Erik Scott

Zach Evan

Jacson Andrew

Nour Skaf
email: nour.skaf@obspm.fr

Olivier Guyon

Éric Gendron

Kyohoon Ahn

Arielle Bertrou-Cantou

Anthony Boccaletti

Jesse Cranney

Thayne Currie

Vincent Deo

Billy Edwards

Florian Ferreira

Damien Gratadour

Julien Lozi

Barnaby Norris

Arnaud Sevin

Fabrice Vidal

Sébastien Vievard

Eric Pantin

Philippe Thebault

Quentin Kral

Camilla Danielski

Raphael Galicher

Julien Milli

Anne-Marie Lagrange

Clément Baruteau

Matthew Kenworthy

Olivier Absil

Maud Langlois

Johan Olofsson

Gael Chauvin

Nuria Huelamo

Philippe Delorme

Benjamin Charnay

Michael Bonnefoy

Faustine Cantalloube

H Jens Hoeijmakers

Ulli Käufl

Markus Kasper

Anne-Lise Maire

Mathilde Mâlin

Ralf Siebenmorgen

Ignas Snellen

Gérard Zins

On-sky validation of image-based adaptive optics wavefront sensor referencing

Keywords: instrumentation: adaptive optics -instrumentation: high angular resolution -methods: numerical Exoplanets, Direct Imaging, High Angular Resolution

PhD experience became far more enjoyable and fulfilling under his supervision, bringing an exciting project to work on and a safe, caring, and supportive presence. He gave me incredible freedom, especially the freedom to remain in Hawai'i for one extra year, making him have meetings at sometimes unacceptable time of his nights. It is once back in Paris at the end of my PhD that I truly got to appreciate the value of his supervision, and mainly, his human qualities, with endless conversations and laughters. His support over the writing period -an intense 6-week sprint -has been exceptional, it is thanks to him that I, or I should say, we, could submit this thesis (almost

Life. Quite an experience, right? Isn't it funny that one of the first things people look at in a PhD thesis is the acknowledgements section. This is a very special section as it is an insight into the human being behind the scientist. Before even wanting to know about the science, we crave this insight about the life of the one who accomplished it. This fascination about life is to me what is at the core of science. And it sure is at the core of my motivation behind my scientific work over the last few years. I was far to imagine how wondering about life in the universe made me desire to understand life on Earth. I see the PhD as a human experience, before being a scientific one. And this experience is only possible thanks to many people, who entirely influence the course of the PhD. I have been extremely lucky to have been surrounded by exceptional mentors, teachers, coworkers, and friends, who made this PhD possible, and I can't take credit for any of it. I wish there were words to truly express the depth of my gratitude for all the people that contributed to it, too many for giving an exhaustive list here.

My first words go to my two PhD supervisors. Olivier and Anthony. They both taught me far more on a human level than a technical one. They both made me understand that a scientist is before all a human, and how important it is to keep having fun throughout what we do. Olivier, a.k.a "Boss-san", is the one who got me started on this academic adventure, when I was a young and naive 22-year-old who couldn't really speak English. Olivier, the least human of all humans, who somehow can run up Mauna Kea from Hale Pohaku 1 in less than two hours to find a lost intern (and failing)(*cough cough*). And yet, one of the most human people I have ever met, with a deep (although often hidden) sense of wisdom, equity, philosophy of life, sometimes unacceptable sense of humor, but mainly one of the most supportive people to me. The human interactions we shared and what I have learned from him on that level over the years, are by far greater than the scientific knowledge I acquired (also because supervising the work of a student is not really his thing).

Anthony, who generously accepted to adopt me almost a year after I started my PhD. My 1. A " six-mile hike, from 9200 feet / 2800 meters, to " 13,000 feet / 4000 meters.

vii The SCExAO team. Seb, Vince, Julien, Jennifer, Kyohoon. A professional family to me. They saw me evolve, through the laughs, the tears, the injuries. We shared many memorable adventures and conversations, during the days and mainly the endless observing nights, where tiredness turned us into all sorts of weird animals. I am also grateful to Subaru day crew, for the laughs and help to do the mechanics on my car. A special thanks to Jimmy and Lucio, for their friendships. And, Matt, for giving me his surf board, on which I had one of my best meditation moments and life lessons. I started my PhD withing the adaptive group of LESIA, in the batiment 12. The first couple of months of my PhD there were really fun, and I have learnt a lot from the whole team. A special word for Eric Gendron (and his legendary sofa), who has an endless generosity of his time to explain with patience and fun even the stupidest questions a student can ask. I spent the last 6 months of my PhD within the dynamic revolving around the IMODEX group, where I enjoyed the conversations and laughs of the other PhD students and post-docs.

Thanks to Anthony, I had the incredible opportunity to join the crew of "La Guyane vers les Etoiles", for an outreach mission in French Guiana for a couple of weeks, and the gift to witness the historical JWST launch in Kourou. I feel a very soft heart toward all this wonderful team, we shared many deep moments, with intensity and laughters. Grateful for the friendships that remained from this journey.

On a more personal note, after spending years surrounded by a majority men throughout my academic studies, this PhD has opened me to the world of women, which was mysterious to viii

Introduction ‹

Nearly thirty years ago, an astronomical discovery had one of the biggest impacts on the history of astronomy, and probably of Humanity, as it opened the door to a completely new field. The first exoplanet, 51 Pegasi b, was detected [START_REF] Mayor | A Jupiter-mass companion to a solar-type star[END_REF]. Exoplanets are celestial bodies that orbit stars other than our own. Since the discovery of the first exoplanet in 1995, which led to a Nobel Prize in physics in 2019, more than 5200 planets have been detected. They are abundant and very diverse, almost completely changing our understanding of planet formation and evolution.

In a post-Covid world threatened by global warming, at a time when society gets increasingly polarized over differences, when people question their trust in science, with a lack of trust in governments, and other existential questions such as "is humanity's intelligence destined to self destroy itself?" 3 , one may legitimately question the point of spending time, energy, and money wondering about the universe. Introduction other forms of life out there? Are they also wondering about their existence in the vastness of space? Through this quest of searching for life in the universe, we understand how unique and remarkable life on Earth is. Especially, we now know it is extremely difficult to travel to an exoplanet, and will likely not become possible for generations, which brings even greater awareness and inspiration to take care of our precious planet, the only place we know that harbors life. Furthermore, as human species, we have always wondered about our place in the universe to understand who we truly are, and every single culture in the world was once connected to the stars. The discovery of exoplanets and the potential for finding other forms of life can lead to a greater understanding of our small place in this majestic universe, and inspire a sense of unity and connectedness among humanity. This would lead to the understanding that we are all part of the same cosmic journey, raising considerable human emotions. It fits here to quote Carl Sagan:

For small creatures such as we the vastness is bearable only through love.

And in fact, astronomy is what intrinsically connects us all, by the very nature of our origin. We are the remnants of the Big Bang, the result of 13.8 billion years of evolution. Humans' existential questions about life are linked to the universe in their essence. Astronomy, on a personal level, offers a unique fulfillment of one's quest for meaning and is a potent tool for selfdevelopment and well-being. And, it is indeed in the cosmic depths that we discover ourselves (cf Figure 1). It offers the unique potential to unite people for a goal beyond our individualities. The James Webb space telescope is the perfect example of that: over three decades, more than 20,000 people have worked together for one of humanity's greatest achievements, despite the cultural, political, religious, and ethnic differences. This is a powerful example of the fact that peace will come from our understanding that we are actually no different from one another. Astronomy, and especially exoplanet science, sheds the spotlight on that. Finally, this is what can be deeply inspiring, and have an unquantifiable impact on culture and society.

