this is not considered as a significant error term for our tests that take at most a few hours.

Centring accuracy specification

The performance of HDC instruments is essentially driven by the overall transmission of system. The planetary signal is several orders of magnitude fainter than the star, so the final signal can easily become limited by either photon noise (ideal case) or instrumental noise sources such as the background or readout noise (worst case).

Injection into SMF can quickly lead to significant flux losses if the centring is not accurate, which is why this parameter is critical. The simulations by Otten et al. (2021) show that a centring accuracy of 0.1 λ/D is a necessary requirement for HiRISE. With this accuracy we expect a maximum peak coupling efficiency loss of five percentage points compared to a case with perfect centring of the PSF on the science fibre. This is a tight requirement that is illustrated in Fig. 5, which shows a normalised injection map of the star's PSF into the centring fibre on MITHiC, with two circles delimiting the 0. injected into the S and C fibres, as measured by the corresponding power meters. Each point of the injection map corresponds to a tip-tilt mirror position and a PSF position in the focal plane of the tracking camera. The radial profile of the injection map shown in Fig. 6 demonstrates that at 0.1 λ/D the loss is estimated to 2.6 percentage points on MITHiC. Although VLT/HiRISE and MITHiC have slightly different optical parameters, this value is consistent with the values obtained by simulation for HiRISE. A slightly lower accuracy of 0.2 λ/D could be acceptable for HiRISE, but at the cost of a loss of approximately ten percentage points compared to the perfectly centred case.

Implementation of the centring strategies

In this section, we present the practical implementation of the centring strategies on MITHiC described in Sect. 2 with the goal of estimating the positioning accuracy of the planet's PSF on the science fibre. We first describe some key calibrations that are required in Sect. 4.1, then we present the data acquisition in Sect. 4.2, and finally we present the performance results in Sect. 4.3.

Calibrations

Centres of the fibres

The first necessary calibration is the ability to locate the S and C fibres in the tip-tilt commands space, so we compute a coarse injection map. For a more accurate determination of the fibres centre, we used the tip-tilt mirror position associated with the maximum of the injection map as input to a gradient descent algorithm based on the Nelder-Meade approach, which maximises the flux injection into the fibres. Because the core of the PSF is a convex envelope, the convergence is highly repeatable and we did not encounter problems related to local minimums. From here on, this optimisation of the injection based on the gradient descent algorithm is referred to as an injection optimisation.

C-S fibre distance

The second important calibration is the accurate C-S distance, which is required to be able to apply a tip-tilt offset to switch between fibres in the first and third centring strategies. To calibrate this offset, we performed 100 measurements (50 measurements on each fibre) based on the following steps. First, the PSF is centred on the S fibre using the injection optimisation described in Sect. 4.1.1; then a coarse tip-tilt offset is applied to switch to the C fibre; and finally the PSF is accurately centred using the injection optimisation. This provided 100 measurements of the accurate distance between the two fibres, and the final adopted value corresponds to their average. The calibration accuracy of the C-S distance is illustrated in Fig. 7, where each point represents the displacement position in tip-tilt before and after the optimisation. We find that 99% of the points are A171, page 7 of 14 within the accuracy requirement of 0.1 λ/D with a mean estimated at -4.416 mrad in tip and -2.183 mrad in tilt and a standard deviation of 0.007 mrad (0.04 λ/D) in both tip and tilt. We conclude that the C-S distance calibration matches our accuracy requirement since the standard deviation is below the requirement. Finally, we note that the standard deviation estimation is approximately equal to the PSF's jitter uncertainty, so the C-S distance calibration precision and accuracy are certainly limited by the jitter of the PSF.

Offset between the retro-injection and tracking branches

In the second and third strategies, the calibration fibres F 1-4 are retro-fed at the same time with a LED signal and re-imaged on the tracking camera superimposed on the science image. This is illustrated in Fig. 8, where the stellar PSF is visible close to the centre with the four images of the retro-injection fibres. In this image the PSF was previously centred on the science fibre using the method described above. In theory, the diagonal intersection (I) of the four spots, retrieved by a 2D Gaussian fit, should determine the position of the science fibre on the tracking camera with respect to the retro-injection fibres. However, the mirror positioned behind the beam splitter is slightly skewed with respect to the optical axis and introduces an offset between the tracking branch and the retro-injected beam. Although the PSF is centred on the S fibre in Fig. 8, this is why its image on the tracking camera shows a significant offset with respect to I. The I-S offset is accurately measured during a dedicated calibration procedure and used for the second strategy. For the third FoV.

An alternative approach would be to use a classical AOlike interaction matrix, where the relationship between the focal plane position and the tip-tilt commands is calibrated by introducing a single known offset in tip and tilt. However, this approach assumes that the offset value does not matter because there is a strictly linear relationship. This is not the case in our system because of optical distortions introduced between the tiptilt mirror and the tracking camera, which is why an interpolation grid was adopted.

We estimated the accuracy of the positioning by using the interpolation function to place the PSF on a test grid of 48 × 48 points interleaved with the original calibration grid. For each target position, the position of the PSF was estimated on the tracking camera image and compared to the target position to compute the residuals. We find that 6% of the outliers are located at more than 20σ from the sample data mean. We reject all outliers located beyond three standard deviations from the sample data mean. The histogram of the residuals for the full test grid is displayed in Fig. 9. The residuals are quasi-Gaussian with a standard deviation of 0.03 λ/D, which is well below 0.1 λ/D. Even taking into account the wings of the distribution, 97.61% of the residuals fall within ±0.1 λ/D. Even though the accuracy for most positions is well within our specification of 0.1 λ/D, the presence of outliers can potentially have a negative impact. In Fig. 10, we plot the measured position on the tracking camera of all points in the test grid, colour-coded with the position error with respect to the requested target position. The positions of the C and S fibres are indicated with crosses. We note an area of particularly poor accuracy located close to the position of the C fibre, in the direction that corresponds to the planet's position angles (in tip-tilt space) between ∼45°and ∼100°. For those tip-tilt commands, the beam starts hitting the edge of one of the lenses, which impacts significantly the PSF's image quality on the camera. A combination of aberrations is noticed in the PSF's shape, the coma being the main contributor, which affects significantly the shape of the PSF. As a result, the 2D Gaussian fit of the PSF is less accurate, which is problematic since the PSF's centroid is used to create the interpolation calibration grid. The presence of the outliers could explain the loss of accuracy.

The calibration grid used to build the interpolation function is based on the acquisition of the stellar PSF on the tracking camera; consequently, its stability relies on the bench limitation. The calibration grid takes approximately 6 min to be computed and is stable over approximately 30 min in optimal conditions due to the PSF's drift estimated in Sect. 3.2 at 0.02 λ/D.

ZELDA calibration

The overall optical quality of the bench would normally allow the centring strategies to be investigated without requiring a dedicated optimisation of the wavefront. However, the standard operations of the MITHiC testbed include a calibration of the aberrations of the bench using the ZELDA wavefront sensor (Pourcelot et al. 2021). We maintain this calibration at the beginning of each test as a sanity check and to benefit from the best possible PSF quality. A wavefront quality better than 20 nm rms is typically obtained.

Data acquisition

In this section, we test the centring strategies and quantify their respective accuracy. We recall that the goal, in the context of HiRISE, is to place the planet's PSF as close as possible to the centre of the S fibre so as to maximise the injection efficiency and therefore the planetary flux that will be transmitted to a highresolution spectrograph.

On MITHiC we do not have the capability to create a true off-axis point source that would simulate a planet. To create the planet's PSF, we introduce a sinusoidal modulation on the SLM that creates two symmetric satellite spots and take one of these spots as the planet's PSF. The spatial frequency and orientation of the sine wave enables choosing the angular separation and position angle of the planet. Contrary to an actual planet for which the astrometry will be known beforehand based on previous direct imaging measurements, in our tests we measure the relative star-planet astrometry on a tracking camera image just after the planet has been introduced with the SLM. The amplitude of the sine wave is set to 100 nm rms, which results in a star-planet contrast ratio of a factor 3.48. The contrast is modest, but does not impact the final performance results because on-sky the system is blind to the planet's signal during the centring procedure. However, having a modest contrast ratio in the laboratory is necessary to check the final accuracy.

At the end of each centring procedure (regardless of the strategy), a verification optimisation (VO) is performed to evaluate how close the planet's PSF is to the centre of the S fibre. The displacement in tip and tilt between the position before the VO and after the VO, , provides a direct measurement of the distance to the centre. This is the error that defines the success or failure status of the performance test by comparing it to the specification accuracy of 0.1 λ/D. However, the VO is performed only in the laboratory and cannot be used on-sky to test if the planet is accurately injected into the science fibre. The science fibre will be connected to the CRIRES+ spectrograph and in any case the planet's signal will be several orders of magnitude fainter than that of the star.

For the performance study, we performed five series of 20 centring tests for planets introduced at 12 different position angles around the star. The star-planet angular separation was set to 10 λ/D for all tests, which corresponds to the average separation where known companions have recently been imaged with HCI. We had to take into consideration the drift of the PSF (see Sect. 3.2) and its impact on the temporal stability of the calibration grid. This is why between each series we recompute the calibration grid used as input to the interpolation function. For each position angle, all the values are combined to compute an overall success rate when compared to centring accuracy specifications of 0.1, 0.2, and 0.3 λ/D. This repeatability test is decisive to achieve the performance study since it highlights the accuracy of each strategy.

Strategy 1

The centring procedure starts by measuring an injection map to coarsely position the star's PSF on the C fibre, then an injection A171, page 9 of 14 A&A 667, A171 (2022) optimisation is performed to accurately centre the star on the C fibre. The pre-calibrated C-S offset is applied to the tip-tilt command to position the star on the science fibre as an intermediate step. Then we use the pre-calibrated interpolation function to measure the offset command to switch between the stellar PSF and the planetary PSF on the science fibre, based on the relative astrometry computed on the tracking camera images. Finally, a VO is performed to evaluate the error.

Strategy 2

The second strategy starts by switching on the four feedback fibres and taking an image on the tracking camera. In the focal plane the position of the four feedback fibres is determined by a 2D Gaussian fit. The positions are used to compute the intersection I and compare its position to the stellar PSF. Then, by applying a tip-tilt command retrieved by the interpolation function, the stellar PSF is placed into the science fibre by using the previous I-S calibration. The offset command in tip-tilt to move the planet into the science fibre is calculated using the same method described previously. Finally, the VO is performed to estimate the final error.

Strategy 3

The third strategy combines the first and the second strategies. The initial step is to scan the mirror in tip-tilt to coarsely position the star on the C fibre and perform an injection optimisation to refine the centring. Then, we use the same steps described for the second strategy to place the star into the centring fibre based on its relative position with respect to I. The calibration is now not performed between I and S but between I and C. After the star is positioned on the C fibre, we apply the corresponding tip-tilt offset command to place the planet on the C fibre and we apply the pre-calibrated offset to switch from the centring fibre to the science fibre. Finally, a VO is performed to check if the planet is accurately injected into the science fibre and to measure the error .

Results

Performance with position angle

Our results for a planet located at different position angles around the star and with an angular separation of 10 λ/D are summarised in Fig. 11. The figure shows the success rate of each strategy for three specification accuracies of 0.1, 0.2, and 0.3 λ/D.

We note a correlated trend between all strategies, particularly emphasised in the plot's 40-150°region (Fig. 11, grey region). In this region all the strategies show a clear decrease in the success rate. This region roughly corresponds to the range of angles where a significant number of outliers have been identified in the calibration of the interpolation function (see Sect. 4.1.4). This is very likely correlated to the poor results now obtained in this region. Since this is an issue related to our specific setup, we do not consider the consider the results in the 40-150°range as representative of the final expected performance.

For the first strategy (Fig. 11, top panel), we never reach a success rate of 1.0 for a specification accuracy of 0.1 λ/D or 0.2 λ/D for all position angles, while a success rate of 1.0 is reached for all position angles when considering a specification accuracy of 0.3 λ/D. For a specification of 0.1 λ/D the success Fig. 12. Success rate as a function of the angular separation from the star. The results for the first, second, and third strategies are plotted in the upper, middle, and lower panels, respectively. The black dashed lines at 90°and 210°represent the angles for which additional tests are performed and demonstrated in Fig. 14.

success rate obtained at a separation of 10 λ/D is consistent with the previous test. However, there are minor differences that can be explained by the fact that the results shown here were acquired in a completely separate data acquisition sequence.

For the first strategy (Fig. 12, top panel) the angle 90°shows the lowest success rate since it drops drastically as a function of the angular separation. It reaches 0.0 at worst with the specification of 0.1 λ/D and 0.2 λ/D, and it drops below 0.4 for the 0.3 λ/D specifications for planets at 20 λ/D. In contrast, for the two other position angles, the success rate is higher than 0.4 at all separations for the 0.1 λ/D specification, and better than 0.95 at all angles for 0.2 λ/D and 0.3 λ/D.

The second strategy (Fig. 12, middle panel) shows a success rate higher than 0.9 with an accuracy of 0.2 λ/D and 0.3 λ/D at all position angles and all angular separations. For a specification of 0.1 λ/D the success rate is on average below 0.8 and shows a decrease with angular separation. There is no apparent strong correlation with the position angle for the 0.1 λ/D specification.

For the third strategy (Fig. 12, bottom panel), the results are consistent with the ones previously seen in Fig. 11: the success rates for the different specifications at position angles of 90°and 210°are worse than for the first or second strategy, and at 330°t hey are similar. The drop in performance for the three specifications at a position angle of 90°is even sharper than for the first strategy, confirming that whatever limits the performance of the first strategy has an even stronger impact in the case of the third strategy.

Understanding the limitations

The results above demonstrate that reaching a specification accuracy of 0.1 λ/D is extremely challenging, whatever the centring strategy. In the case of the first and third strategies we hypothesise that the loss of accuracy in the centring of the planet likely occurs at the level of the switch between the C fibre and the S fibre, although the C-S distance is accurately pre-calibrated A171, page 11 of 14 using the tip-tilt mirror to inject the light, alternating between the two fibres (see Sect. 4.1).

To validate this assumption, we conduct a series of additional tests. In the first we follow the process of the first centring strategy with the goal of simply centring the stellar PSF on the S fibre. The results for 100 independent tests are presented in Fig. 13 and show a success rate of 0.94 for a 0.1 λ/D specification and 1.0 for a specification of 0.2 λ/D on the S fibre. We see that on the science fibre most points are well centred, although there is a visible scatter. Nonetheless, the success rate is very high and the test demonstrates that we are able to accurately place the stellar PSF on the science fibre.