Enough of cosmic therapy sessions for humanity; time to start this cosmic journey as we explore the mysteries of exoplanetary systems and try not to get lost in the vastness of space while remembering to laugh at the absurdity of it all.

The next decade could be when proof of extraterrestrial life is obtained 4 . To enable such a momentous discovery, we need to observe rocky, temperate exoplanets, study their dynamics and atmospheres, and possibly detect biosignatures. While the transit technique, and the sensitivity of the James Webb space telescope, will be optimal for studying rocky worlds in the habitable zone of cool stars (e.g., the TRAPPIST-1 planets), direct imaging is the only technique in the Introduction foreseeable future ability to deliver images and spectra of rocky worlds in the habitable zone of Sun-like stars.

Existing large ground-based telescopes already have the potential to image and study a large sample of gaseous planets, provided that contrast at small angular separations is further improved by developing wavefront sensing techniques and advanced data processing. The next generation of ground and space-based facilities (e.g. JWST (Greene et al., 2016), E-ELT, Ariel (Tinetti et al., 2018), Roman telescope [START_REF] Kasdin | The Nancy Grace Roman Space Telescope Coronagraph Instrument (CGI) technology demonstration[END_REF]) will be capable of characterizing the atmospheres of a large number of exoplanets. These telescopes will undoubtedly unveil many mysteries about planet formation, composition, and atmospheric diversity, and potentially even observe biosignatures.

We need to be prepared to succeed in this ambitious science goal. Understanding exoplanetary systems is a conundrum with many facets, requiring state-of-the-art instrumentation and a holistic understanding of planet formation and their atmospheres. There are several open questions for the next decades of exoplanet study that can be summed up with these questions:

1. What are the processes of planet formation? 2. What is the exoplanet population demographic?

3. Where does the exoplanet diversity come from? 4. Can exoplanets be suitable for life? These questions are connected. They all require an understanding of how planets form. For that, there is a need to observe young systems and circumstellar disks, and exoplanets' atmospheres bring crucial insight into the formation processes. On the other end, these two questions require the detection of more planets and a more diverse sample of exoplanets. With current exoplanet detection methods, we are sensitive to (mainly giant) planets close-in to their host star with the radial velocity and transit method and the young giant planets far away from their star with direct imaging. We are missing the intermediate distances due to observational biases, meaning we are missing a big chunk of giant planets in terms of demographics. Furthermore, there is a bias on super-Earth-sized planets, detected either close to their star with transit or further away with micro-lensing. There is no visibility over the small planets at intermediate distances.

Completing the demographic diagram and understanding the origins of diversity are a priority of the exoplanet field. Eventually, answering these questions is necessary to understand the conditions that would make a planet suitable for life.

My PhD work offers a step forward in both directions, and the preparation of the upcoming generation of telescopes, with the long-term goal of enabling the detection of habitable planets around the nearest stars with the forthcoming generation of 30m-class telescopes. My thesis is focused on three axes:

1. Developing innovative instrumentation for direct imaging, to contribute in observing more planets closer-in -through the DrWHO algorithm, presented in Chapter 3;

2. Observing a circumstellar disk in direct imaging, to contribute to a better understanding of the formation processes of giant planets. I focused on the β Pictoris system, which is presented in Chapter 4;

3. Study exoplanets' atmospheres, with transit spectroscopy, and contribute to understanding atmospheric diversity and their link to planet formation. I focused on three hot jupiters, observed with the Hubble space telescope; this is presented in Chapter 5.

I introduce the necessary material over two chapters. Chapter 1 presents the scientific picture of the exoplanet field: after presenting different detection methods, I focus on giving an overview of planet formation and atmospheric characterization, especially for giant planets. In fact, giant planets are what connect these two fields. In Chapter 2, I introduce the instrumentation challenges behind the direct imaging of exoplanetary systems. With current telescopes and technologies, this method can only observe giant planets orbiting far away from their host star.

NB: the sections that are readable to a non-specialized audience are marked with a ‹.

EARTH DAY

In the cosmic depths we discover ourselves Chapter 1

Scientific picture of the exoplanet field

Studying exoplanetary systems -planets orbiting other stars than our Sun -is one of the greatest challenges of modern astronomy. Although every culture in the world has connected to the stars, and some have wondered about our place in the Universe, studying worlds beyond ours started only about three decades ago. This chapter is dedicated to providing a brief overview of this new field of astronomy that is helpful for the rest of this thesis. After giving a brief historical introduction, I will describe a few detection and characterization techniques in Section 2. I will then introduce the mechanisms behind planet formation in Section 3, before describing the basics of the study of exoplanets' atmospheres in Section 4. Both of these sections focus on giant planets. I will close this chapter by comparing ground and space-based astronomy regarding the exoplanet field.

1 Worlds beyond: a brief human history ‹ Human beings have always looked up to the stars and wondered about our place in the universe, and the existence of other worlds. Cosmic pluralism, or the belief that there are other worlds beyond Earth, started in Antiquity and evolved along with the atomist movement, which proposed that the entire universe is composed of individual indivisible components: atoms. The first concepts of cosmic pluralism came from Greek philosophers as a metaphysical argument about infinity (Apeiron), starting with Anaximander (610-546 B.C.), a pupil of Thales, and master 1 of Pythagoras. Several other prominent Greek philosophers, such as Epicurus (341-270 B.C.), father of the Epicurean philosophy, believed in the infinite number of other worlds in the universe, while others, such as Plato (428-348 B.C.) and his pupil Aristotle (384-322 B.C.) believed in the uniqueness and singularity of our world. Aristotle's system had a greater historical impact, especially with the rise of Christian ideas, arguing the uniqueness of Earth, seeing in cosmic pluralism a threat to Creationism [START_REF] Weintraub | Religions and Extraterrestrial Life[END_REF]. Later, in the Golden Age of the Muslim world, several Muslim scholars endorsed the idea of cos-1. Worlds beyond: a brief human history ‹ mic pluralism, such as Muhammad al-Baqir (676-733), the theologian and scientist 2 and Fakhr ad-Din ar-Razi . They based their reasoning on one of the main verses of the Quran "All praise belongs to God, Lord of the Worlds", with worlds being plural. In fact, life beyond our planet has historically been intrinsically linked with how one defines God: would God create Humans in his image, and thus humans beings must be unique, and the Earth unique, or would God create the universe in his own image, immensely diverse and complex, with a multitude of worlds. Not until the late years of the sixteenth century, after heliocentrism in Copernicus' De revolutionibus orbium coelestium (1543), did this link between religion and the cosmos slowly started to break, with Giordano Bruno (1548-1600) reintroducing the concept of cosmic plurality within a Christian society -his claims, along with his rebellious free spirit, eventually got him executed. Still, they contributed to the so-called "scientific revolution" and further open-mindedness on the topic. With the affirmation of Modern science (Galileo, Descartes, Kepler, Newton, Halley) and telescopic observations of celestial bodies (Galileo, Huygens), likely based on older studies from Hellenists and Arabs [START_REF] Russo | The Forgotten Revolution: How Science Was Born in 300 BC and Why it Had to Be Reborn[END_REF], the question of plurality of inhabited worlds emerges at the center stage of scientific controversy in the mid-seventeenth century. French author and scientist Bernard le Bouyer de Fontenelle published in 1686 a book of popular science Entretien sur la pluralité des mondes 3 , written in French and not Latin to popularize the idea of the diversity of worlds to any citizen, based on the work of René Descartes and Nicolaus Copernicus. Later in history, with modern science, the first serious thoughts on scientifically finding alien life started. On this matter, Albert Einstein said:

"Why should the earth be the only planet supporting human life? It is not singular in any other respect. But if intelligent creatures do exist, as we may assume they do elsewhere in the universe, I should not expect them to try to communicate with the earth by wireless (radio). Light rays, the direction of which can be controlled much more easily, would more probably be the first method attempted."

We will later see how the study of light revolutionized this question on other worlds. The "Space Race" between the United States and Russia during the Cold War in the 20th century triggered a profusion of science fiction books and movies on the topic of alien life, democratizing to the general public the idea that extraterrestrial life beyond our planet may exist. Later in the century, the prominent scientist and author Carl Sagan, inspired a whole generation on the topic of life in the universe. He was often portrayed as the main one who contributed to the conciliation between science and spirituality -although independently from religion-, turning a historical chapter, with new reflections on spirituality and extraterrestrial life [START_REF] Weintraub | Religions and Extraterrestrial Life[END_REF]. Several of Sagan's quotes are now part of the general culture, including this one:

"The universe is a pretty big place. If it's just us, seems like an awful waste of space." 4 2. Yes, that time when one could be an expert in medicine, chemistry, physics, astronomy, cosmology, literature, theology, ontology, philosophy, history, and jurisprudence, all at once.

3. Conversations on the Plurality of Worlds 4. From his book and movie Contact.

Chapter 1. Scientific picture of the exoplanet field Carl Sagan died just after the discovery of the first extraterrestrial world. Over the last three decades, planetary science has undergone a second Copernican revolution. This radical change was prompted by observing a star with a highly stable and high-resolution spectrograph, which opened the door to a new field. The first planet orbiting a star other than the sun, the exoplanet 51 Pegasi b, was discovered through the radial velocity technique [START_REF] Mayor | A Jupiter-mass companion to a solar-type star[END_REF]. This detection has since led to the revival of many scientific and philosophical questions, with now new and concrete consequences, bringing us a step closer to answering the question, "are we alone in the Universe?". Since then, over 5200 exoplanets have been detected, some having characteristics that raised significant excitements with the general public, such as the possible detection of a planet within the habitable zone of their host star, having an atmosphere containing water (Tsiaras et al., 2019). Not only are there other planets in the universe orbiting other stars, but they are abundant and very diverse, almost completely changing our understanding of planet formation. The next generation of telescope facilities will be capable of characterizing many exoplanet systems. They will undoubtedly unveil many mysteries about planet formation, composition, and atmospheric diversity, and potentially even observe indications of biosignatures.

Detection and characterisation techniques

Detection is the inception of any study on exoplanets. Yet, it is a challenging technological task. Although the first exoplanet was discovered less than three decades ago, astronomers have developed several complex techniques to detect and study extrasolar systems. These techniques allow us to better understand the processes of exoplanet formation and evolution. There are several direct and indirect detection methods. Each has its own strengths and observes or detects different kinds of exoplanets, from relatively small, close-in, rocky exoplanets, to relatively big, gaseous, close-in exoplanets, then massive gaseous, with a large orbital period. These detection technique differences complement each other in studying different kinds of planets.

The different detection methods could be grouped into two main categories: direct and indirect, and what is measured in both cases corresponds to different effects:

-The gravitational effect between the planet and its star: astrometry and radial velocity.

In fact, a planet orbiting a star will impact its location, as it is a two-body problem. Since the star is much more massive than its planet, its orbit will be much smaller, and the center of mass will be within its radius.

-The photometric effect the planet has, either on its star: transit, and microlensing; or on its own emission: direct imaging. Direct imaging includes both reflected starlight, and thermal emission.

-The temporal effect: transit timing variation (TTV), or pulsar timing (I will not get into the details of these).

Figure 1.1 shows the mass period relationship of detected exoplanets, pointing out the different scientific merits of each technique. Each detection method has its own strengths, limitations,

Indirect observations methods

To date, nearly all exoplanets discovered have been detected through indirect methods. In this section, I will briefly describe four different indirect observation methods.

Radial velocity

The radial velocity (RV) method is historically significant since it is through this method that the first exoplanet was detected, back in 1995 at the Observatoire de Haute Provence, in the South of France [START_REF] Mayor | A Jupiter-mass companion to a solar-type star[END_REF]. Over a thousand planets have now been detected with this method. It is based on Doppler spectroscopy and consists of acquiring high-resolution spectra of starlight to detect slight spectral shifts, resulting from the gravitational pull of a planetary companion around the barycenter of the system, its center of mass. In fact, a star is not precisely stationary when an exoplanet orbits it. The star's spectrum is shifted toward blue when it moves toward the observer, and red when it moves away. This method allows for determining the planet's minimum mass, M p sinpiq, with M p being the planet's mass and i its inclination with respect to the plane of the sky. This method allows detecting massive planets having short to medium semi-major axis and orbital periods (from a few days to a few years), as Figure 1.2 can testify, showing the planets detected via RV (as of December 2022). RV alone doesn't provide the exact planet mass, nor its radius: these are provided by combining observations with other methods, mainly transit and astrometry. There are several dedicated instruments to the RV observations of exoplanets. For example, the state-of-the-art Echelle SPectrograph for Rocky Exoplanets and Stable Spectroscopic Observations (ESPRESSO) instrument adding the light from the four VLT telescopes, is dedicated to high precision RV for small planet detections and characterization, with a precision reaching 10 cm s ´1.

The motivation for near-infrared (NIR) RV is to target low-mass stars around which lowermass planets can be detected, probing potentially habitable planets (for example Proxima Centauri b, cf Section 2.1). There are several other NIR ground-based instruments used for RV observations: the Infrared Doppler (IRD) at the Subaru Telescope [START_REF] Tamura | Infrared Doppler instrument for the Subaru Telescope (IRD)[END_REF], the High Accuracy Radial velocity Planet Searcher (HARPS) at La Silla observatory Mayor et al., 2003, the Near Infra-Red Planet Searcher (NIRPS), an extension of HARPS, and the SPIRou instrument on the Canada-France-Hawai'i-Telescope (CFHT [START_REF] Artigau | SPIRou: the near-infrared spectropolarimeter/high-precision velocimeter for the Canada-France-Hawaii telescope[END_REF].

Transit

The transit method is the most widely used method for discovering exoplanets, with over 3700 planets detected as of December 2022. The first exoplanet observed through this method, the hot jupiter 5 HD 209458b, also nicknamed Osiris, was detected initially following the radial velocity measurements of that same star [START_REF] Charbonneau | Detection of Planetary Transits Across a Sun-like Star[END_REF]. A transit event occurs when the observer's line of sight is aligned, or almost aligned, with the planet's orbit around its 5. Hot jupiters are giant planets having a radius nearing the one of Jupiter, and orbiting very close to their host star, with an orbital period between 3 to 10 days.

Chapter 1. Scientific picture of the exoplanet field 500 pc to 8 kpc in the Galactic Bulge. Currently, it is sensitive to planets down to a few Earth masses, orbiting all kinds of stars and even white dwarfs. With the NASA Roman telescope [START_REF] Spergel | WFIRST-2.4: What Every Astronomer Should Know[END_REF], microlensing will provide demographics down to the mass of Mars, from the habitable zone to planets on wide orbits or free-floating. It provides a statistical statement and constraints for planetary formation scenarios.

Figure 1.6 -Conference with my picture on the background: taken on July 14, 2021, the two Keck telescopes were using a laser guide star. The left one was observing the galactic center, and the right one was observing a microlensing event.