The second test is similar, but this time it is performed on planets located at a separation of 10 λ/D and position angles of 90°and 210°. The results for 100 independent tests are shown in Fig. 14. At both position angles the centring is both relatively precise and accurate on the centring fibre, but the accuracy is lost when switching on the science fibre, especially for the 90°position angle. At this position angle, the success rate is almost zero with the 0.1 λ/D specification and >0.9 with the 0.2 λ/D specification. The PSF's jitter uncertainty appears compatible with the scatter of the points for the 100 tests; however, it cannot explain the loss of accuracy so there must be another limitation in the system.

The interpolation function, which is used in all three strategies to place the stellar PSF at any position in the FoV, is potentially the limiting factor. We show in Sect. 4.1.4 that a significant part of the tip-tilt space close to the centring fibre C in the range of position angles 45-110°shows a reduced accuracy that is likely due to optical aberrations on the testbed. Interestingly, this range closely corresponds to the range of position angles in Fig. 11 where the success rates significantly decrease. Figure 10 also shows that the accuracy is worse when going away from the C fibre's position (i.e. for planets injected at larger angular separations). This is highly consistent with the drop in performance observed with angular separation in Fig. 12. We conclude that for planets in the 45-110°range of position angles, the centring on the C fibre is biased because of the limited accuracy of the interpolation function and the error gets amplified when switching to the S fibre.

For the second strategy, the C-S offset is not involved since we use the I-S distance to place the planet's PSF into the science fibre. However, the low success rate as a function of the angle positions for a specification accuracy of 0.1 λ/D could be explained by the defocus of the four retro-injected spots imaged on the camera. It impacts the accuracy of the 2D Gaussian fit and consequently the accuracy of the I position determined on the camera. The loss of accuracy with angular separation is actually less pronounced than for the other two strategies, so it could be that several error factors add up and limit our accuracy to only 0.2 λ/D.

Conclusions and discussion

The first exoplanet was detected a few decades ago, and thousands of them have been detected and confirmed since then by indirect or direct techniques. The characterisation of these exoplanets remains crucial to understanding their atmospheric composition, and their formation and evolution mechanisms. The combination of HCI with HRS promises great potential to answer some of these fundamental questions. HiRISE proposes to implement a coupling between SPHERE and CRIRES+ at the VLT. One of the main constraints in the project is the ability to inject a known planet's PSF on the science fibre to transmit it to the spectrograph with the highest possible throughput. Previous studies for HiRISE have determined that a specification of 0.1 λ/D would be the best choice to maximise the transmission (Otten et al. 2021).

To study the best centring approach, we used the MITHiC testbed at LAM, which has been upgraded to closely emulate the setup used in HiRISE. The FIM part is divided into three branches: the science branch that images the focal plane on the tracking camera, the injection branch that injects the light into a small bundle of fibres using a collimator, and the retro-injecting branch following the reverse injection branch and A171, page 12 of 14 images feedback fibres on the tracking camera. With this setup, three strategies were implemented and tested on MITHiC to assess the feasibility of reaching a specification of 0.1 λ/D.

We conducted a performance study to verify the planet's PSF centring on the science fibre S for several angular separations and for several position angles around the star. Regardless of the strategy, we conclude that reaching an accuracy of 0.1 λ/D is extremely challenging. It requires a high level of accuracy at every calibration step, which is difficult to reach, especially in a non-optimised system built from off-the-shelf components. In our case the final performance over a range of planet position angles (or conversely a range of tip-tilt positions) can be explained by a lower accuracy in the calibrations used to performed the first and third centring strategies.

The first performance tests were achieved for several planet position angles with a separation angle of 10 λ/D. For the first strategy we reach an average success rate of 0.7 for the specification accuracy of 0.1 λ/D, and 0.95 or higher for accuracies greater than 0.2 λ/D. For the second strategy the success rate is on average equal to 0.6 for an accuracy of 0.1 λ/D, and again the success rates are higher than 0.95 for an accuracy of 0.2 λ/D and 0.3 λ/D. Finally, the third strategy demonstrates a success rate slightly worse than the first and second strategies.

The second performance tests were performed with planets located at different angular separations; we only tested three position angles: 90°(located in the grey area), 210°, and 330°. The first strategy shows the lowest performance for 90°, with a success rate that severely drops as a function of the angular separations. It reaches 0.0 at worst for an accuracy of 0.1 λ/D and 0.2 λ/D, and is below 0.4 for an accuracy of 0.3 λ/D. This is not surprising as this position angle is clearly identified as problematic in the calibrations. For the two other position angles we reach a success rate higher than 0.4 for 0.1 λ/D and higher than 0.95 for an accuracy of 0.2 λ/D and 0.3 λ/D. The observed trends for the first strategy are found again in the results for the third strategy, but with even poorer results. Finally, the results for the second strategy are much better, with very high rates at all position angles for the 0.2 and 0.3 λ/D specifications, and slightly decreased success rates for a specification of 0.1 λ/D, but not as bad as for the first and third strategies.

Some aspects related to performance can be explained by limitations in the system, such as the PSF jitter and the accuracy of the interpolation function. The interpolation function is used in all three strategies to place the stellar PSF at any position in the FoV. Even though most of the interpolation function's uncertainty distribution is within the accuracy specification of ±0.1 λ/D, the presence of outliers negatively impacts the interpolation function in certain areas. These outliers originate from hardware limitations inherent to the MITHiC testbed, which hopefully will not be present for HiRISE.

The FIM implemented in SPHERE will benefit from the complete instrument's infrastructure (stability, high-quality optics, ExAO, coronagraph). As in the MITHiC testbed implementation, we will have an optimised system with a dedicated C fibre connected to a power meter in HiRISE, which will allow the stellar PSF injection to be verified during the centring procedure. However, a major difference between the laboratory environment and the final implementation is that the S fibre will be connected to the CRIRES+ spectrograph. This will prevent the output flux from being measured directly, which will affect the centring of the stellar or planetary PSF on the science fibre.

From the operational point of view there are important differences between the three centring strategies. The first strategy mainly relies on an accurate determination of the C-S distance, which will have been calibrated in the laboratory during the assembly integration test phase (AIT). The main advantage of this strategy is that no flux measurement is theoretically necessary at the output of the bundle on a daily basis. On the other hand, we see on MITHiC that issues related to the differential distortion between the injection and science branches, or to the accurate calibration of the interpolation matrix, can significantly impact the accuracy when injecting an off-axis point into the fibre instead of the star. At this stage, it is still uncertain if the same problems will arise on HiRISE, where we have an optimised system. Fortunately, SPHERE includes a distortion calibration grid (Wildi et al. 2010) that could be extremely useful to fully characterise the differential distortion in the final system.

The second strategy is inspired by the first calibration step used on KPIC phase I (Delorme et al. 2021), so it has the advantage of already being demonstrated on-sky. They report that they are able to place the planet's PSF on the science fibre with a precision of less than a 0.2 λ/D (<10 mas) in K band, which is similar to the values that we obtained on MITHiC. For HiRISE, the retro-injection takes into account the differential distortion between the two branches. On the other hand, it requires calibrating the I position when the star has been perfectly centred on the science fibre. This calibration could be completed in the laboratory during the AIT. Even so, the temporal stability of the opto-mechanical elements between the retro-injection and the science branches are uncertain, so there is a risk that the calibration needs to be redone regularly. Once the bundle is installed at the telescope, it will not be possible to disconnect it easily to perform any calibration directly at the output of the science fibre. The recalibration of the exact position of the S fibre with respect to I will therefore require using data directly acquired with the spectrograph, which may be less straightforward than in the laboratory where a simple photometer can be used. This is nonetheless a possibility that will be carefully considered during commissioning.

The third strategy will hopefully combine the advantages of the first and the second strategies. It includes by design the compensation of the differential distortion using the retro injection and the C fibre, and we will have a direct measurement of the flux injected into the C fibre. On the other hand, the switch from the C to the S fibres for an off-axis object seems to be the limiting point in the first strategy. In the light of the performance study on MITHiC and considering the operational point of view, the first strategy is considered for HiRISE. However, it will be necessary to wait for the AIT to verify the strategy feasibility in the case of HiRISE.

The AIT phase of HiRISE in Europe is just starting. The alignment of the system will be based on a simplified SPHERE simulator that will reproduce the main characteristics of the SPHERE IFS beam using off-the-shelf components (LED source, lenses, and a pupil stop). This simulator will be used to align the bench and verify the image and wavefront quality. However, the simulator will be highly chromatic, which means that the system will be aligned with a monochromatic source at 1.6 µm and simply checked at other wavelengths. This implies that the centring strategies will not be fully testable during the AIT phase. Contrary to the MITHiC setup, HiRISE uses a dichroic filter to transmit all the science photons in H band and uses the shorter wavelengths for the centring and calibrations. Some conclusions regarding the best centring strategy for HiRISE will come from the AIT phase, but the final decision will have to wait the first on-sky tests.

Due to the strong dependence of the performance to the global transmission of the system (Otten et al. 2021), the centring A171, page 13 of 14 A&A 667, A171 (2022) procedures are crucial for HiRISE. In this particular case we work with existing systems, which implies strong constraints on the specifications in order to maximise the transmitted flux. These constraints will undoubtedly be relaxed for future instruments optimised end-to-end for HDC. Developing IFS instruments offering very high spectral resolution is challenging and costly, so it is likely that HDC will remain largely based on fibrefed spectrographs in the foreseeable future. Our study therefore prepares the ground for instruments like RISTRETTO on the VLT [START_REF] Lovis | [END_REF]) and, in the longer term, PCS on the ELT (Kasper et al. 2021) or post-JWST space instruments.

INTRODUCTION

In 1995, the first exoplanet was detected and thousands of them have been detected and confirmed since then by indirect or direct methods. 1 The characterisation of these exoplanets remains essential to understanding their atmospheric composition, 2 and their formation and evolution mechanisms. 3 High-contrast imaging (HCI) currently focuses on the direct detection of young (< 300 Myr) giant (> 1 M Jup ) exoplanets orbiting at large orbital separation (> 10 au) from their host star. The high contrast (> 10 mag) and small angular separation (< 1 ′′ ) of these planets with respect to their host star are a severe limitation to their detection, but especially to their atmospheric characterisation.

High contrast imaging combines coronagraphy and extreme adaptive optics 4 techniques to respectively attenuate the on-axis stellar light 5, 6 and to compensate for the atmospheric distortion in ground-based observations. However, HCI is limited by quasi-static speckles in the focal plane, 7 which emulate the planetary signal. To overcome this constraint, a new generation of exoplanet imagers has been implemented on large ground-based telescopes such as VLT/SPHERE, 8 Gemini/GPI, 9 and Subaru/SCExAO 10 to great success. Nevertheless, the spectral resolution of these instruments (e.g., R = λ/∆λ = 50 for IFS/SPHERE) are a limitation to characterise exoplanets. 11 The characterisation of exoplanets atmosphere using infrared spectrographs such as Keck/NIRSPEC 12 or VLT/CRIRES 13 has been performed using high dispersion spectroscopy (HDS). For ground based observation, HDS in the near-infrared (NIR) had proven to be a powerful technique to retrieve key information of transiting exoplanets 14 and to spectrally resolve molecular features of species in the atmosphere of exoplanets. 15 In 2014, VLT/CRIRES detected the CO lines at 2.3 µm in β Pictoris b using the combination of the MACAO AO system 16 and the implementation of medium-to high-spectral resolution (R = 100000 in the H band), which constrained β Pictoris b's rotational velocity and orbital motion. 2 In order to reproduce CRIRES feat, it would be necessary to have access to high-resolution spectrographs supplied with extreme adaptive optics, however, such instruments do not currently exist.

Recently, the combination of high-contrast imaging and high dispersion spectroscopy, named high dispersion coronagraphy (HDC) have started to rise as a robust technique to directly characterise young giant exoplanets. 17 For ground based observations, the combination of HCI and HDS can in theory reach a planet-star contrast of 10 -7 or better 18 and several on-going projects have implemented HDC on existing telescopes such as Keck/KPIC, 19 Subaru/REACH, 20 and VLT/HiRISE. 21 The aim of these three projects, amongst others, consists of coupling existing high-contrast instruments with medium to high resolution spectrographs using single mode fibres (SMF). 22 SMFs are advantageous for feeding light into spectrographs due to their precision and stability properties. They are usually used in the focal planes of telescopes due to their spatial filtering capabilities. 23 However, efficiently coupling a point spread function (PSF) into a SMF is challenging, mainly due to the fact that they only accept a quasi-Gaussian fundamental mode. Furthermore, the central obstruction and spiders on ground-based telescopes significantly affect the coupling efficiency, typically the VLT offers a maximum coupling efficiency of ∼73%. 24 In order to maximise the coupling efficiency of the telescope PSF into a SMF in the context of HiRISE, Otten et al. 24 demonstrate that the PSF must be centred with the core of the fibre within 0.1 λ/D to achieve a coupling efficiency better that 95% of the maximally achievable. Any offset impacts the coupling, in the case of the High-Resolution Imaging and Spectroscopy of Exoplanets (HiRISE), we can tolerate a coupling efficiency as low of 59% of the maximum, which corresponds to an offset between the PSF and the SMF of 0.2 λ/D. HiRISE offers a very unique opportunity at the VLT to couple two flagship instruments implemented on the Nasmyth platforms of the unit telescope 3 (UT3): the exoplanet imager SPHERE on one side, and the NIR high-resolution spectrograph CRIRES+ 25 on the other side. HiRISE aims to link SPHERE and CRIRES+ with optical fibre to achieve the characterisation of known directly imaged young giant exoplanets at a spectral resolutions up to R = 100000 in H-band. HiRISE will take advantage of both SPHERE and CRIRES+ capabilities in H-band to act as a HDC instrument and is composed of three independent parts: (i) the fibre injection module (FIM) that will be implemented downstream of the ExAO and Lyot stop wheel in the IFS arm of SPHERE, (ii) the fibre bundle (FB) that will link SPHERE and CRIRES+, and (iii) the fibre extraction module (FEM) that will be installed on the calibration stage of CRIRES+.

The main challenge of HiRISE is to blindly centre the planet's PSF on top the SMF located in the FB, ideally with an accuracy better than 0.1 λ/D. The FIM plays a key role during observations since it will pick up the planet's PSF and inject it into a SMF. Therefore, different strategies are investigated and presented in this paper to fulfil the centring requirement for HiRISE.