Direct imaging

In this section, I will introduce direct imaging (DI) and the types of targets it focuses on. I will then present the limitation induced by the presence of optical aberrations materializing in the image in the form of the so-called speckles. I will briefly describe a non-exhaustive list of a few post-processing methods and keep the instrumentation description for Chapter 2. Further details on DI can be found in the recent review of Currie et al., 2022a.

Description and conditions

Among all the detection methods of exoplanets, DI of exoplanets holds a specific place. It is also one of the most challenging techniques. Indeed, imaging an Earth-like planet in reflected light requires achieving a star-planet flux ratio (i.e., the contrast) in the order of 10 ´10 , meaning for one photon received from the planet, 10 billion photons are received from its host star.

To do so, there are several limitations to overcome:

-the stellar brightness, far greater than the planet one;

-the telescope's diffraction limit;

-the Earth's atmosphere, adding optical aberrations to the wavefront. The Earth's atmosphere is corrected with a complex technological trick: adaptive optics (AO). I discuss it in Section 2. Once the atmospheric distortions are corrected, a coronagraph is used to block the starlight, and operate closer to the telescope diffraction limit [START_REF] Guyon | Theoretical Limits on Extrasolar Terrestrial Planet Detection with Coronagraphs[END_REF]. Coronagraphs are usually a trade-off between coronagraphic rejection and throughput, inner working angle (IWA), and angular resolution. The achieved contrast and inner working angle determine the types of planets an instrument can observe, as shown in Figure 1.7. This is why coronagraphy has been an active field of research in the last two decades, allowing us to go to deeper contrast and smaller inner working angles. Furthermore, achieving high contrast to the star is necessary to study planet formation by imaging both planets and disks in young systems and spectroscopy, allowing to constrain the mass vs. age vs. luminosity relationship (with overlap with RV) and to capture the reflected light of older planets.

In the last decade, the DI community has focused on overcoming these challenges and has been developing high-contrast instruments and extreme AO (ExAO) with SPHERE, GPI, SCExAO, MagAO-X, and KPIC [START_REF] Beuzit | SPHERE: a planet finder instrument for the VLT[END_REF]Macintosh et al., 2014;[START_REF] Guyon | The subaru coronagraphic extreme AO (SCExAO) system: Wavefront control and detection of exoplanets with coherent light modulation in the focal plane[END_REF]Males et al., 2018;[START_REF] Mawet | Keck Planet Imager and Characterizer: concept and phased implementation[END_REF], in the NIR and the visible. DI, in its current state-ofthe-art, looks at young and warm planets, emitting in the infrared (IR) [START_REF] Burrows | A Nongray Theory of Extrasolar Giant Planets and Brown Dwarfs[END_REF]. The goal of DI is to be able to get closer in observations at greater contrast, to detect more planets, and better characterize them. The telescope size plays a key role in this goal since the telescope diameter drives the angular resolution. Along with the telescope size, post-processing methods and technological developments of DI instruments are crucial for observing exoplanets closer-in to their host star.

Detection and characterisation techniques

-they are between 4 to 10 orders of magnitude fainter than their host star; -the host star must be relatively close by, within 150 parsecs from Earth. The further they are, the more challenging it is to angularly separate them;

-the host star must be relatively young;

-this technique is currently primarily sensitive to planets orbiting beyond 5 AU.

Introduction to the speckle challenge

The principal limit to directly imaging an exoplanet is the residual starlight that contaminates the regions of interest. This contamination results from the light going through the optics and thus being subjected to optical diffraction. Furthermore, the optics are never perfect and add to the diffraction. As a result, there is speckle noise resulting from the diffraction of the light through the Earth's atmosphere, the telescope, and instruments (including a coronagraph). The wavefront errors of the light in the beam create a pattern of random interferences between different areas of the pupil -the speckles -in the image in the focal plane. As a result, the detection of planets is strongly impacted by the presence of speckles, sharply reducing the signal-to-noise ratio (SNR). Figure 1.8 shows the planetary system HR8799, and how much speckles are detrimental to exoplanet imaging since they imitate the exoplanet signal. They are by far the biggest issue for any high-contrast observation. Those speckles have an angular size that is directly equal to the diffraction limit of the telescope, equal to λ{D, with λ being the wavelength and D the diameter of the telescope's primary mirror, which is also the entrance pupil (thus linked to the focal plane and the pupil plane through Fourier theory). The location and brightness of those speckles change as the wavefront errors change. When observing from the ground, pupil amplitude features, especially the telescope spiders and static optical aberrations of the instrument, interfere with the speckles due to the atmospheric turbulence [START_REF] Guyon | Extreme Adaptive Optics[END_REF].

Controlling and correcting these speckles is a field on its own, with a plethora of instrumentation and post-processing tools developed for it.

Post-processing

In direct imaging, post-processing algorithms are critical for finding and studying planets. The raw contrast from a high-contrast instrument is of " 10 ´4 at best within the seeing disk (0.5") in optical-NIR, which would be barely enough to detect the warmest exoplanet and most angularly separated exoplanet. Deeper contrasts are mandatory to detect exoplanets. In fact, even with high-performance ExAO control (that will be described in Section 2), the planet image is still embedded in a much brighter halo of starlight, which must be removed during data analysis. Post-processing methods allow a gain of at least an order of magnitude in contrast. Thus, in recent years, a significant focus has been placed on developing these techniques for groundbased and space-based telescopes. Post-processing methods are used to identify and subtract the static and quasi-static speckles, stables, or varying slowly. There are continuously new postprocessing methods developed, I will give a non-exhaustive description of a few of these methods.

Chapter 1. Scientific picture of the exoplanet field of data. Out of those synthetic data, they injected a fake planet's PSF at a low-intensity level in some images to create a sample of synthesized positive examples. Then, they applied a CNN (convolutional neural network) to differentiate between images with and without exoplanets. New planets have not been detected with this method, however, they could detect previously detected ones, the HR8799 system in HST data.

Combined with other methods, direct imaging is crucial for studying the external zones of planetary systems and understanding the different formation mechanisms, as well as interactions between the protoplanetary disk and the planets after their formation. While the transit technique, and the sensitivity of the JWST, will be optimal for studying rocky worlds in the habitable zone of cool stars (e.g., the TRAPPIST-1 planets), DI is the only technique in the foreseeable future ability to deliver images and spectra of rocky worlds in the habitable zone of Sun-like stars, with the next generation of AO-assisted ELTs, and space telescopes such as the Habitable Worlds Observatory 8 (offspring from the LUVOIR and HabEx concepts) [START_REF] Gaudi | The Habitable Exoplanet Observatory (HabEx) Mission Concept Study Final Report[END_REF]The LUVOIR Team, 2019;Astro2020, 2021. Furthermore, DI can characterize the nearest exoplanets, which generally do not transit. Figure 1.10 presents how DI, combined with other methods, paves the road to detecting and characterizing an Earth-like planet. I will further elaborate on DI in Chapters 2 and 3.

The mid-infrared window

As described above, in the last decade, HCI instruments focused in the NIR and visible wavelengths. This is because young exoplanets emit light mainly in NIR wavelengths, given their high temperature (500-2000K). In fact, transmitted light (for transit) and thermal emission (for phase-curve measurements or spatially resolved observations) are in both NIR and MIR wavelengths, mainly because this is where the molecules mainly absorb thermal emission and present spectral signatures, on top of the planets' temperatures. In the visible, we detect more energetic lines, such as atomic transitions. In the IR, the lines are due to the atomic bonding within molecules, hence less energetic and emitting are greater lambda. I will briefly describe the opportunities offered by mid-infrared (MIR) wavelengths, from 3 to "25 µm, for probing exoplanets and protoplanetary disks in DI. These MIR opportunities are also valuable with other methods, including transit spectroscopy and atmospheric characterization.