In this proceeding three different strategies are investigated to fulfil the required centring specification for HiRISE. To explore these strategies we used an upgraded version of the Marseille Imaging Testbed for High-Contrast (MITHiC). 26 In Sect. 2 we present a brief overview of HiRISE and we describe the PSF centring strategy procedures. In Sect. 3 we present the MITHiC testbed and detail the description of the FIM located on MITHiC. We also explain the characterisation of the setup and the specifications required for the centring strategies. In Sect. 4, we introduce the description of the centring strategy procedures in laboratory, and we discuss the performance results. Finally, in Sect. 5 we conclude.

HIGH DISPERSION CORONAGRAPHY IN THE CASE OF HIRISE 2.1 Description of HiRISE

HiRISE redirects the SPHERE/IFS beam and injects the light of a known exoplanet into a SMF connected to the NIR spectropgraph CRIRES+. The FIM is inserted as a vertical bench on the IFS arm of SPHERE, where a pick-off mirror redirect the light towards the FIM instead of the IFS as shown in Fig. 1. Then, the SPHERE pupil is reimaged onto a mirror mounted on a S335 piezo-tip-tilt platform from Physik Instrumente and the beam is recollimated thanks to a custom achromatic doublet. The light goes through a dichroic filter that reflects the YJ bands to the tracking camera arm and transmits the H band to the fibres arm. The tracking camera is a C-RED 2 camera from First Light Imaging, the image is formed in the focal plane of the tracking camera at F/40 and is Nyquist-sampled at 12.25 mas/pix. In the injection arm, the beam is refocused using an air gap doublet at F/3.5 that matches the numerical aperture (NA = 0.16) of the on-axis science fibre implemented in the fibre bundle. Furthermore, three additional fibres, implemented off-axis are used to sample the stellar light in the speckle field and four 'feedback fibres' are connected to a calibration source and are used to retro inject light into the optical setup. The outputs of the feedback fibres are reimaged on the tracking camera superimposed on the science image, the position of the feedback fibres with respect to the science fibre position acts as a possible approach to accurately centre the planet's PSF onto the science fibre. After the alignment of the system, the FB remains static and the tip-tilt mirror is used to move the focal plane with respect to the science fibre to place the planet's PSF onto the fibre.

Description of the centring strategies

The role of the FIM consists in centring the planet's PSF on the science fibre with the required accuracy. Due to S/N constraints, the planet's PSF will not be visible on the tracking camera, thus, the planet's acquisition will be performed blindly based on its known relative astrometry with respect to the stellar PSF and the calibrations carried out during the day.

The choice to investigate only three strategies and select the best one to implement for HiRISE have been driven by the fact that the strategies require only a limited amount of hardware and they are usable from the operational point of view at the VLT.

• The first strategy (Fig. 2, top row):

It relies only on a centring fibre located close to the science fibre. The first step in a non coronagraphic configuration consists on coarsely place the stellar PSF onto the centring fibre. The following step is to refine the position with an optimisation algorithm that maximises the coupling efficiency of the stellar PSF in the centring fibre (Fig. 2, panel 2). Then, by applying the pre-calibrated offset (Fig. 2, panel 1), we place the stellar PSF into the science fibre (Fig. 2, panel 4). Finally, by using the interaction matrix and the astrometry offsets (right ascension and declination), we apply the corresponding offset to the tip-tilt mirror to place the planet on the science fibre (Fig. 2, panel 5).

• The second strategy (Fig. 2, middle row): It uses the science fibre and the four feedback fibres in the non coronagraphic configuration. In theory, the diagonal intersection (I) of the four feedback fibres reimaged on the tracking camera provides the position of the science fibre. The first step consists on switching on the four feedback fibres and acquire an image with the tracking camera, find the intersection (I) and determine the position of the science fibre (Fig. 2, panel 2). An offset may occur between I and the position of the science fibre. It is due to an alignment mismatch between the science arm and the retroinjection arm, and would need to be calibrated beforehand during the laboratory validation of the instrument (Fig. 2, panel 1). Then, by moving the tip-tilt mirror, we place the stellar PSF onto the science fibre and by applying an offset Figure 2: Centring strategy schemes. Each row represents a strategy. The blue frames represent the calibration procedure for each strategy, while the black frames are assigned to the centring procedure. The panels labelled 1-5 show the steps followed to place the planet's PSF into the science fibre. Reproduced with permission from El Morsy et al. 27 as described for the first strategy (Fig. 2, panel 4), we finally move the planet's PSF into the science fibre (Fig. 2, panel 5).

• The third strategy (Fig. 2, bottom row): It combines the first and the second strategy using all the fibres mentioned below. The first step consists in switching on the feedback fibres and to retrieve the intersection (I) (Fig. 2, panel 2). The tip-tilt mirror is use to place the stellar PSF into the centring fibre (Fig. 2, panel 3). Then, we use the pre-calibrated offset (Fig. 2, panel 1) to move the star onto the science fibre science fibre (Fig. 2, panel 4) and finally, we apply an offset to place the planet onto the science fibre (Fig. 2, panel 5).

In HiRISE, the science fibre S will be connected to CRIRES+ preventing any verification of the planet's injection in the fibre during the observation. The challenge to accurately centre the planet's PSF into the science fibre relies on the calibration accuracy performed at each procedure step. In the first strategy, the challenge is to accurately centre the stellar PSF onto the centring fibre, while for the second and the third strategies the crucial first step consists of placing the stellar PSF on the intersection I.

FIBER INJECTION INTO A SMF ON THE MITHIC TESTBED

Description of MITHiC

MITHiC is a HCI testbed located at the Laboratoire d'Astrophysique de Marseille (LAM). It is composed of a telescope simulator (TS), a wavefront sensor (WFS) to measure and compensate for the non-common aberrations (NCPA), a classical Lyot coronagraph (CLC) as shown in Fig. 3. The stellar PSF is generated by the TS through a polarised monochromatic fibre-coupled super-luminescent diode at a wavelength of 670.7 nm. The spatial light modulator (SLM), placed in the pupil plane allows to apply in closed-loop a phase correction to flatten the wavefront. On MITHiC, the creation of an off-axis planet is not feasible, so the SLM is used to create satellite spots. The WFS is a Zernike wavefront sensor called ZELDA. 26 We modified MITHiC by implementing the FIM in order to emulate the setup that will be implemented on HiRISE. In the foreground of Fig. 4, we can see the implementation of the FIM. A mirror glued on a piezo tip-tilt mount (PI-S335) was used to re-image the pupil of the bench. The mirror is located after the WFS stage and is oriented at 45 • with respect to the optical axis Fig. 4 (blue inset). The testbed is monochromatic, so we use a 50/50 beam-splitter cube to create two separate arms. In the tracking arm, the stellar PSF is imaged on a Coolsnap HQ2 CCD camera from Teledyne positioned at the focal plane with a 4.26 pixel/(λ/D) sampling. In the injection arm, the beam is refocused using a Thorlabs F810SMA-635 collimator to generate a focal plane image at the tip of the FB.

The FB is a custom bundle manufactured by Thorlabs. It is composed of seven 4.5/125 SMF, 2m length, mounted with one SMA connector in the collimator. In Fig. 4 (purple inset), the fibres are labelled S for the science fibre, C for the centring fibre, and F 1-4 for the feedback fibres, and one space fibre that is not used in the setup. At the centre of the FB, the seven fibres are separated from each others and the ends of the fibres are FC connectors. The S fibre and the C fibre are connected to two Thorlabs PM101 power meters with S150C cells to record the injected flux. The F 1-4 fibres are fed through a home-built system based on four LEDs controlled by a micro-controller Fig. 4 (yellow inset). The light goes to the collimator that acts as an injector in this configuration, then the beam goes through the beam-splitter cube and is reflected to the system thanks to a plane mirror placed closely behind the beam-splitter cube to avoid differential defocus between the tracking arm and the retro-injection arm.

Characterisation of the testbed

The MiTHIC testbed is enclosed by aluminium protective panels and is subject to daily variations since it is not controlled either in temperature and humidity. Some active devices located on the testbed contribute to heating it, creating turbulences and frequency vibrations. We noticed a vibration at approximately 56 Hz in fast sampled focal plane images and that was traced to acoustic coupling of a DC power supply near the bench. After moving the DC power supply, the 56 Hz signal fell to the background level as shown in Fig. 5. However, even if these disturbances have been attenuated some effects remain and contribute to the limitation of the testbed. Some impacting terms contribute to the limitation of the testbed and are quantified in this section. The jitter of the PSF, intrinsic to the turbulence or the vibration within the enclosure, is estimated at 0.04 λ/D. The PSF's drift computed from the standard deviation is estimated for both X and Y axis to 0.02 λ/D over 30 min. 27 to calibrate the offset between the two fibres, 99% of the points are within the requirement of 0.1 λ/D. We also noticed that the standard deviation estimation in tip-tilt is 0.02 λ/D, which is approximately equal to the PSF's jitter uncertainty.

• Offset between the retro-injection and tracking arm:

The calibration fibres F 1-4 are retro-fed simultaneously with a LED signal and re-imaged on the tracking camera superimposed on the science image. In theory, the diagonal intersection (I) of the four spots retrieved by a 2D Gaussian fit, should determine the position of the science fibre on the tracking camera. However, the mirror placed behind the beam splitter cube is tilted with respect to the optical axis and introduces an offset between the two arms. For the second strategy, the I-S offset is accurately measured during the calibration procedure. For the third strategy, the calibration follows the same path, but measures the I-C offset.

• Accurate positioning of the PSF: A calibration is necessary to accurately position the stellar PSF at any coordinate on the tracking camera. To fulfil this necessary calibration, a non linear approach with an interpolation function based on a full 2D calibration of the tip-tilt mirror as seen by the tracking camera is performed. The resulting interpolation function allow to obtain the tip-tilt command to place the stellar PSF at any position in the camera's field of view (FoV). El Morsy et al. 27 computed the residual of the interpolation function as measured on the tracking camera and demonstrated that the residual are quasi-Gaussian with a standard deviation of 0.03 λ/D, which is below 0.1 λ/D and noticed that 97.61% of the residuals fall within ±0.1 λ/D. The stability of the calibration grid used to build the interpolation function relies on the bench stability. It takes approximately 6 minutes to be computed and is stable over approximately 30 minutes due to the PSF's drift estimated at 0.02 λ/D.

• ZELDA calibration:

The calibration is computed at the beginning of each test as a sanity step and to obtain the best possible PSF quality.

A wavefront quality better than 20 nm RMS is typically obtained in normal conditions.

Data acquisition

We do not have the possibility to create an off-axis point source on MITHiC to simulate a planet so to overcome this constraint, we introduce a sinusoidal modulation on the SLM to create two symmetric satellite spots and take one of these satellite spot as the planet's PSF. The spatial frequency and orientation of the sine wave allow choosing the angular separation and position angle of the planet. The performance tests required several steps to be computed such as (i) measuring the relative star-planet astrometry on the tracking camera image, (ii) evaluating the star-planet contrast ratio.

The contrast of a factor 3.48 is modest but does not impact the performance results on-sky because the system is blind to for several angular separations and for several position angles around the star. Regardless of the strategy, we conclude that reaching an accuracy of 0.1 λ/D is extremely challenging mainly because it requires a high level of accuracy at every calibration step, which is difficult to reach in a non-optimised system.

Some performance results can be explained by limitations in the system, such as the PSF jitter and the accuracy of the interpolation function. The interpolation function is used in all three strategies to place the stellar PSF at any position in the FoV. Even though 97.61% of the interpolation function's residuals are within the accuracy specification of ±0.1 λ/D, the presence of outliers negatively impacts the interpolation function in certain areas. These outliers originate from hardware limitations inherent to the MITHiC testbed, which should not be present for HiRISE integrated into SPHERE.

The AIT phase of HiRISE in Europe has started. The alignment of the system is based on a simplified SPHERE simulator that reproduces the main characteristics of the SPHERE IFS beam using off-the-shelf components. This simulator will be used to align the bench and verify the image and wavefront quality. The conclusions regarding the best centring strategy for HiRISE will come from the AIT phase, but the final decision will have to wait the first on-sky tests.

  et d'autres détections directes de planètes ont suivi dans les décennies suivantes (par exemple Fomalhaut b (KALAS et al., 2008), β pictoris b (LAGRANGE et al., 2010, 2009), HD 106906b (BAILEY et al., 2014). En 2008, une image directe de planètes géantes a été détectée autour de HR8799 (MAROIS et al., 2008, 2010) et plus récemment 51 Erdiani b

  Eri b (MACINTOSH et al., 2015 ; SAMLAND et al., 2017) et HIP 65426b (CHAUVIN et al., 2017). Même si les faibles résolutions spectrales de ces instruments, typiquement R = 50 pour l'IFS SPHERE (ZURLO et al., 2014), sont une limitation majeure pour la caractérisation des exoplanètes, ils fournissent des informations clés sur la composition, la structure de l'orbite et les caractéristiques de la planète. L'utilisation d'instruments à moyenne résolution spectrale (environ 1000) permet d'accéder à la couche inférieure de l'atmosphère des exoplanètes. VLT/SINFONI (R = 5000 ; EISENHAUER et al., 2003), Keck/OSIRIS (R = 4000 ; LARKIN et al., 2006) et VLT/MUSE (R = 3000 ; BACON et al., 2010) ont permis la détection de molécules dans l'atmosphère de HR8799 b et c (BARMAN et al., 2015 ; KONOPACKY et al., 2013 ; PETIT DIT DE LA ROCHE et al., 2018), β Pictoris b (HOEIJMAKERS et al., 2018 ; RAMEAU et al., 2021), kappa and b (TODOROV et al., 2016 ; WILCOMB et al., 2020) et HIP65426 b (PETRUS et al., 2021), mais aussi des mesures de la vitesse radiale de HR8799 b et c (RUFFIO et al., 2019) et la compréhension de la formation de PDS70 b.

3. 21 .