With flux measurement over a limited spectral range in the NIR alone, atmospheric characterization can be ambiguous and present degeneracies in the analysis, in particular, due to the presence of clouds in the planet's atmosphere, so that the main parameters like temperature, radius, and surface gravity can have large error bars. In that respect, the MIR breaks these degeneracies and offers several decisive advantages. First, the star-to-planet contrast is favorable for warm planets, because of the black-body emission peaks at this wavelength range. Second, MIR observations measure a planet's flux at a wavelength less affected by clouds [START_REF] Morello | Phase-curve Pollution of Exoplanet Transmission Spectra[END_REF]. Furthermore, MIR data complements the NIR ones by increasing the spectral coverage, Chapter 1. Scientific picture of the exoplanet field 270K), provides insights into the planetary systems. However, exozodiacal dust is a strong thermal background that can impede the detection capabilities of planets forming in their habitable zone [START_REF] Kral | Exozodiacal clouds: hot and warm dust around main sequence stars[END_REF][START_REF] Hughes | Debris Disks: Structure, Composition, and Variability[END_REF]. All these advantages were soon recognized and motivated the implementation of a high contrast channel in the MIRI instrument on JWST [START_REF] Wright | The Mid-Infrared Instrument for the James Webb Space Telescope, II: Design and Build[END_REF] and for ground-based telescopes as well with E-ELT instruments such as the Mid-infrared ELT Imager and Spectrograph (METIS, [START_REF] Brandl | METIS: The Mid-infrared ELT Imager and Spectrograph[END_REF]), and other ground-based instruments [START_REF] Kasper | NEAR: Low-mass Planets in α Cen with VISIR[END_REF][START_REF] Wagner | Imaging low-mass planets within the habitable zones of nearby stars with ground-based mid-infrared imaging[END_REF]Wagner et al., 2021a). In Chapter 4, I will describe the NEAR instrument, which combines MIR with high-contrast imaging.

Planet formation

Introduction

Along with the solar system, exoplanets' observations opened the door to understanding how planets form. However, over the last three decades, exoplanet observations have considerably challenged our understanding of planetary formation, bringing extensive evidence on the diversity of planets and formation processes. Much progress has been made through ground and space-based observations and theoretical modeling. However, many questions remain unsolved. Giant planets, although expected not abundant [START_REF] Mayor | The HARPS search for southern extra-solar planets XXXIV. Occurrence, mass distribution and orbital properties of super-Earths and Neptune-mass planets[END_REF][START_REF] Fernandes | Hints for a Turnover at the Snow Line in the Giant Planet Occurrence Rate[END_REF][START_REF] Vigan | The SPHERE infrared survey for exoplanets (SHINE). III. The demographics of young giant exoplanets below 300 au with SPHERE[END_REF] as seen in Figure 1.11 (yet GAIA DR4 may change our perspective on the demographic of giant planets), are the most observed, as seen in Figure 1.1. They bring crucial elements to understanding the planet formation processes, which is one of the main objectives of exoplanetary science, as they rule the system and the other smaller planets dynamically. Indeed, giant planets hold a special place, as it is expected they bring the most direct link between atmospheric composition and their formation process: their bulk composition gives a unique insight to compare theoretical predictions to constrain the planetary formation and evolution scenarios [START_REF] Guillot | A correlation between the heavy element content of transiting extrasolar planets and the metallicity of their parent stars[END_REF][START_REF] Öberg | The Effects of Snowlines on C/O in Planetary Atmospheres[END_REF][START_REF] Emsenhuber | The New Generation Planetary Population Synthesis (NGPPS). I. Bern global model of planet formation and evolution, model tests, and emerging planetary systems[END_REF][START_REF] Helled | The nature of gas giant planets[END_REF], given the bulk composition must be inferred with theoretical models.

Different steps of planet formation

Stars form in molecular clouds, nebulae, which collapse into protostars. The remaining dust and gas orbiting the young star then evolve into an accretion disk, which grows into different stages over time. The lifetime of such disks is a few Myr, and they are found around at least 30% of stars. Planets are expected to form in the first million years when the disk is rich in gas and dust [START_REF] Hughes | Debris Disks: Structure, Composition, and Variability[END_REF]. Then, planetesimals collide, which generates a debris disk. Observing various types of disks at high angular resolution provides a unique insight into the different stages of planet formation. Figure 1.12 provides a timeline of the planet formation processes, with the different disk stages.

Planet formation

to creating spiral arms in the disk, to which the planet contributes; in fact, when massive planets form, a consequence is the apparition of spiral arms, which become an indirect detection means. In this case, the instability leads to molecular line kinematic signatures across the disk [START_REF] Pinte | Kinematic Evidence for an Embedded Protoplanet in a Circumstellar Disk[END_REF], and one can infer the presence of a planet by looking at the RV speed of the CO lines. These characteristics make it helpful to determine the occurrence of this mechanism, as well as give an insight into the disk mass [START_REF] Hall | Predicting the Kinematic Evidence of Gravitational Instability[END_REF]. This mechanism does not work for forming a planet close to its star, as the high temperature does not allow a gravitational collapse so close to the host star due to photoevaporation [START_REF] Owen | The Evaporation Valley in the Kepler Planets[END_REF], due to the thermal pressure supporting the local gas at an early stage of the planetary formation. Direct imaging observations have shown that planets which form via gravitational instability are rare [START_REF] Vigan | The SPHERE infrared survey for exoplanets (SHINE). III. The demographics of young giant exoplanets below 300 au with SPHERE[END_REF].

Orbit evolution for giant planets

In Chapter 5 we present a study of hot Jupiters. I will describe here how, in their formation process, they reach their final orbit. Once formed, planets can either remain in their orbit or migrate inward or outward, accreting more gas and dust in their atmosphere on their way. It is considered highly unlikely, if not impossible, that hot jupiters form at their current orbit. They necessarily form further away and migrate inward. This phenomenon can be explained with two scenarios:

1. gas-disk migration, 2. migration resulting from gravitational interaction with another planet, which increases its eccentricity and reduces its semi-major axis after the disk disappears.

The gas-disk migration scenario (1) proposes that a Jupiter-like giant planet formed beyond the ice line 10 by core and gas accretion, and then gets pulled in the protoplanetary disk and migrates inwards to the host star [START_REF] D'angelo | Evolution of Migrating Planets Undergoing Gas Accretion[END_REF]. There are three types of migration, depending on the initial mass of the planet prior to the migration, or the disk's mass. Type I is for a relatively small planet, the interaction with spiral density waves generates a loss of angular momentum to the planet. For type II, a more massive planet (" 10MC or greater) creates an annular gap into the disk due to the core accretion, which then generates a tidal torque on the gas, transferring angular momentum to the outward gas of the planet's trajectory, and the opposite for the inward gas; as a result, the planet spirals inward the disk, performing a runaway gas accretion. Type III, more rare, happens when the disk is very massive, leading to a co-orbital torque with the planet [START_REF] D'angelo | Evolution of Migrating Planets Undergoing Gas Accretion[END_REF].

2-

The migration happens by adopting a highly eccentric orbit, followed by a tidal migration process, shortening the orbit. The high eccentricity is generated when the planet exchanges angular momentum with one or multiple objects, turning its pseudo-circular orbit into a highly eccentric orbit. Raising the eccentricity of the planet's orbit reduces its angular momentum.