 21 Mirror gluing procedure on the piezo tip-tilt platform. The image is divided into three rows with three panels per row and follows several steps in time. The first row, first panel represents the schematic draw realised to understand the challenge regarding the size of the piezo platform and the size of the mirror. The second panel represents the 3D printed aid used to perfectly centre the mirror on the platform. The third panel of the first row shows the tip-tilt without the mirror. The second row, all panels, display the positioning of the wires on the platform, the automatic glue dispensing device and the mirror centred due to the aid. The last row shows the last steps of the gluing procedure and the TTM on MITHiC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.22.View of the tip-tilt platform with the infrared camera. Temperature elevation with respect to ambient for the tip-tilt platform during calibration is similar to what is expected in HiRISE. The tip-tilt stage was on for approximately 2 hours when this picture was taken. Point number 5 corresponds to the temperature sensor located in front of the TTM. . . 3.23.View of the tip-tilt controller and power supply with the infrared camera.

3 . 24 .

 324 Tip-Tilt linearity test on MITHiC. The linearity is realised for each axis separately and the residuals are shown for the entire tip-tilt range. . . . 3.25.PSF behaviour in time as a function of temperature and humidity. . . . 3.26.PSF coordinates in X and Y axis as a function of humidity and temperature.139 3.27.Power spectral density (PSD) plots from experimental data acquired on the MITHiC testbench. The PSF centroid data is sampled at a high frequency using a tracking camera placed at the focal plane between the L4 lens and the mirror (Fig. 3.2) and only the PSDs in the X-axis are shown in this figure. The upper panel shows a peak at 56.4 Hz due to the vibration of a nearby electronic device. The lower panel shows the PSD after mitigating steps were undertaken. No major sources of vibration at specific frequencies remain. . . . . . . . . . . . . . . . . . . . . . . . . . 3.28.Plot of the PSF jitter estimated in the laboratory. The blue crosses represent the data and the red circle represents the uncertainty. . . . . . . . 3.29.Injection map obtained with the centring power meter by scanning a grid of 6×6 λ/D with a pitch of 0.05 λ/D in both directions. The red circle represents the required accuracy of 0.1λ/D. . . . . . . . . . . . . . 3.30.Radial profile of the injection map computed with the centring fibre on MITHiC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.31.Calibration map used to perform the interpolation function. The blue lines represent the FoV of the tracking camera in pixel. Each dots represent a tip-tilt position in mrad for which a stellar PSF image is acquired on the tracking camera. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.32.Distribution of the residual interpolation function: the probability density as a function of the δ distance. It represents the accuracy of the interpolation function to place the stellar PSF at any position on the camera FoV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 3.33.Residual of the interpolation function as measured on the tracking camera. The red cross and the blue cross give the positions of the science and centring fibre, respectively. The concentric rings in white represent the different angular separations (5, 10, 15 and 20 λ/D) and the different angular positions of the planet when the star is well centred on the centring fibre. The colour bar corresponds to the uncertainty error on the interpolation function. We note that 97.61% of the points mentioned in Fig. 3.32 are within the specification accuracy of 0.1 λ/D. . . . . . . . . 149 3.34.Measurements of the distance between the centring fibre and the science fibre for 100 consecutive tests. The red circle represents the accuracy requirement of 0.1 λ/D. The blue cross corresponds to the mean position of -4.416 mrad in tip, -2.183 mrad in tilt and the standard deviation is estimated at 0.007 mrad in both directions. . . . . . . . . . . . . . . . . . 150 3.35.Log-scale image acquisition on the tracking camera. The four feedback fibres represented as green fibres are imaged in the focal plane camera and used to localise the science fibre. The beacon's spot represents the stellar PSF injected into the science SMF and the planet's PSF is not displayed. The ghosts are caused by the reflection of light in the optical system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 3.36.Success rate as a function of position angle around the star. The results for the first, second, and third strategies are plotted in the upper, middle, and lower panels, respectively. The grey area represents the region where an emphasised trend is found. The black dashed lines at 90˚and 210˚represent the angles for which additional tests are performed and demonstrated in Fig. 3.39. . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 3.37.Success rate as a function of the angular separation from the star. The results for the first, second, and third strategies are plotted in the upper, middle, and lower panels, respectively. The black dashed lines at 90˚and 210˚represent the angles for which additional tests are performed and demonstrated in Fig. 3.39. . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 3.38.Success rate in the science fibre for the positioning of the star. Each dot is obtained for one entire centring procedure. The circles correspond to the different accuracies and the error bar gives the PSF's jitter uncertainty.157 3.39.Success rate in the centring and science fibre for the positioning of the planet. Top panel: Success rate in the centring and science fibre for the planet at a position angle of 90˚from the star. Bottom panel: Same results, but for a position angle of 210˚. Each dot is obtained for one entire centring procedure. The circles correspond to the different accuracies and the error bar gives for the PSF's jitter uncertainty. . . . . 158

Figure 1 .

 1 Figure 1.1. -Cumulative number of detections by year and discovery methods. Generated by NASA Exoplanet Archive on January 28, 2023.

Figure 1 . 2 .

 12 Figure 1.2. -Mass-period distribution of detected exoplanets. Generated by the NASA Exoplanet Archive on January 28, 2023.

Figure 1 . 3 .

 13 Figure 1.3. -Illustration of the radial velocity method. Credits: Johan Jarnestad/The Royal Swedish Academy of Sciences.

Figure 1 .

 1 Figure 1.4. -Picture of the telescope T193 at OHP.The white cylinder contains the fibre head for the Elodie spectrograph. Credit: E. Perrin.

Figure 1 . 5 .

 15 Figure 1.5. -Radial velocity curve of the star 51 Peg obtained with the ELODIE spectrograph (Mayor and Queloz 1995)

Figure 1 . 6 .

 16 Figure 1.6. -Illustration of a Light Curve of a Planet Transiting Its Star. Credit: NASA Ames.

Figure 1 . 7 .

 17 Figure 1.7. -Planetary transit detection by the CoRoT satellite. Credit: CoRoT/CNES

  , β Pictoris b (Lagrange et al., 2010, 2009), HD 106906 b (Bailey et al., 2014). In 2008, a four-planet system was detected around HR8799 (see, Fig. 1.8, Marois et al., 2008, 2010 ). More recently, the new generation of exoplanet imagers have provided detections around 51 Eridani b (Macintosh et al., 2015), HIP 65426 b (Chauvin et al., 2017) or PDS 70 (Haffert et al., 2019; Keppler et al., 2018).

1. 2 .

 2 Figure 1.8. -Direct images of HR 8799 system with the four planets (a, b, c, d) performed with the Keck at different epochs. Credit: Marois et al. (2010)

Figure 1 .

 1 Figure 1.9. -Light intensity curves for several planetary bodies compared with the Sun in yellow. These curves are normalised with respect to the maximum light intensity of the Sun. Credit: thesis Jacques-Robert Delorme.

Figure 1 .

 1 Figure 1.10. -Schematic of Fourier formalism application. Credit: Fabrice Vidal.

Figure 1 .

 1 Figure 1.11. -Representation of the Zernike polynomials and corresponding types of aberration. (Y. H. Hsieh, 2020).

Figure 1 .

 1 Figure 1.12. -Principle of adaptive optics. Credit: LLNL, Center for Adaptive optics.

1. 2 .

 2 High contrast imaging

Figure 1 .

 1 Figure 1.13. -Light propagation through a Lyot coronagraph. Credit: Emiel Por (PhD thesis)

  al., 2016; Chauvin et al., 2017, 2018; P. Delorme et al., 2017; Greenbaum et al., 2018; Mesa et al., 2020; Rajan et al., 2017; Samland et al., 2017; Uyama et al., 2020). However, these studies had led to diverging conclusions regarding the atmospheric composition shift (Rajan et al., 2017; Samland et al., 2017).

Figure 1 .

 1 Figure 1.14. -Color-color diagrams for HR 8799bcde. All exoplanets and brown dwarfs start as M-type objects, cooling and moving redward to the L spectral type and then transitioning to a T spectral type. Credit: Charnay et al. (2018)

Figure 1 .

 1 Figure 1.15. -The effect of increasing spectral resolution. The two panels represent different wavelength regions of a hot Jupiter atmospheric model containing water and carbon monoxide. Top panel: Credit: Birkby (2018)

Figure 1 .

 1 Figure 1.16. -Illustration of integral field spectrographs: the lenslet array, the fibre bundle with a lenslet array, and the image slicer. Extracted from Westmoquette et al. (2009), itself adapted from Allington-Smith et al. (1998).

Figure 1 .

 1 Figure 1.17. -Comparison diagram between single-mode fibres and multimode fibres.

Figure 1 .

 1 Figure 1.18. -Coupling efficiency to a SMF simulated for VLT-like pupil. Credit: HiRISE team.

Figure 1 .

 1 Figure 1.19. -Coupling efficiency to a SMF simulated for several telescopes as a function of the relative size of their central obstruction and with and without spiders for several major observatories. Credit: Jovanovic et al. (2017).

Figure 2 . 1 .

 21 Figure 2.1. -HiRISE implementation concept at the UT3/VLT. On the opposite Nasmyth platforms lay SPHERE and CRIRES+, and the fibre bundle which connects them.

  2.2): (i) the common path and infrastructure (CPI) including the fore optics, the ExAO, the NIR and VIS coronagraphs, (ii) the Zurich Imaging Polarimeter (ZIMPOL; (Schmid et al., 2018)), (iii) the Infrared Dual Imager and Spectrograph (IRDIS; Dohlen 2008b), and (iv) the Integral Imager and Spectrograph (IFS; Claudi 2008).

Figure 2 .

 2 Figure 2.2. -SPHERE block diagram. The instrument is divided into four subsystems: the common path infrastructure (CPI), the Zurich Imaging Polarimeter (ZIMPOL) and the Infrared Dual Imager and Spectrograph (IRDIS). Blue and orange arrows indicate the optical path to NIR and VIS, respectively. Credit: (Beuzit et al., 2019).

Figure 2 .

 2 Figure 2.3. -Top view of the SPHERE CAD. The CPI bench comprising the wavefront sensor and the other components are detailed in Fig. 2.4. The light coming from the telescope is coming from the top (window, shutter). Credit: (Beuzit et al., 2019)

Figure 2 .

 2 Figure 2.5. -Adaptive optics bloc diagram of SPHERE. The VIS+NIR optical path is represented in orange, the VIS in dark blue and the NIR in red. The light blue paths represent the control loops.

Figure 2 .

 2 Figure 2.6. -Top: Theoretical and measured (purple circles) SAXO Strehl ratio as a function of R magnitude for good seeing conditions (0.8 ′′ -1.2 ′′ ) and different wavelength ranges from V to K. Bottom: SPHERE PSF shape and Strehl ratio as a function of R magnitude. Credit: SPHERE, system analysis report

Figure 2 .

 2 Figure 2.7. -IFS layout with its own Lyot stop and internal calibration sources. Credit: SPHERE consortium.

Figure 2 .

 2 Figure 2.8. -IFS spectrum of HIP 65426 b (grey circles) compared with the BT-SETTL best-fit atmospheric model in blue, computed at a T e f f of 1660 K (Chauvin et al. 2017, ESO-ANN17041).

Figure 2 .

 2 Figure 2.9. -Optical layout of CRIRES+. The instrument is located in a cryostat (dark area). The AO system, the derotator, and calibration devices are in a warm part between the telescope and the spectrograph (grey area). The red cylinder represents the new absorption gas cell. Credit: CRIRES+ consortium

Figure 2 .

 2 Figure 2.10. -Fibre injection module implemented as a vertical bench in the IFS arm of SPHERE.

Figure 2 .

 2 Figure 2.11. -Picture of the pre-assembly of the FIM mechanical structure at the Laboratoire d'Astrophysique de Marseille.

Figure 2 .

 2 Figure 2.12. -Schematic of the design of the HiRISE/FIM. The main optical components are labelled, as are the photon sharing between wavelengths for the tracking (0.95-1.3 µm) and the science (1.4-1.8 µm). Reproduced with permission from (El Morsy et al., 2022).

2. 1 .

 1 High-Dispersion Coronagraphy on the VLT with HiRISE below:

Figure 2 .

 2 Figure 2.13. -Temperature increase with regards to the ambient air in the laboratory for the C-RED 2 tracking camera and its power supply running at high cadence.

Figure 2 .

 2 Figure 2.14. -Schematic of the optical design of the HiRISE/FEM. The bundle output is located on the top of the vertical part of the layout.

Figure 2 .

 2 Figure 2.15. -CAD view of the FEM implementation in CRIRES+. The upper image represents the FEM view without the cover.

Figure 2 .

 2 Figure 2.16. -Global concept for the fibre bundle. The bundle manufactured by Fibertech Optica is divided in three sections: section A on the SPHERE side, section B around the telescope structure, and section C on the CRIRES+ side (Vigan et al., 2022).

Figure 2 .

 2 Figure 2.17. -Picture of the HiCab with the devices installed on the racks

Figure 2 .

 2 Figure 2.18. -Coupling efficiency as a function of displacement between the PSF core and the Gaussian mode of the fibre simulated for three different coronagraph options and evaluated at 1.6 µm (Otten et al., 2021).

Figure 2 .

 2 Figure 2.20. -Expected SNR of the CCF analysis on HiRISE science targets during 2 hours exposure time. The grey diamonds represent the HiRISE targets foreseen in the future. Reproduced with the permission of A. Vigan .

Figure 2 .

 2 Figure 2.21. -Expected detection limits for targets around a star (H = 6.3) similar to HD 4113 during 1 hour exposure time. Reproduced with the permission of A. Vigan .

Figure 2 .

 2 Figure 2.22. -Expected detection limits for targets around a bright star (H = 4.7) similar to 51 Eri during 2 hours exposure time. Reproduced with the permission of A. Vigan.

Figure 2 .

 2 Figure 2.23. -Centring strategy schemes. Each row represents a strategy. The blue frames represent the calibration procedure for each strategy, while the black frames are assigned to the centring procedure. The panels labelled 1-5 show the steps followed to place the planet's PSF into the science fibre. Reproduced with permission from (El Morsy et al., 2022).

  Paul et al., 2013), the ZELDA wavefront sensor (N'Diaye et al., 2013; Pourcelot et al., 2021), and the Roddier and Roddier coronagraph (N'diaye et al., 2010; N´Diaye, M. et al., 2012; Soummer, Aime, et al., 2003; Soummer, Dohlen, et al., 2003b).

Figure 3 .

 3 Figure 3.1. -Picture of the MITHiC testbed. The red inset represents the laser source mount used to generate the stellar PSF. In the purple inset, there is the system used to polarise the light going to the system. The blue inset shows the SLM device, placed in the corner of the bench and operating in reflection.

Figure 3 . 2 .