10. The ice line is the distance to the host star beyond which volatile substances condense into solid due to the decreasing temperature. This line depends on the volatile considered, as they do not solidify at the same temperature.

4. Exoplanetary atmospheres exploration 5.

Introduction to exoplanet spectroscopy: history and description

Interestingly, when the first exoplanets were detected, and the first questions on their atmospheric characterization were raised at the end of the 20th century, it was expected "on paper" that transit spectroscopy would be extremely challenging, while DI appeared far easier, technologically speaking. But in reality, it happened to be the exact opposite. In 2001, [START_REF] Brown | Transmission Spectra as Diagnostics of Extrasolar Giant Planet Atmospheres[END_REF] started the shift in mentalities by presenting the concepts of transit spectroscopy for exoplanets' atmospheric characterization. This was implemented a year later with spectrophotometric observations of a transiting planet, HD 209458, with a photometric dimming interpreted as sodium absorption in the planet's atmosphere [START_REF] Charbonneau | Detection of an Extrasolar Planet Atmosphere[END_REF]. At the same time, the first directly imaged spectra happened several years later, with one of the first conclusive studies being of HR8799 b [START_REF] Barman | Clouds and Chemistry in the Atmosphere of Extrasolar Planet HR8799b[END_REF].

There was first a focus on using optical and UV wavelengths to detect atoms and molecules in transit spectroscopy. Then, in 2004, the Spitzer IR space telescope started its operation, with the Infrared Array Camera (IRAC), offering four different wavelength measurements. This allowed a shift in the spectral range to look out for detecting molecules in exoplanets' atmospheres, with the understanding that molecules absorb in the IR, especially water, which was already known to be abundant in the universe. In fact, the IR spectral range allows probing molecular species [START_REF] Tinetti | Spectroscopy of planetary atmospheres in our Galaxy[END_REF] as well as exploring the thermal structures [START_REF] Knutson | A map of the day-night contrast of the extrasolar planet HD 189733b[END_REF][START_REF] Line | No Thermal Inversion and a Solar Water Abundance for the Hot Jupiter HD 209458b from HST/WFC3 Spectroscopy[END_REF]. IRAC offered data for the first detection of water vapor in an exoplanet atmosphere (Tinetti et al., 2007). The NICMOS instrument onboard the Hubble Space Telescope (HST) was then used for transit spectroscopy in the IR, within 0.8 to 2.5 µm, allowing further molecular detection in exoplanet atmospheres, such as methane (Swain et al., 2008). Later, the Wide Field Camera 3 (WFC3) spectro-imager camera was installed in 2009 on the HST, providing spectroscopic measurement in the 0.7-1.8 µm wavelength range. Despite the narrow wavelength range, resulting in a difficult and limited accurate interpretation of the spectra due to the high degeneracy of the molecular abundances, this allowed acquiring numerous atmospheric spectra both in transmission and reflection light, leading to different population studies [START_REF] Changeat | Five Key Exoplanet Questions Answered via the Analysis of 25 Hot-Jupiter Atmospheres in Eclipse[END_REF][START_REF] Edwards | Exploring the Ability of HST WFC3 G141 to Uncover Trends in Populations of Exoplanet Atmospheres Through a Homogeneous Transmission Survey of 70 Gaseous Planets[END_REF].

To date, the majority of atmospheric studies have been done on hot Jupiters (Sing et al., 2016;[START_REF] Edwards | Exploring the Ability of HST WFC3 G141 to Uncover Trends in Populations of Exoplanet Atmospheres Through a Homogeneous Transmission Survey of 70 Gaseous Planets[END_REF], as they are the easiest to detect and study with transit and eclipse spectroscopy. Up to now, the available spectral range allowed the detection of mainly water vapor (Tinetti et al., 2007;[START_REF] Deming | Infrared Transmission Spectroscopy of the Exoplanets HD 209458b and XO-1b Using the Wide Field Camera-3 on the Hubble Space Telescope[END_REF], with some detection of other carbon-bearing molecules, metal hydrides and oxides (e.g. FeH, TiO, VO) in the atmospheres (Swain et al., 2008;[START_REF] Von Essen | An optical transmission spectrum of the ultra-hot Jupiter WASP-33 b. First indication of aluminum oxide in an exoplanet[END_REF][START_REF] Skaf | ARES. II. Characterizing the Hot Jupiters WASP-127 b, WASP-79 b, and WASP-62b with the Hubble Space Telescope[END_REF]. Available data were not good enough to break degeneracies and bring conclusive results on a full understanding of exoplanets' atmosphere, however, the JWST is now opening a new era, offering a far greater spectral range, spectral resolution and sensitivity, allowing us to detect new molecules with greater confidence [START_REF] Rustamkulov | Early Release Science of the exoplanet WASP-39b with JWST NIRSpec PRISM[END_REF].

Chapter 1. Scientific picture of the exoplanet field Direct imaging spectroscopy of young giant planets in emission light has been growing over the last years as better instruments allow for better data and spectra, both from ground-based instruments [START_REF] Steiger | SCExAO/MEC and CHARIS Discovery of a Low-mass, 6 au Separation Companion to HIP 109427 Using Stochastic Speckle Discrimination and High-contrast Spectroscopy[END_REF][START_REF] Brown-Sevilla | Revisiting the atmosphere of the exoplanet 51 Eridani b with VLT/SPHERE[END_REF]Currie et al., 2022a), and JWST [START_REF] Hinkley | The JWST Early Release Science Program for the Direct Imaging and Spectroscopy of Exoplanetary Systems[END_REF]. We will soon enter an era allowing us to compare the chemical compositions of young giant directly imaged planets, and their migrating sisters the giant planets observed with transit, which will provide clues to shed light on the formation processes and migration roles.

In DI of exoplanets, the planets were detected with photometry only for several years until spectroscopic measurements were acquired. Both the SPHERE and GPI instruments acquired high-contrast spectra of HR8799 e [START_REF] Bonnefoy | First light of the VLT planet finder SPHERE. IV. Physical and chemical properties of the planets around HR8799[END_REF] and 51 Eridani b [START_REF] Macintosh | Discovery and spectroscopy of the young jovian planet 51 Eri b with the Gemini Planet Imager[END_REF] respectively, followed by first spectra of β Pictoris b (Chilcote et al., 2017). SCExAO provided spectra of several planets as well, including HR8799 c [START_REF] Wang | Retrieving C and O Abundance of HR 8799 c by Combining High-and Low-resolution Data[END_REF] and κ And b [START_REF] Currie | SCExAO/CHARIS Near-infrared Direct Imaging, Spectroscopy, and Forward-Modeling of κ And b: A Likely Young, Low-gravity Superjovian Companion[END_REF]. As introduced in Section 2.3, going to MIR wavelengths brings great benefits. Interferometry recently opened the floor to exoplanet spectroscopy, with GRAVITY (Collaboration et al., 2020;[START_REF] Lacour | First direct detection of an exoplanet by optical interferometry. Astrometry and K-band spectroscopy of HR8799 e[END_REF]. These recent spectroscopic observations with GRAVITY at a resolution of 500 will benefit a posteriori from MIR observations to constraint the Spectral Energy Distribution (SED) of the β Pictoris b planet and achieve higher precision on atmospheric parameters in the retrieval process, as demonstrated with the very first MIR photometric data of an exoplanet obtained with MIRI JWST coronagraph [START_REF] Carter | The JWST Early Release Science Program for Direct Observations of Exoplanetary Systems I: High Contrast Imaging of the Exoplanet HIP 65426 b from 2-16 µm[END_REF]. This is true for every NIR observation, with special care when combining them with data at different wavelengths (mainly with wavelength overlap), of ground and space-based data [START_REF] Yip | On the Compatibility of Ground-based and Space-based Data: WASP-96 b, an Example[END_REF]. In addition, a planet flux in the MIR linearly depends on the effective temperature (Rayleigh-Jeans law), as opposed to the NIR, hence can provide, in turn, a better measurement of planet radius, whose estimation is sometimes poorly constrained, being unreasonably too small or too large at shorter wavelengths. All these advantages were soon recognized and have motivated the implementation of a high contrast channel in the MIRI instrument on JWST [START_REF] Boccaletti | The Mid-Infrared Instrument for the James Webb Space Telescope, V: Predicted Performance of the MIRI Coronagraphs[END_REF][START_REF] Boccaletti | JWST/MIRI coronagraphic performances as measured on-sky[END_REF], as well as the NEAR program [START_REF] Kasper | NEAR: Low-mass Planets in α Cen with VISIR[END_REF], which I will describe in Chapter 4.