 32 Figure 3.2. -Schematic drawing of the MITHiC testbed. The blue box indicates the fibre injection module (FIM) and the orange box indicates the telescope and SPHERE. Focal planes are represented as red dots and pupil planes are in green. The bench control computer is not represented. The scale and distances between optics are not respected in this drawing. Reproduced with permission from (El Morsy et al., 2022).

Figure 3

 3 Figure 3.3. -Schematic drawing of the LCOS-SLM principle. Source:http://www.piphotonics.co.jp/EN/hologram/slm.html

Figure 3 . 4 .

 34 Figure 3.4. -Schematic diagram of the ZELDA analysis with wavefront errors in the entrance pupil plane A. The mask is centred on the stellar PSF in the next focal plane B and the intensity measurement in the pupil plane is re-imaged in the plane C. The aberration reconstruction is performed from the measured intensity. Credit: (N'Diaye et al., 2013)

Figure 3 . 6 .

 36 Figure 3.6. -ZELDA Wavefront map in a unit of Optical Path Difference (OPD). Wenotice that there are no remaining wrinkles in the pupil. These wrinkles are generated from a slight offset between the SLM and the beam. These offsets explain the difficulty to achieve a correction below 20 nm.

Figure 3 . 7 .Figure 3 . 8 .

 3738 Figure 3.7. -Optimisation of the CLC Lyot stop size with respect to mean contrast (Credit: A. Vigan)

Figure 3 . 9 .

 39 Figure 3.9. -Lyot stop on MITHiC. Left panel: schematic specification drawing. Right panel: picture of the Lyot stop on its mount.

Figure 3 .

 3 Figure 3.10. -Picture of the custom 2m length fibre bundle from Thorlabs used onMITHiC. The bundle is composed of one common part followed by seven split ends. The common part of the bundle, represented as the black part is connected to the collimator by an SMA connector and the seven SMF in yellow have FC/PC connectors, and are either connected to the power meters or the calibrations sources.

Figure 3 . 3 . 1 .

 331 Figure 3.11. -View of the Thorlabs fibre bundle with a binocular. The seven dark circles are the cladding of the seven fibres (125 µm diameter). In the centre of each of these fibres, the core (4.5 µm diameter) is visible (bright spots). The science and centring fibres are respectively represented in red and blue and connected with SMF to two power meters. The four retro-injection fibres are represented in green and are connected with SMF to the retro-injection home-built setup. The spare fibre is not labelled. Reproduced with the permission of (El Morsy et al., 2022)

Figure 3 . 13 123 3 . 1 .Figure 3 .

 313313 Figure 3.12. -Picture of the Home build LEDs setup controlled by an Arduino microcontroller. The red inset shows the four electronic boards placed on the rack beneath the fibres. The electronic diagram used to build this setup is shown in Fig. 3.13

Figure 3 .

 3 Figure 3.14. -Plot of the computed Modulation transfer function of the tracking camera on MITHiC. The threshold value is used to establish the correspondence between λ/D and pixel units.

Figure 3 .

 3 Figure 3.15. -Picture of PICMA actuators with electrodes with a 20 A charging current.The meander-shaped design of the strips ensures stable electrical contact with all inner electrodes.

Figure 3 .

 3 Figure 3.16. -Design of the piezo tip-tilt system. Left: Motion directions of parallel kinematics. Right: schematic diagram of a piezo tip/tilt mirror with a piezo actuator. Source: PI

Figure 3 .

 3 Figure 3.17. -Controller diagram for piezo-system interacting between actuator, sensor and user in a closed loop. Source: Nanofaktur

  .20) is the one with the least optical aberrations with 19.68 nm PV which is within the HiRISE specification accuracy of λ/20 (31.6 nm PV).

Figure 3 .

 3 Figure 3.18. -Fizeau Phase-shifting laser interferometer principle draw. The reference is moved in precise steps with regard to the test surface. Source: 4D Technology.

Figure 3 .

 3 Figure 3.19.-Laboratory setup used to perform the metrology study of the mirror that is to be glued on the tip-tilt platform. The Fizeau Phase-shifting laser interferometer is on the left on the picture with the reference surface directly implemented in the device (black ring). On the right side of the picture, we see the tested mirror on its mount. The mirror has been tilted only when the picture has been taken.

Figure 3 .

 3 Figure 3.20. -Screenshot of the metrology wavefront error for the selected mirror.

Figure 3 .

 3 Figure 3.21. -Mirror gluing procedure on the piezo tip-tilt platform. The image is divided into three rows with three panels per row and follows several steps in time. The first row, first panel represents the schematic draw realised to understand the challenge regarding the size of the piezo platform and the size of the mirror. The second panel represents the 3D printed aid used to perfectly centre the mirror on the platform. The third panel of the first row shows the tip-tilt without the mirror. The second row, all panels, display the positioning of the wires on the platform, the automatic glue dispensing device and the mirror centred due to the aid. The last row shows the last steps of the gluing procedure and the TTM on MITHiC.

Figure 3 .

 3 Figure 3.22. -View of the tip-tilt platform with the infrared camera. Temperature elevation with respect to ambient for the tip-tilt platform during calibration is similar to what is expected in HiRISE. The tip-tilt stage was on for approximately 2 hours when this picture was taken. Point number 5 corresponds to the temperature sensor located in front of the TTM.

Figure 3 .

 3 Figure 3.23. -View of the tip-tilt controller and power supply with the infrared camera.Temperature elevation with respect to the ambient air for the tip-tilt stage controller and its power supply. The black rectangle on top of the controller is the aluminium tape that holds the temperature sensor, which has a different emissivity than the rest of the controller surface.

3. 1 .Figure 3 .

 13 Figure 3.24. -Tip-Tilt linearity test on MITHiC. The linearity is realised for each axis separately and the residuals are shown for the entire tip-tilt range.

Fig. 3 .

 3 Fig. 3.25 displays the data recorded during a week-end. It represents the position of the PSF in both the X and Y axis recorded on the tracking camera as a function of time, humidity and temperature. The PSF drifted by more than a pixel during the week-end, and a trend with the temperature and humidity is noticed.

Figure 3 .

 3 Figure 3.25. -PSF behaviour in time as a function of temperature and humidity.

Figure 3 . 3 . 1 .

 331 Figure 3.26. -PSF coordinates in X and Y axis as a function of humidity and temperature.

Figure 3 .

 3 Figure 3.27. -Power spectral density (PSD) plots from experimental data acquired on the MITHiC testbench. The PSF centroid data is sampled at a high frequency using a tracking camera placed at the focal plane between the L4 lens and the mirror (Fig. 3.2) and only the PSDs in the X-axis are shown in this figure. The upper panel shows a peak at 56.4 Hz due to the vibration of a nearby electronic device. The lower panel shows the PSD after mitigating steps were undertaken. No major sources of vibration at specific frequencies remain.

Figure 3 .

 3 Figure 3.28. -Plot of the PSF jitter estimated in the laboratory. The blue crosses represent the data and the red circle represents the uncertainty.

Figure 3 . 144 3Figure 3 .

 31443 Figure 3.29. -Injection map obtained with the centring power meter by scanning a grid of 6×6 λ/D with a pitch of 0.05 λ/D in both directions. The red circle represents the required accuracy of 0.1λ/D.

Figure 3 .

 3 Figure 3.31. -Calibration map used to perform the interpolation function. The blue lines represent the FoV of the tracking camera in pixel. Each dots represent a tip-tilt position in mrad for which a stellar PSF image is acquired on the tracking camera.

3. 3 .Figure 3 .

 33 Figure 3.32. -Distribution of the residual interpolation function: the probability density as a function of the δ distance. It represents the accuracy of the interpolation function to place the stellar PSF at any position on the camera FoV.

Figure 3 .

 3 Figure 3.33. -Residual of the interpolation function as measured on the tracking camera. The red cross and the blue cross give the positions of the science and centring fibre, respectively. The concentric rings in white represent the different angular separations (5, 10, 15 and 20 λ/D) and the different angular positions of the planet when the star is well centred on the centring fibre. The colour bar corresponds to the uncertainty error on the interpolation function. We note that 97.61% of the points mentioned in Fig. 3.32 are within the specification accuracy of 0.1 λ/D.

Figure 3 .

 3 Figure 3.34. -Measurements of the distance between the centring fibre and the science fibre for 100 consecutive tests. The red circle represents the accuracy requirement of 0.1 λ/D. The blue cross corresponds to the mean position of -4.416 mrad in tip, -2.183 mrad in tilt and the standard deviation is estimated at 0.007 mrad in both directions.

Figure 3 .

 3 Figure 3.35. -Log-scale image acquisition on the tracking camera. The four feedback fibres represented as green fibres are imaged in the focal plane camera and used to localise the science fibre. The beacon's spot represents the stellar PSF injected into the science SMF and the planet's PSF is not displayed. The ghosts are caused by the reflection of light in the optical system.

Figure 3 .

 3 Figure 3.36. -Success rate as a function of position angle around the star. The resultsfor the first, second, and third strategies are plotted in the upper, middle, and lower panels, respectively. The grey area represents the region where an emphasised trend is found. The black dashed lines at 90˚and 210˚represent the angles for which additional tests are performed and demonstrated in Fig.3.39.

Figure 3 .Figure 3 .

 33 Figure 3.38. -Success rate in the science fibre for the positioning of the star. Each dot is obtained for one entire centring procedure. The circles correspond to the different accuracies and the error bar gives the PSF's jitter uncertainty.

Figure 4 .

 4 Figure 4.2. -Pictures of the pre-assembly of the FIM in the mechanical workshop.Left: the FIM as it will be inserted in SPHERE. The cover (on the table) will be used to baffle the core optics bench. Middle: we can see the core optics bench, the fibre mount and the helicoils implemented in their holes. Right: we see the position of the pick-off mirror and the bottom part of the FIM.

Figure 4 . 3 .

 43 Figure 4.3. -Picture of the SPHERE Simulator in the clean room at LAM

Figure 4 .

 4 Figure 4.4. -Picture of the optical cube. Top panel: a mechanical overview of the optical cube. Bottom Left: mechanical pieces and tools required to assemble the optical cube. Bottom right: optical cube after its assembly and alignment.

Figure 4 . 5 .

 45 Figure 4.5. -Picture of the core optics bench

Figure 4 . 6 .

 46 Figure 4.6. -Picture of the FIM sub-system tested with the WFS (Phasics).

Figure 4 . 7 .

 47 Figure 4.7. -Diagram showing the contribution of the expected aberrations (Model as-built) and the aberrations measured after aligning the COB (Data). The model as-built corresponds to the Zemax model with the thickness and radius of curvature values of the real lenses manufactured by Fichou.

Figure 4 .

 4 Figure 4.8. -CAD views of the FIM sub-system implemented vertically. The red boxes represent the perspective view from the IFS beam entering the FIM and the mirror at the ends corresponds to the pick-off mirror.

Figure 4 .

 4 Figure 4.9. -Top: CAD view of the FIM main bench with the COB and its components implemented. Bottom: Picture of the lenses and mirrors located on the main bench. These optics have been carefully glued to their Polaris mount.

Figure 4 .

 4 Figure 4.10. -Left: CAD image of the FIM with these alignment tools and pinholes in place. Right: Picture of one of the 3D printed alignment tools for the FIM (red inset).

Figure 4 .

 4 Figure 4.12. -Picture of the FEM mechanical assembly steps in the clean room. The red box corresponds to the ferrule, where the FB will be connected in the FEM side.

FIMFigure 4 .

 4 Figure 4.13. -Picture of one of the foreseen alignment tests of the FEM. The SMF will be carefully inserted all the way down into the ferrule. The beam output is located at the left FEM's side in the picture. Lenses would be probably used to test the quality of the image on the Phasics and the camera.

4. 1 .

 1 Figure 4.14. -Pictures of the 3D printed mounts to be interfaced with the SMF.

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  al. (2017) developed a detailed model of HDC observations and analysed the trade-off between starlight suppression and spectral resolution for the characterisation of young giant exoplanets in the NIR. This framework opened the path for HDC, which is now implemented in several projects on existing telescopes: Keck/KPIC (Delorme et al. 2021), Subaru/REACH (Kotani et al. 2020), and VLT/HiRISE (Vigan et al. 2018).

A171, page 2 of 14 MFig. 1 .

 141 Fig. 1. Schematic of the design of the HiRISE/FIM. The main optical components are labelled, as are the photon sharing between wavelengths for the tracking (0.95-1.3 µm) and the science (1.4-1.8 µm).

2. 1 .

 1 Description of HiRISEConceptually, HiRISE diverts the SPHERE/IFS beam downstream of the ExAO and coronagraph, and injects the light of a known exoplanet into a SMF. This fibre is connected to the NIR spectrograph CRIRES+ on the opposite Nasmyth platform, which is used to disperse the light of the planet at high spectral resolution. The practical implementation requires three interconnected elements: the FIM implemented inside of SPHERE that takes care of properly injecting the planetary signal into the science fibre, the FB around the telescope that routes the science fibre and additional fibres between the two Nasmyth platforms, and the FEM implemented inside of CRIRES+ that reimages the science fibre's output at the entrance of the spectrograph with the right optical properties. Since the current work focuses on the strategies to best inject the planet's signal into the science fibre, we describe in greater detail the FIM, and refer the reader to other works for the descriptions of the other elements(Vigan et al. 2018; Otten et al. 2021).

3. 1 .

 1 Optical setup MITHiC is a HCI testbed located in the optics laboratory at the Laboratoire d'Astrophysique de Marseille (France). It was developed in 2010 and has been used to develop and test various methods for HCI, such as COFFEE (Paul et al. 2013), the ZELDA wavefront sensor (N'Diaye et al. 2013; Pourcelot et al. 2021), and the Roddier and Roddier coronagraph (Soummer et al. 2003a,b; N'Diaye et al. 2010, 2012). The testbed has already been described in detail in Pourcelot et al. (2021), so we only mention the key elements in this section.

Fig. 3 .

 3 Fig. 3. Schematic drawing of the MITHiC testbed. The blue box indicates the fibre injection module (FIM) and the orange box indicates the telescope simulator. Focal planes are represented as red dots and pupil planes are in green. The bench control computer is not represented. The scale and distances between optics are not respected in this drawing.

Fig. 4 .

 4 Fig.4. View of the Thorlabs fibre bundle with a binocular. The seven dark circles are the cladding of the seven fibres (125 µm diameter). In the centre of each of these fibres, the core (4.5 µm diameter) is visible (bright spots). The science and centring fibres are respectively represented in red and blue and connected with SMF to two power meters. The four retro-injection fibres are represented in green and are connected with SMF to the retro-injection home-built setup. The spare fibre is not labelled.

  1 λ/D and 1 λ/D regions around the centre. The injection map represents the flux A171

Fig. 5 .Fig. 6 .

 56 Fig. 5. Injection map obtained with the centring power meter by scanning a grid of 6 × 6 λ/D with a pitch of 0.05 λ/D in both directions. The red circle represents the required accuracy of 0.1 λ/D.

Fig. 7 .

 7 Fig. 7. Measurements of the distance between the centring fibre and the science fibre for 100 consecutive tests. The red circle represents the accuracy requirement of 0.1 λ/D. The blue cross corresponds to the mean position of -4.416 mrad in tip, -2.183 mrad in tilt and the standard deviation is estimated at 0.007 mrad in both directions.

Fig. 8 .

 8 Fig. 8. Log-scale image acquisition on the tracking camera. The four feedback fibres represented as green fibres are imaged in the focal plane camera and used to localise the science fibre. The beacon's spot represents the stellar PSF injected into the science SMF and the planet's PSF is not displayed. The ghosts are caused by the reflection of light in the optical system.

Fig. 9 .

 9 Fig. 9. Distribution of the residual interpolation function: the probability density as a function of the δ distance. It represents the accuracy of the interpolation function to place the stellar PSF at any position on the camera FoV.strategy, the calibration follows the same steps, but measures the I-C offset.4.1.4. Accurate positioning of the PSFA final calibration is required to be able to accurately position the stellar PSF at any coordinate on the tracking camera. We use a non-linear approach with an interpolation function based on a full 2D calibration of the response of the tip-tilt mirror(Yelda et al. 2010;Service et al. 2016), as seen by the tracking camera. To create the interpolation function, we build a calibration grid by scanning a 12.5 × 12.5 mrad area in tiptilt, with a pitch of 2 mrad. For each tip-tilt position, the stellar PSF is imaged on the tracking camera and a 2D Gaussian fit is used to compute the PSF's centre in pixels. The Gaussian fit accuracy has been estimated to ∼0.01 pix, which corresponds to 0.03 λ/D. The calibration grid is then provided as input data to the LinearNDInterpolator function from the scipy library (Virtanen et al. 2020), which uses the Delaunay triangulation method to perform interpolations in N dimensions. Using the resulting interpolation function, it is possible to obtain the tip-tilt command to place the stellar PSF at any position in the camera's FoV.An alternative approach would be to use a classical AOlike interaction matrix, where the relationship between the focal plane position and the tip-tilt commands is calibrated by introducing a single known offset in tip and tilt. However, this approach assumes that the offset value does not matter because there is a strictly linear relationship. This is not the case in our system because of optical distortions introduced between the tiptilt mirror and the tracking camera, which is why an interpolation grid was adopted.We estimated the accuracy of the positioning by using the interpolation function to place the PSF on a test grid of 48 × 48 points interleaved with the original calibration grid. For each target position, the position of the PSF was estimated on the tracking camera image and compared to the target position to compute the residuals. We find that 6% of the outliers are located at more than 20σ from the sample data mean. We reject all outliers located beyond three standard deviations from the sample data mean. The histogram of the residuals for the full test grid is displayed in Fig.9. The residuals are quasi-Gaussian with a standard deviation of 0.03 λ/D, which is well below 0.1 λ/D. Even taking into account the wings of the distribution, 97.61% of the residuals fall within ±0.1 λ/D.

Fig. 10 .

 10 Fig. 10. Residual of the interpolation function as measured on the tracking camera. The red cross and the blue cross give the positions of the science and centring fibre, respectively. The concentric rings in white represent the different angular separations (5, 10, 15 and 20 λ/D) and the different angle positions of the planet when the star is well centred on the centring fibre. The colour bar corresponds to the uncertainty error on the interpolation function. We note that 97.61% of the points mentioned in Fig. 9 are within the specification accuracy of 0.1 λ/D.

Fig. 13 .

 13 Fig.13. Success rate in the science fibre for the positioning of the star. Each dot is obtained for one entire centring procedure. The circles correspond to the different accuracies and the error bar gives the PSF's jitter uncertainty.

Fig. 14 .

 14 Fig.14. Success rate in the centring and science fibre for the positioning of the planet. Top panel: success rate in the centring and science fibre for the planet at a position angle of 90°from the star. Bottom panel: same results, but for a position angle of 210°. Each dot is obtained for one entire centring procedure. The circles correspond to the different accuracies and the error bar gives for the PSF's jitter uncertainty.

Figure 1 :

 1 Figure 1: Schematic of the design of the HiRISE/FIM. Reproduced with permission from El Morsy et al.27

Figure 3 :

 3 Figure 3: Schematic drawing of the MITHiC testbed. The blue box indicates the fibre injection module (FIM) and the orange box indicates the telescope simulator. Focal planes are represented as red dots and pupil planes are in green. The bench control computer is not represented. The scale and distances between optics are not respected in this drawing.Reproduced with permission from El Morsy et al.27

Figure 4 :

 4 Figure 4: Picture of the MITHiC testbed. The red inset represents the laser source mount used to generate the stellar PSF.In the blue inset, we notice the tip-tilt mirror placed at 45 • with regard of the optical axis. The purple inset represents the fibre bundle manufactured by Thorlabs, it is composed of several SMF. Two of these SMFs are connected to two different power meters while four feedback fibres (in green) are connected to calibration sources placed outside of the bench. The yellow inset shows the home-build setup used to retro-inject light into the four feedback fibres.

Figure 5 :

 5 Figure 5: Power spectral density (PSD) plots from experimental data acquired on the MiTHIC testbench. The PSF centroid data is sampled at a high frequency using a tracking camera placed at the focal plane between the L4 lens and the mirror (Fig. 3) and only the PSDs in the X-axis are shown in this figure. The upper panel shows a peak at 56.4 Hz due to the vibration of a nearby electronic device. The lower panel shows the PSD after mitigating steps were undertaken. No major sources of vibration at specific frequencies remain.

Figure 7 :

 7 Figure 7: (a) left panel: coupling efficiency as a function of displacement between the PSF core and the Gaussian mode of the fibre simulated for three different coronagraph options and evaluated at 1.6 µm. 24 (b) right panel: radial profile of the injection map computed with the centring fibre on MiTHIC. Reproduced with permission from El Morsy et al.27

GENERALScaleScale

  DESIGN LIMITS (except special instruction) Mechanical part : ISO 2768-1&2-mK-E / ISO 2768-1&2 Facing surface : Ra3.2 / NFE 05-016 Technopole de Chateau Gombert -Site de Marseille Etoile 38, rue Frédéric Joliot-Curie -13388 MARSEILLE cedex 13 Tel. (33) 04 91 05 59 00 -www.lam.fr Ce plan est notre propriété. Il ne peut être copié, reproduit ou transmis à des tiers sans autorisation écrite. VLT-DWG-SPH-14690-1-662110-6054-A (except special instruction) Mechanical part : ISO 2768-1&2-mK-E / ISO 2768-1&2 Facing surface : Ra3.2 / NFE 05-016 Technopole de Chateau Gombert -Site de Marseille Etoile 38, rue Frédéric Joliot-Curie -13388 MARSEILLE cedex 13 Tel. (33) 04 91 05 59 00 -www.lam.fr Ce plan est notre propriété. Il ne peut être copié, reproduit ou transmis à des tiers sans autorisation écrite.VLT-DWG-SPH-14690-1-662200-6058-A

  William Shakespeare, Julius Caesar "Three Rings for Elven-Kings under the sky Seven for the Dwarf-Lords in their halls of stone Nine for Mortal Men doomed to die One for the Dark Lord on his dark throne In the Land of Mordor where the Shadows lie".

	Alexandre Dumas, Le Comte de Monte-Cristo
	"... the snow keeps falling, like a ceaseless repetition of the same infinitesimally small
	mistake."
	Sally Rooney, Normal People

J.R.R. Tolkien, The Lord of the Rings "The way love can disregard fears, however, is an age-old wonder. No fear is able to spoil love's development or keep it from dreaming of its appointed hour." Naguib Mahfouz, Palace Walk "Avec l'amour maternel, la vie vous fait, à l'aube, une promesse qu'elle ne tient jamais." Romain Gary, La Promesse de l'aube "Something may be a sort of fulfillment of yourself, and it may not be great to other people, but it is just as essential to yourself as if it is a great masterpiece." Zelda Fitzgerald, Save Me the Waltz "Your defect is a propensity to hate everybody." "And yours," he replied with a smile, "is willfully to misunderstand them." Jane Austen, Pride and Prejudice Oui, ma fille, dit Monte Cristo; tu sais bien que ce n'est jamais moi qui te quitterai. Ce n'est point l'arbre qui quitte la fleur, c'est la fleur qui quitte l'arbre. "E quindi uscimmo a riveder le stelle." Dante Alighieri, Divina Commedia

  .3. Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . State of the art of spectrographs . . . . . . . . . . . . . . . . . . . 1.4. High dispersion coronagraphy . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction 1.1. Is there life out there? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1. State of the art and methods of exoplanet detection . . . . . . . 1.2. High contrast imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1. Limitations of the technique . . . . . . . . . . . . . . . . . . . . . 1.2.2. Image formation through a telescope . . . . . . . . . . . . . . . . 1.2.3. AO system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.4. Coronagraphy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.5. Post-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.6. Discoveries with Ground-based telescopes . . . . . . . . . . . . . 11.3.1. Historical introduction . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.2. Resolving power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.3. From Low to High-Resolution Spectroscopy . . . . . . . . . . . . 1.3.4. 1.4.1. Combining HCI and HDS . . . . . . . . . . . . . . . . . . . . . . . 1.4.2. Optical fibres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.3. Coupling a telescope PSF into a SMF . . . . . . . . . . . . . . . . 1.5. This thesis and outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  2.1. High-Dispersion Coronagraphy on the VLT with HiRISE . . . . . . . . . 74 2.1.1. The SPHERE high-contrast imager on the VLT . . . . . . . . . . . 75 2.1.2. CRIRES+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 2.1.3. Combining SPHERE and CRIRES+ to obtain HiRISE . . . . . . . 83 2.1.4. HiRISE instrument description . . . . . . . . . . . . . . . . . . . . 85 2.1.5. Expected performance of HiRISE . . . . . . . . . . . . . . . . . . . 2.1.6. First targets objective of HiRISE . . . . . . . . . . . . . . . . . . . 2.2. Centring strategies for HiRISE . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1. Centring strategies in a non-coronagraphic configuration . . . . 2.2.2. Centring strategies in a coronagraphic configuration . . . . . . .

  Integration and alignment of the FIM . . . . . . . . . . . . . . . . 4.1.3. Integration and alignment of the FEM . . . . . . . . . . . . . . . . 4.2. HiRISE AIT at the VLT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1. Unpacking and verification . . . . . . . . . . . . . . . . . . . . . .