From the atmosphere to interior and formation

Characterizing exoplanet atmospheres is crucial as they hint at how and where the planets formed by looking at different elements and their main molecular carriers [START_REF] Turrini | The contribution of the ARIEL space mission to the study of planetary formation[END_REF]. Spectroscopy gives their composition and precious information on where and how they were formed. The elements in the protoplanetary disk vary radially as the disk temperature drops and volatiles condense: the ice line is a consequent limit. In particular, the C/O ratio in the composition is relevant to where the hot Jupiter formed, predominantly because it regulates the atmospheric chemistry in it (Öberg et al., 2011). As a result, a hot Jupiter coming from the in situ formation mechanism would have a composition relevant to the inner protoplanetary disk, while a hot Jupiter coming from the high eccentricity and tidal migration mechanism would have a composition relevant to the outer protoplanetary disk. Regarding the gas disk migration 4. Exoplanetary atmospheres exploration mechanism, as the hot Jupiter accretes gas on its way, it might have a broader spectrum of composition [START_REF] Piso | C/O and Snowline Locations in Protoplanetary Disks: The Effect of Radial Drift and Viscous Gas Accretion[END_REF]. However, the C/O ratio present in the atmosphere is not enough to conclude regarding the formation processes at play for a planet. Two other chemical elements, sulfur and nitrogen, play a crucial role in connecting the chemistry of giant planets and the chemistry of disks, complementing the information provided C/O [START_REF] Turrini | The formation history of giant planets seen through multiple elemental ratios[END_REF][START_REF] Pacetti | Chemical Diversity in Protoplanetary Disks and Its Impact on the Formation History of Giant Planets[END_REF].

Other processes, such as atmospheric evaporation, impact the planet's properties. Figure 1.15 presents a schematic view of the exoplanet demographic and their different formation and evolutionary paths.

Comparing hot Jupiter's atmospheric compositions with their host stars' provides clues about their formation and migration mechanism [START_REF] Saffe | Chemical analysis of early-type stars with planets[END_REF]. In fact, comparisons between stellar abundances of carbon and oxygen for hot Jupiters and their host stars have been made, leading to understanding correlations between the formation mechanism and the stellar properties. For example, the gas disk migration mechanism leads to a composition of the hot Jupiter significantly super-stellar in O/H and sub-stellar in C/O [START_REF] Brewer | C/O and O/H Ratios Suggest Some Hot Jupiters Originate Beyond the Snow Line[END_REF].

The planet's mass is another necessary parameter to determine a better understanding of the planet's formation history. Combining transit with RV allows us to measure the mass, hence the bulk density. Furthermore, as Ariel will provide, a wider spectral coverage will allow us to infer the planetary mass directly [START_REF] Batalha | The Precision of Mass Measurements Required for Robust Atmospheric Characterization of Transiting Exoplanets[END_REF]. In fact, short spectral coverage leads to degeneracies caused by the clouds and the mean molecular weight, as clouds mask spectral features and bias the estimation of the molecular content of an atmosphere. Thus, broader spectral coverage allows us to break this degeneracy and to put more accurate constraints on the planetary mass (Changeat et al., 2020a) Many recent studies look into the connection between atmospheric composition and the formation processes, giving hints about the planetary interiors. Whether it is from observing protoplanetary disks spectra and the resulting composition of planets [START_REF] Morlok | Dust from collisions: A way to probe the composition of exo-planets?[END_REF], or the other way around, from atmospheres spectra to planet formation (Helled et al., 2022a), the relationships between these subfields are shaping our global understanding of planetary systems.

From a light curve to a spectrum

Observing an exoplanet atmosphere from transit spectroscopy is actually observing the star's light that went through the exoplanet atmosphere. In Figure 1.3, I presented the planet with an atmosphere: some of the star's light travels through the atmosphere, resulting in different transit depths at different wavelengths.

The measured spectrum S is directly retrieved from the star's flux and normalized to the star spectra without planets, and can be expressed as:

S λ " 1 ´ˆR p,λ R s,λ ˙2 " 2 R 2 s ż Rmax 0 p1 ´e´τ λ prq qrdr (1.2)

Different methods of spectrum analysis

Transit spectroscopy leads to a direct measurement of the atmospheric spectrum. The measured quantity from this remote sensing, however complicated it can be, is a well of information that can be studied with several methods.

Retrievals

This method was first used to observe and study the Earth's atmosphere from space in the late 1950s [START_REF] Kaplan | Inference of atmospheric structure from remote radiation measurements[END_REF]. It was further developed for observations of solar system planets (Encrenaz et al., 1979a), and other fields of astrophysics, such as galaxy analysis (Encrenaz et al., 1979b). With the first exoplanet detections, this method was then developed for studying their atmospheric spectra [START_REF] Line | A Systematic Retrieval Analysis of Secondary Eclipse Spectra. I. A Comparison of Atmospheric Retrieval Techniques[END_REF], and retrievals became far more accessible as there has been an increasing availability of high-power computing technologies at limited costs, which used to be the main limitation. There are several retrieval software available based on different approaches, although the main idea remains the same, I will here focus on the TauREx (Tau Retrieval for Exoplanets) retrieval code (Waldmann et al., 2015a;[START_REF] Al-Refaie | TauREx 3: A Fast, Dynamic, and Extendable Framework for Retrievals[END_REF], as it is the one I used in the paper presented in Chapter 5.

The retrieval method, also known as the inverse method, determines the atmospheric composition by fitting a forward model onto a spectrum. A Bayesian approach is used to determine posterior probabilities for each parameter space, given the spectrum's low signal-to-noise (SNR). The retrieval also outputs a best-fit model to the data. Figure 1.16 presents a schematic view of a retrieval algorithm.

Simply put, a retrieval determines the state vector x of a model given a data vector y. The state vector is the parameter we want to study, such as the molecular abundances, the temperatures, etc., and the data vector is the spectrum to analyze. The two vectors x and y can be related such as:

y " Mpxq `ǫ (1.3)
Where Mpxq is the forward model, and ǫ is the error vector. The forward model encapsulates our understanding of the physics measurements.

Bayesian statistics is the cornerstone for retrieval analysis, providing a consistent approach to estimating the parameters. The first approach is the construction of the forward models, followed by the formulation of a prior distribution, which represents a model of our current limited theoretical knowledge of the physical and chemical characteristics of the planet to analyze. The prior distribution is the starting point of the numerous following iterations. Then, we use Baye's theorem after the data input to obtain a posterior distribution of the underlying parameters to identify, taking into account the prior and the spectrum.