4.1. HiRISE AIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1. Pre-assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2. 4.2.2. Telescope installation . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3. Commissioning plan for HiRISE . . . . . . . . . . . . . . . . . . . 4.3. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  A. Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.1. El Morsy et al., Astronomy & Astrophysics, 2022, Volume 667, id. A171 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.2. El Morsy et al., Proceedings of the SPIE, 2022, Volume 12185, id. 121858O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Centring strategy: application to the object selection mechanism (OSM) prototype for HARMONI/ELT . . . . . . . . . . . . . . . . . . . . . . . . . C. FEM mechanical design . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  1.1. Cumulative number of detections by year and discovery methods. Generated by NASA Exoplanet Archive on January 28, 2023. . . . . . . . . . 1.2. Mass-period distribution of detected exoplanets. Generated by the NASA Exoplanet Archive on January 28, 2023. . . . . . . . . . . . . . . . . . . . 1.3. Illustration of the radial velocity method. Credits: Johan Jarnestad/The Royal Swedish Academy of Sciences. . . . . . . . . . . . . . . . . . . . . 1.4. Picture of the telescope T193 at OHP.The white cylinder contains the fibre head for the Elodie spectrograph. Principle of adaptive optics. Credit: LLNL, Center for Adaptive optics. 1.13.Light propagation through a Lyot coronagraph. Credit: Emiel Por (PhD thesis) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.14.Color-color diagrams for HR 8799bcde. All exoplanets and brown dwarfs start as M-type objects, cooling and moving redward to the L spectral type and then transitioning to a T spectral type. Credit: Charnay et al. (2018) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.15.The effect of increasing spectral resolution. The two panels represent different wavelength regions of a hot Jupiter atmospheric model containing water and carbon monoxide. Top panel: Credit: Birkby (2018) . 1.16.Illustration of integral field spectrographs: the lenslet array, the fibre bundle with a lenslet array, and the image slicer. Extracted from Westmoquette et al. (2009), itself adapted from Allington-Smith et al. (1998). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.17.Comparison diagram between single-mode fibres and multimode fibres. 1.18.Coupling efficiency to a SMF simulated for VLT-like pupil. Credit: HiRISE team. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.19.Coupling efficiency to a SMF simulated for several telescopes as a function of the relative size of their central obstruction and with and without spiders for several major observatories. Credit: Jovanovic et al. (2017). 2.1. HiRISE implementation concept at the UT3/VLT. On the opposite Nasmyth platforms lay SPHERE and CRIRES+, and the fibre bundle which connects them. . .7. IFS layout with its own Lyot stop and internal calibration sources. Credit: SPHERE consortium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8. IFS spectrum of HIP 65426 b (grey circles) compared with the BT-SETTL best-fit atmospheric model in blue, computed at a T e f f of 1660 K (Chauvin et al. 2017, ESO-ANN17041). . . . . . . . . . . . . . . . . . . . . . . . 2.9. Optical layout of CRIRES+. The instrument is located in a cryostat (dark area). The AO system, the derotator, and calibration devices are in a warm part between the telescope and the spectrograph (grey area). The red cylinder represents the new absorption gas cell. .10.Fibre injection module implemented as a vertical bench in the IFS arm of SPHERE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.11.Picture of the pre-assembly of the FIM mechanical structure at the Laboratoire d'Astrophysique de Marseille. . . . . . . . . . . . . . . . . . . . . 2.12.Schematic of the design of the HiRISE/FIM. The main optical components are labelled, as are the photon sharing between wavelengths for the tracking (0.95-1.3 µm) and the science (1.4-1.8 µm). Reproduced with permission from (El Morsy et al., 2022). . . . . . . . . . . . . . . . . 2.13.Temperature increase with regards to the ambient air in the laboratory for the C-RED 2 tracking camera and its power supply running at high cadence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.14.Schematic of the optical design of the HiRISE/FEM. The bundle output is located on the top of the vertical part of the layout. . . . . . . . . . . . 2.15.CAD view of the FEM implementation in CRIRES+. The upper image represents the FEM view without the cover. . . . . . . . . . . . . . . . . 2.16.Global concept for the fibre bundle. The bundle manufactured by Fib-Expected SNR of the CCF analysis on HiRISE science targets during 2 hours exposure time. The grey diamonds represent the HiRISE targets foreseen in the future. Reproduced with the permission of A. Vigan . . 104 2.21.Expected detection limits for targets around a star (H = 6.3) similar to HD 4113 during 1 hour exposure time. Reproduced with the permission of A. Vigan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 2.22.Expected detection limits for targets around a bright star (H = 4.7) similar to 51 Eri during 2 hours exposure time. Reproduced with the permission of A. Vigan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 2.23.Centring strategy schemes. Each row represents a strategy. The blue frames represent the calibration procedure for each strategy, while the black frames are assigned to the centring procedure. The panels labelled 1-5 show the steps followed to place the planet's PSF into the science fibre. Reproduced with permission from (El Morsy et al., 2022). . . . . 3.1. Picture of the MITHiC testbed. The red inset represents the laser source mount used to generate the stellar PSF. In the purple inset, there is the system used to polarise the light going to the system. The blue inset shows the SLM device, placed in the corner of the bench and operating in reflection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Schematic drawing of the MITHiC testbed. The blue box indicates the fibre injection module (FIM) and the orange box indicates the telescope and SPHERE. Focal planes are represented as red dots and pupil planes are in green. The bench control computer is not represented. The scale and distances between optics are not respected in this drawing. Reproduced with permission from (El Morsy et al., 2022). . . . . . . . . 3.3. Schematic drawing of the LCOS-SLM principle. Source:http://www.piphotonics.co.jp/EN/hologr 3.4. Schematic diagram of the ZELDA analysis with wavefront errors in the .9. Lyot stop on MITHiC. Left panel: schematic specification drawing. Right panel: picture of the Lyot stop on its mount. . . . . . . . . . . . . . . . . 3.10.Picture of the custom 2m length fibre bundle from Thorlabs used on MITHiC. The bundle is composed of one common part followed by seven split ends. The common part of the bundle, represented as the black part is connected to the collimator by an SMA connector and the seven SMF in yellow have FC/PC connectors, and are either connected to the power meters or the calibrations sources. . . . . . . . . . . . . . . 3.11.View of the Thorlabs fibre bundle with a binocular. The seven dark circles are the cladding of the seven fibres (125 µm diameter). In the centre of each of these fibres, the core (4.5 µm diameter) is visible (bright spots). The science and centring fibres are respectively represented in red and blue and connected with SMF to two power meters. The four retro-injection fibres are represented in green and are connected with SMF to the retro-injection home-built setup. The spare fibre is not labelled. Reproduced with the permission of (El Morsy et al., 2022) . . 3.12.Picture of the Home build LEDs setup controlled by an Arduino microcontroller. The red inset shows the four electronic boards placed on the rack beneath the fibres. The electronic diagram used to build this setup is shown in Fig. 3.13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.13.The electronic diagram used for one circuit represented as the red inset in Fig. 3.12. We soldered to the circuit several electronic components such as a LED, resistors, and MOSFETs. . . . . . . . . . . . . . . . . . . . 3.14.Plot of the computed Modulation transfer function of the tracking cam-

Credit: E. Perrin. . . . . . . . . 1.5. Radial velocity curve of the star 51 Peg obtained with the ELODIE spectrograph (Mayor and Queloz 1995) . . . . . . . . . . . . . . . . . . . . . 1.6. Illustration of a Light Curve of a Planet Transiting Its Star. Credit: NASA Ames. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7. Planetary transit detection by the CoRoT satellite. Credit: CoRoT/CNES 1.8. Direct images of HR 8799 system with the four planets (a, b, c, d) performed with the Keck at different epochs. Credit: Marois et al. (2010

) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.9. Light intensity curves for several planetary bodies compared with the Sun in yellow. These curves are normalised with respect to the maximum light intensity of the Sun. Credit: thesis Jacques-Robert Delorme. . . . 1.10.Schematic of Fourier formalism application. Credit: Fabrice Vidal. . . 1.11.Representation of the Zernike polynomials and corresponding types of aberration. (Y. H. Hsieh, 2020). . . . . . . . . . . . . . . . . . . . . . . . . 1.12.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. SPHERE block diagram. The instrument is divided into four subsystems: the common path infrastructure (CPI), the Zurich Imaging Polarimeter (ZIMPOL) and the Infrared Dual Imager and Spectrograph (IRDIS). Blue and orange arrows indicate the optical path to NIR and VIS, respectively. Credit: (Beuzit et al., 2019). . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Top view of the SPHERE CAD. The CPI bench comprising the wavefront sensor and the other components are detailed in Fig. 2.4. The light coming from the telescope is coming from the top (window, shutter). Credit: (Beuzit et al., 2019) . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Zoomed view of the SPHERE CPI with the VIS wavefront sensor and the ADCs elements. Credit: (Beuzit et al., 2019) . . . . . . . . . . . . . . . . 2.5. Adaptive optics bloc diagram of SPHERE. The VIS+NIR optical path is represented in orange, the VIS in dark blue and the NIR in red. The light blue paths represent the control loops. . . . . . . . . . . . . . . . . . . . 2.6. Top: Theoretical and measured (purple circles) SAXO Strehl ratio as a function of R magnitude for good seeing conditions (0.8 ′′ -1.2 ′′ ) and different wavelength ranges from V to K. Bottom: SPHERE PSF shape and Strehl ratio as a function of R magnitude. Credit: SPHERE, system analysis report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Credit: CRIRES+ consortium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2ertech Optica is divided in three sections: section A on the SPHERE side, section B around the telescope structure, and section C on the CRIRES+ side (Vigan et al., 2022). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.17.Picture of the HiCab with the devices installed on the racks . . . . . . . 2.18.Coupling efficiency as a function of displacement between the PSF core and the Gaussian mode of the fibre simulated for three different coronagraph options and evaluated at 1.6 µm (Otten et al., 2021). . . . . . . . 101 2.19.(Top) Transmission budget for HiRISE, based on the final hardware (FIM, FEM), on simulations (fibre coupling), on laboratory measurements and theoretical values (fibre transmission), on measurements provided by SPHERE and CRIRES+ consortia and on theoretical values (sky, telescope) (Vigan et al., 2022). (Bottom) Expected end-to-end transmission of the system based on the transmission budget (in blue). The plot includes a comparison with the former transmission budget established by (Otten et al., 2021). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 2.20.entrance pupil plane A. The mask is centred on the stellar PSF in the next focal plane B and the intensity measurement in the pupil plane is re-imaged in the plane C. The aberration reconstruction is performed from the measured intensity. Credit: (N'Diaye et al., 2013) . . . . . . . . 3.5. Picture of the Zelda mask on its mount with the Zelda camera placed in a pupil plane on MITHiC. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6. ZELDA Wavefront map in a unit of Optical Path Difference (OPD). We notice that there are no remaining wrinkles in the pupil. These wrinkles are generated from a slight offset between the SLM and the beam. These offsets explain the difficulty to achieve a correction below 20 nm. . . . 3.7. Optimisation of the CLC Lyot stop size with respect to mean contrast (Credit: A. Vigan) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8. Focal plane mask on MITHiC. Top row, left panel: focal plane mask specification drawing. Top row, right panel: image of the focal plane mask on its mount. Bottom row, left and right panels: views of the mask and fiducials with a binocular. . . . . . . . . . . . . . . . . . . . . . . . . 3era on MITHiC. The threshold value is used to establish the correspondence between λ/D and pixel units. . . . . . . . . . . . . . . . . . . . . . 3.15.Picture of PICMA actuators with electrodes with a 20 A charging current. The meander-shaped design of the strips ensures stable electrical contact with all inner electrodes. . . . . . . . . . . . . . . . . . . . . . . . 3.16.Design of the piezo tip-tilt system. Left: Motion directions of parallel kinematics. Right: schematic diagram of a piezo tip/tilt mirror with a piezo actuator. Source: PI . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.17.Controller diagram for piezo-system interacting between actuator, sensor and user in a closed loop. Source: Nanofaktur . . . . . . . . . . . . . 3.18.Fizeau Phase-shifting laser interferometer principle draw. The reference is moved in precise steps with regard to the test surface. Source: 4D Technology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.19.Laboratory setup used to perform the metrology study of the mirror that

  4.1. AIT Block Diagram. Several paths are developed individually (horizontal line). All the sub-systems are represented as red insets, the SPHERE simulator is here a tool used to align HiRISE (blue inset). The dashed frames represent the AIT at the VLT and will not be described in this thesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Pictures of the pre-assembly of the FIM in the mechanical workshop. Left: the FIM as it will be inserted in SPHERE. The cover (on the table) will be used to baffle the core optics bench. Middle: we can see the core optics bench, the fibre mount and the helicoils implemented in their holes. Right: we see the position of the pick-off mirror and the bottom part of the FIM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Picture of the SPHERE Simulator in the clean room at LAM . . . . . . . 4.4. Picture of the optical cube. Top panel: a mechanical overview of the optical cube. Bottom Left: mechanical pieces and tools required to assemble the optical cube. Bottom right: optical cube after its assembly and alignment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5. Picture of the core optics bench . . . . . . . . . . . . . . . . . . . . . . . 4.6.Picture of the FIM sub-system tested with the WFS (Phasics). . . . . . . Picture of one of the foreseen alignment tests of the FEM. The SMF will be carefully inserted all the way down into the ferrule. The beam output is located at the left FEM's side in the picture. Lenses would be probably used to test the quality of the image on the Phasics and the camera. . . 4.14.Pictures of the 3D printed mounts to be interfaced with the SMF. . . .

	4.13..1. Left: The Smaract goniometer is a 2-axes platform. Both axes are sharing
	the same rotation point, allowing a flat mirror to rotate around its centre.
	Right: The HARMONI optical setup for prototyping the OS function,
	inside a cold chamber for 2˚C compatibility. The fibre-fed source is in
	the background, the goniometer is in the middle (mirror facing 45 ˚up),
	and the camera is in the foreground. . . . . . . . . . . . . . . . . . . . . .
	.2. Top: OS function performance. In red, the calibration grid is acquired
	for different commands sent to the goniometre. The pincushion shape
	is visible by the naked eye. The blue map in the background shows the
	OS function's performance in the field of view. An RMS value of this map
	is 3 mas. The interpolation residuals begin to appear and are visible
	in between the calibration points as larger error values. Bottom: OS
	function performance but with a smaller number of calibration points 4.7. Diagram showing the contribution of the expected aberrations (Model used as inputs for the model. The centring performance is worst (4 as-built) and the aberrations measured after aligning the COB (Data). against 3 mas), and the centring error is clearly visible in between the The model as-built corresponds to the Zemax model with the thickness and radius of curvature values of the real lenses manufactured by Fichou. calibration points as an additional error. . . . . . . . . . . . . . . . . . .
	4.8. CAD views of the FIM sub-system implemented vertically. The red boxes
	represent the perspective view from the IFS beam entering the FIM and
	the mirror at the ends corresponds to the pick-off mirror. . . . . . . . .
	4.9. Top: CAD view of the FIM main bench with the COB and its components
	implemented. Bottom: Picture of the lenses and mirrors located on
	the main bench. These optics have been carefully glued to their Polaris
	mount. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	4.10.Left: CAD image of the FIM with these alignment tools and pinholes in
	place. Right: Picture of one of the 3D printed alignment tools for the
	FIM (red inset). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	4.11.Picture of the FEM mechanical preparation at LAM. Pictures 1 and 2
	show the different steps to clean the FEM. Picture 3 represents some
	of the FEM components in the clean room. Picture 4 is an example of
	one of the mechanical drawings I used to verify the feasibility of the
	assembly. Different technical drawing provided by the LAM mechanical
	engineer has been useful to assemble the HiRISE sub-systems. Picture 4
	represents the screw nomenclature of the entire FEM. . . . . . . . . . .
	4.12.Picture of the FEM mechanical assembly steps in the clean room. The
	red box corresponds to the ferrule, where the FB will be connected in
	the FEM side. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Table 2 .

 2 2. -List of the HiCab devices with their peak power consumption.

			HiCab devices list
	Device	Manufacturer Model	Peak	Value
				Power[W]
	TCAM power	FLI	CRED-2	25	Measured
	supply
	Frame grabber	Pleora	iPort CL-Ten	12	Specification
	& power sup-
	ply
	TT controller &	PI	E-727.3SDA	25	Measured
	power supply
	Power meter	Thorlabs	PM101	1	Specification
	Source 1 (IR	TBD		expected <50
	LED) & power
	supply
	Source 2 (tung-	TBD	SLS201L/M	50	Specification
	sten) & power
	supply
	PLC computer	Beckhoff	CX2030	50	Specification
	& power sup-
	ply
	PLC modules	CX2030	TBD	expected <30	Specification

  al., 2021).

			1.0			Transmission budget
			0.8
	Transmission	0.4 0.6
	Transmission	1400 0.2 0.0 0.02 0.03 0.04 0.05 0.06 0.07	1450 Sky Telescope	1500 SPHERE CPI 1550 FIM Wavelength [nm] 1600 1650 Fiber (coupling) Fiber (transmission) End-to-end transmission	1700 Design as-built 1750 FEM CRIRES+ Otten et al. (2021) 1800
		0.01
		1400 0.00	1450	1500	1550 Wavelength [nm] 1600 1650	1700	1750	1800

Figure 2.19. -(Top) Transmission budget for HiRISE, based on the final hardware (FIM, FEM), on simulations (fibre coupling), on laboratory measurements and theoretical values (fibre transmission), on measurements provided by SPHERE and CRIRES+ consortia and on theoretical values (sky, telescope) (Vigan et al., 2022). (Bottom) Expected end-to-end transmission of the system based on the transmission budget (in blue). The plot includes a comparison with the former transmission budget established by (Otten et al., 2021).

Table 3 .

 3 1. -PSF drift quantification as a function of temperature and humidity.

		A: Bench Tem-	B: Humidity [%] C: offset
		perature [˚C]
	Cx coordinates	-6.53	12.70	204.00
	[pixels]
	Cy coordinates	-5.62	-0.19	187.80
	[pixels]

Table 3 .

 3 2. -Error Budget for the centring of a PSF into a SMF

			MITHiC		HiRISE (SPHERE and FIM)
		Contributors	Values (λ/D) Values (nm RMS) Values (λ/D) Values (nm RMS)
		PSF Jitter	0.04	-	0.062	2.5 mas
	Low-order	PSF drift	0.02	-	0	0
		Centring strategy	0.19*	-	0.07*	-
		AO static residuals	0.029	20	0.031	50
	High-order AO quasi-static residuals	0.014	10	0.006	10
		AO turbulence	0	-	0.06	100
		Total (quadradic)	0.20		0.12 ± 0.024

Table 3 .

 3 3. -Sub-budget error for the centring strategy

	Centring strategy	MITHiC	HiRISE
		Values (λ/D) Values (λ/D)
	Bench distortion	0.19	0.02
	Calibration precision	0.04	0.04
	Repeatability	0.01	0.05
	Total (quadratic)	0.19	0.07

SPIE Astronomical Telescopes + Instrumentation, 17-22 July 2022, Montréal (Canada)

In the Spirit of Lyot, 27 June -1 July 2022, Leiden (Netherlands)

https://www.pi-usa.us/en/products/fast-steering-mirrors-fsm-and-piezo-tiptilt-platforms-fors-335-piezo-tiptilt-platform-300711/

http://www.eso.org/observing/etc/bin/gen/form?INS.MODE=swspectr+INS.NAME= SKYCALC

https://github.com/avigan/Python-utils/blob/master/vigan/optics/focal_ ratio.py

Similar to the one presented at https://www.phasics.com/en/

Similar to the one presented at https://www.faro.com/fr-FR/Products/Hardware/ Gage-FaroArm

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Remerciements

Acknowledgements. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme, grant agreements no. 757561 (HiRISE) and from Région Provence-Alpes-Côte d'Azur d'Azur under grant agreement 2014-0276 (ASOREX project). ACKNOWLEDGMENTS This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme, grant agreements No. 757561 (HiRISE) and from Région Provence-Alpes-Côte d'Azur under grant agreement 2014-0276 (ASOREX project).

d'Arthur Vigan, dans le respect des principes d'honnêteté, d'intégrité et de responsabilité inhérents à Mona El Morsy

List of Tables

-Success rate as a function of the angular separation from the star. The results for the first, second, and third strategies are plotted in the upper, middle, and lower panels, respectively. The black dashed lines at 90˚and 210˚represent the angles for which additional tests are performed and demonstrated in Fig. 3.39.

I also tested the three strategies with planets located at different angular separations. The results are presented in Fig. 3.37 for three selected position angles: 90˚, 210˚, and 330˚. The 90˚position was selected because it is at the centre of the grey area in Fig. 3.36, where the performance is particularly low. The other two position angles are separated by 120˚. I first note that the success rate obtained at a separation of 10 λ/D is consistent with the previous test. However, there are minor differences that can be explained by the fact that the results shown here were acquired in a completely separate data acquisition sequence. . All the sub-systems are represented as red insets, the SPHERE simulator is here a tool used to align HiRISE (blue inset). The dashed frames represent the AIT at the VLT and will not be described in this thesis.

HiRISE AIT

HiRISE AIT

In this section, I present the opto-mechanical assembly of the FIM and the FEM done at LAM. It is not foreseen to repeat this step in Chile as it will be shipped fully assembled.

Pre-assembly

The optical design (carried out by Dr Edward Muslimov) has determined the toplevel requirements for the FIM and the FEM. In consultation with the mechanical department, the opto-mechanical design has been validated. The realisation of the custom optics by FICHOU has been received, controlled and validated. The realisation of the mechanical parts was carried out by the University of Göttingen in Germany.

The control of the optics was done in the clean room at LAM by analysing the surface Tests using a polychromatic source and the entire Fibre Bundle:

-Perform injection maps into the fibres using a power meter, followed by an optimisation verification. -Perform a calibration map to test the interpolation function and verify the shape of the PSFs. -Test of the C-S distance as a function of time and temperature.

-Test the centring strategies and provide an estimation of their errors to compare them to the ones (asterisk) mentioned in the error budget in Chap. 3.

HiRISE AIT at the VLT

In this section, I present the work that is anticipated in the months after my PhD defence. The AIT plan at the VLT is described in technical documents provided to ESO for which I contributed to the writing. The details regarding these tests are provided in two documents internal to the project: -HIR-DAR-01-01-Overview.pdf -HIR-PLA-07-01-Commissioning.pdf

Unpacking and verification

The first step at the VLT will consist to unpack the boxes, check the integrity of the assembly, reintegrate the instrument in the AT integration room, carry out functional verification and check the alignment of the FIM and FEM.

Telescope installation

The description of the telescope installation is detailed in three documents, internal to the project (DAR-02-01-FIM.pdf, HIR-DAR-03-01-FB.pdf, HIR-DAR-04-01-FEM.pdf) and will not be explained in this thesis. I will participate in all these activities according to the roles the HiRISE team will share during the AIT. The results for the first, second, and third strategies are plotted in the upper, middle, and lower panels, respectively. The grey area represents the region where an emphasised trend is found. The black dashed lines at 90°and 210°represent the angles for which additional tests are performed and demonstrated in Fig. 14. rate goes as low as 0.2, but is on average around 0.7. For a specification of 0.2 λ/D the success rate is significantly improved, with a value of 1.0 for most position angles and a drop at 0.8 for only a single point in our measurements.

ANNEXES A. Publications

For the second strategy (Fig. 11, middle panel), the success rate for a specification of 0.1 λ/D never falls below 0.3, but is on average slightly lower than for the first strategy (∼0.6). The success rates for specification accuracies of 0.2 and 0.3 λ/D are above 0.95 for all position angles.

Finally, the results of the third strategy (Fig. 11, bottom panel) show a more or less equal performance as the first strategy for a specification of 0.1 λ/D, but the results for a specification of 0.2 λ/D appear worse than for the other two strategies. For a specification of 0.1 λ/D, the average success rate is around 0.5, with less extreme variations inside and outside of the grey area. However, the success rate values are clearly lower in the grey area for this third strategy. Since the third strategy is a combination of the first and second strategies, the fact that we do not find a significant increase of the success rate for the 0.1 λ/D specification is not surprising.

Performance with angular separation

We also tested the three strategies with planets located at different angular separations. The results are presented in Fig. 12 for three selected position angles: 90°, 210°, and 330°. The 90°p osition was selected because it is at the centre of the grey area in Fig. 11, where the performance is particularly low. The other two position angles are separated by 120°. We first note that the A171, page 10 of 14 27 The static aberration measured by the ZELDA wavefront sensing are estimated at 7 nm RMS in 15 days if the testbed remains in the configuration where the panels are closed. This error term remains not significant for the tests performed on MiTHIC due to the tests timescale.

Normalised injection efficiency

Centring specification

The performance of HiRISE is driven by the overall transmission of the system. Injecting light into SMF is inherently challenging and can lead to important flux losses if the centring is not accurate. In Fig. 7 (panel a), we notice that the simulations by Otten et al. 24 show that a centring accuracy of 0.1 λ/D is required for HiRISE. In this case, we expect a maximum peak coupling efficiency loss of five percentage points compared to a perfect centring of the PSF on the science fibre. To illustrate the challenging requirement, we performed an injection map of the stellar PSF into the C fibre on MITHiC and it is illustrated in Fig. 6. It represents the flux injected into the C fibre, as measured by the power meter and the two circles delimit the 0.1 λ/D and 1 λ/D around the centre of the fibre. In comparison to the simulations, we computed a radial profile of the injection map, which is shown in Fig. 7 (panel b). It demonstrates that at 0.1 λ/D the loss is estimated to 2.6 percentage points. For HiRISE, an accuracy of 0.2 λ/D could be acceptable but at a cost of a loss of ten percentage points compared to the perfect case.

IMPLEMENTATION OF THE CENTRING STRATEGIES ON MITHIC

Calibrations

• Centre of the fibres:

In order to retrieve the S and the C fibres in the tip-tilt commands space, the first step consists of computing a coarse injection map. To achieve a more accurate determination of the fibres centre, we used the tip-tilt mirror position associated with the maximum of the coarse injection map as an input to a gradient descent algorithm based on a Nelder-Meade approach that maximises the flux injection into the fibres. In this proceeding, the optimisation of the injection based on a gradient algorithm is referred to as an injection optimisation.

• C-S fibre distance: Another important step is to be able to accurately switch between the C and the S. To fulfil this requirement, an accurate calibration of the C-S distance is necessary and the results 27 Reproduced with permission from El Morsy et al. 27 the planet's signal during the centring procedure. However, the modest contrast in the laboratory is essential to check the final accuracy.

Regardless of the strategy, at the end of each centring procedure a verification optimisation (VO) is performed to gauge how close the planet's PSF is to the centre of the S fibre. The tip-tilt displacement before and after the optimisation, ϵ, gives a measurement of the distance to the centre. The success or failure status of the performance are defined by the ϵ error and are compared to the specification accuracy of 0.1 λ/D.

Results

The results for a planet located at different position angles around the star and with an angular separation of 10 λ/D are demonstrated in Fig. 8. The figure shows the success rate of each strategy for three specification accuracies of 0.1, 0.2, and 0.3 λ/D.

For the first strategy we reach an average success rate of 0.7 for the specification accuracy of 0.1 λ/D, and 0.95 or higher for accuracies greater than 0.2 λ/D. For the second strategy the success rate is on average equal to 0.6 for an accuracy of 0.1 λ/D, and again the success rates are higher than 0.95 for an accuracy of 0.2 λ/D and 0.3 λ/D. Finally, the third strategy demonstrates a success rate slightly worse than the first and second strategies.

The second performance tests were performed with planets located at different angular separations; we only tested three position angles: 90 • (located in the grey area), 210 • , and 330 • . The first strategy shows the lowest performance for 90 • , with a success rate that decrease as a function of the angular separations. It reaches 0.0 at worst for an accuracy of 0.1 λ/D and 0.2 λ/D, and is lower than 0.4 for an accuracy of 0.3 λ/D. This position angle is identified as problematic in the calibrations and explained in more details in Section 4 of El Morsy et al. 27 For the two other position angles we reach a success rate higher than 0.4 for 0.1 λ/D and higher than 0.95 for an accuracy of 0.2 λ/D and 0.3 λ/D. The trends for Figure 9: Success rate as a function of the angular separation from the star. The results for the first, second, and third strategies are plotted in the upper, middle, and lower panels, respectively. Reproduced with permission from El Morsy et al. 27 the first strategy are found also in the results for the third strategy, but with even lower results. Finally, the results for the second strategy are highly better, with significant high rates at all position angles for the 0.2 and 0.3 λ/D specifications, and decreased success rates for a specification of 0.1 λ/D, but not poorly as for the two other strategies.

CONCLUSIONS

HiRISE aims to implement a coupling between SPHERE and CRIRES+ at the VLT/UT3. One of the main constraints of HiRISE is to blindly inject a known planet's PSF on the science fibre to transmit it to the spectrograph with the highest possible throughput. Previous studies for HiRISE have determined that a specification of 0.1 λ/D would be the best choice to maximise the transmission. 24 In order to study the best centring strategy, we used the MITHiC testbed at LAM, which has been upgraded to emulate the setup used in HiRISE. On MITHiC, three strategies were implemented and tested to assess the feasibility of reaching a specification of 0.1 λ/D. We conducted a performance study to verify the planet's PSF centring on the science fibre S

B. Centring strategy: application to the object selection mechanism (OSM) prototype for HARMONI/ELT

A part of the work developed in this thesis has been used in the early integration activities for the HARMONI instrument. As the details of this work have not been published so far, I would like to detail it in this appendix.

HARMONI will be one of the first generations of ELT instruments and will shape the visible and near-infrared astronomy landscape. The 3D spectrograph will disperse the light from astronomical objects into its different components, allowing scientists to study the objects in fine detail and go beyond to go beyond the current state of the art concerning spectrographs. HARMONI will be equipped with two flavours of adaptive optics correction: Single Conjugate (SCAO) and Laser Tomography (LTAO) adaptive optics. In the case of very faint science objects, the SCAO sub-system must acquire a star bright enough for the WFS. This star has to be selected in a patrol field of 30 ′′ on-sky away from the science direction. Moreover, the centring of the science object on the IFS slicer has to be precise at a few mas. This differential angle has to be done by tilting optics in the SCAO path, in an absolute way, and blindly, which is similar to the work I conducted during my thesis. The requirement for this "Object selection" function is therefore extremely tight: 30 ′′ on-sky range with a 1 mas precision, translates into a 5˚range with an 1 ′′ precision at the component level.

The HARMONI team, therefore, developed a prototyping activity on the OS function and implemented an optical setup to test the device (a goniometre from Smaract company, shown in In this context, I helped the HARMONI team to understand that the problem of the absolute centring with a tip-tilt platform also involves the calibration and the algorithmic part. I proposed them to re-use the same strategy I developed for HiRISE and tested on MITHiC but in the case of the Object Selection function of HARMONI. Applied to HARMONI, this strategy becomes:

-Calibrate the OS function, by acquiring a set of PSF positions in the focal plane (red dots in the maps).

-Build the model of geometric conversion from command space to focal plane position (using Python Interpolate methods) -Invert the model using the Python embed-ed libraries In particular, one test performed showed that the density of the calibration grid is a very important parameter to reach a correct performance. The difference between using a 25x25 calibration grid and a 13x13 grid is a 1 mas increase of the final error. Although this work has been performed by the HARMONI SCAO prototyping team at LAM (Kacem El Hadi, Jean-François Sauvage, Kjetil Dohlen, Edgard Renault, William Bon), I exchanged regularly with the team and I have expertise with their procedure and challenges.

In particular, the conclusion for the HARMONI team has been that the optical distortion of the prototyping setup, which creates the pincushion-shape of the red grid, will B. Centring strategy: application to the object selection mechanism (OSM) prototype for HARMONI/ELT be improved on the final instrument and should improve the final performance. The HARMONI consortium had decided to include the centring accuracy tested with this method into their global error budget as an acceptable requirement. This conclusion was made very clear thanks to the similar behaviour seen on MITHiC.