Bayes' theorem states the probability relationship between the state vector x and the data vector y, given the forward model M:

Exoplanetary atmospheres exploration

Self-consistent models

When atmospheric characterization of exoplanets started over a decade ago, the method of choice was to determine the composition and temperatures using self-consistent models [START_REF] Fortney | Comparative Planetary Atmospheres: Models of TrES-1 and HD 209458b[END_REF]. This method generates a grid of models reproducing exoplanet spectra based on complex radiative-convective theories. Input parameters such as surface gravity, effective temperature, and elemental composition are given. There are several self-consistent codes; one of them is the Exoplanet Radiative-convective Equilibrium Model (Exo-REM) (Baudino et al., 2015;Charnay et al., 2018). Exo-REM is a cloud model focused on explaining spectra of brown dwarfs and giant planets with a limited number of free parameters to avoid any complexity that would not be grasped in real spectra with a limited spectral range. However, self-consistent models still provide forward models far more complex than the ones used in retrievals. Further details are presented in Charnay et al., 2018.

Self-consistent and retrievals: a comparison of two complementary methods

These two methods have different advantages and downsides, making them complementary. Retrievals are "data-driven", meaning they use the actual spectrum of the planet to identify the possible range of solutions. They present simpler physics in the forward models to prevent biases, especially as the short wavelength coverage does not allow us to dive into the complexity of the physics of the atmospheres. Retrievals explore a larger parameter space with fewer biases but do not fully grasp the complexity of real atmospheres. Retrievals, providing simpler physics in the forward models for computational time reasons, are thus faster than generating a grid of self-consistent models.

Self-consistent models are a "model-driven" approach. In 2D and 3D, they include complex general circulation models to model the dynamic and composition. They output an artificially generated spectrum that can help to explain the actual planet spectrum but does not directly compare to the data. They have a limited range of potential solutions based on the models, making it impossible to characterize the model parameters' uncertainties and degeneracies. There is a bias on the models' assumptions, such as chemical equilibrium, but given the model is known, one can use it to understand the data better. I summed up these points in Table 1.1. To conclude, using both methods is necessary to have an accurate understanding of the data and progress on our model descriptions.

High resolution spectroscopy

For completeness with respect to the previous section, I briefly discuss high-resolution spectroscopy and introduce the molecular mapping method here. This method, focused on DI, is a simplified version of a technique used for transit, where the characterization is performed by correlating a spectrum with a model. In the context of DI, it combines high contrast imaging with high-resolution spectroscopy [START_REF] Snellen | Combining high-dispersion spectroscopy with high contrast imaging: Probing rocky planets around our nearest neighbors[END_REF]. The main idea consists of disentan-Chapter 1. Scientific picture of the exoplanet field

Retrievals

Self-consistent

Ups

-data-driven -simpler models -use the spectrum to identify the possible range of solutions -explores a large parameter space -little biases -model-driven -complex general circulation models -explain the physics of the spectrum

Downs

-does not fully grasp the complexity of real atmospheres -short spectral coverage lead to great degeneracies 11 -does not directly compare to the data -biased on the assumptions of the models -can only explore a few solutions, impossible to characterise the uncertainties and degeneracies -considerable computing time especially for 3D models Table 1.1 -Table summing up the descriptions of retrievals and self-consistent method, both having complementary characteristics for a more complete description of exoplanet atmosphere spectra.

gling the planet from the star, through integral field spectrographs, based on the fact that the two spectra are fundamentally different, allowing cross-correlation with planetary atmospheric models. This method led to the detection of H 2 O and CO in the atmosphere of β Pictoris b (Hoeijmakers et al., 2018).

Spectroscopy from the ground: the telluric problem

When observing from the ground, the Earth's atmosphere isn't only problematic regarding the resolution of the acquired image but also impacts the spectrum with atmospheric contamination, which introduces the telluric lines in the spectrum. A simplistic and not-so-accurate way to remove those lines is to look at a rapidly rotating hot star (type A or B), near the same time and under the same conditions as the observations and then use it as a template for the telluric spectrum. Another way is to generate a theoretical telluric absorption spectrum out of a line list and with given observing conditions. An example of code to do so is the LBLRTM code (Clough et al., 2005, Line By Line Radiative Model Transfer Model).

Exobiology ‹

My thesis work has revolved around developing instrumentation for the direct imaging of exoplanetary systems, as well as contributing to a better understanding of planet formation and the atmospheric characterization of exoplanets. The bigger goal of this work is to contribute, on a small scale, to the dynamic of answering the question of whether some planets can be 5. Ground and space-based astronomy: perspectives ‹ habitable and if some are indeed the place of biological activity.

In the previous sections, I mainly focused on giant planets. Giant planets are indeed part of the framework for studying smaller, rocky planets. In fact, giant planets likely have rocky planetary companions. For example, half or more of the known warm Jupiters are expected to be surrounded by small planets orbiting the star [START_REF] Huang | Warm Jupiters Are Less Lonely than Hot Jupiters: Close Neighbors[END_REF]. The rapidly growing exoplanet census (now over 5200) shows that a significant fraction of our galaxy's 200 billion stars hosts temperate rocky planets [START_REF] Petigura | Prevalence of Earth-size planets orbiting Sun-like stars[END_REF]. One may then legitimately wonder if they hold oxygen-bearing atmospheres or water oceans, if life has emerged and evolved, and with what biochemistry. Many questions get leveraged on whether we could detect biosignatures which could eventually raise the indication of extraterrestrial life. We must observe the nearest potentially habitable planets to answer these questions to study their atmospheres and surfaces. This is one of the multiple goals of exoplanet science, and exobiology is the merging field between planetary science and astrobiology. There are many steps along the way before finding a biosignature in a planet's atmosphere. This requires an interdisciplinary study, with the knowledge of many fields spanning from the understanding of the history of the origin of life on Earth [START_REF] Lyons | Oxygenation, Life, and the Planetary System during Earth's Middle History: An Overview[END_REF], to the study of the evolution of Mars [START_REF] Changela | Mars: new insights and unresolved questions[END_REF] and other solar systems objects, such as the icy moons Europa and Enceladus [START_REF] Hand | On the Habitability and Future Exploration of Ocean Worlds[END_REF], to understanding precisely on physical, chemical, and biological levels, the interactions of bioactivities with the planet's atmosphere [START_REF] Olson | Oceanographic Considerations for Exoplanet Life Detection[END_REF], as well as the impact of the stellar radiations on it [START_REF] Airapetian | Impact of space weather on climate and habitability of terrestrial-type exoplanets[END_REF]. As a vast community of various fields, we are paving the road to a better understanding of the place of life in the universe.

Ground and space-based astronomy: perspectives ‹

Both ground and space-based astronomy have a complementary focus on exoplanet science and the search for life in the Universe as one of their goals.

The atmospheric turbulence limits ground-based telescopes (see Chapter 2). While the impact of the turbulence decreases for longer wavelengths, the thermal background of the atmosphere then becomes a limiting factor, on top of the molecular absorption from the Earth's atmosphere, limiting our access to the electromagnetic spectrum of the light coming from space. Regarding space-based telescopes, the Earth's atmosphere is no longer a limitation, allowing diffraction-limited imaging and full spectral coverage. However, space telescopes are technologically limited compared to ground-based telescopes. Having a large telescope in space is indeed challenging: the technology must be mature enough to be validated for space to ensure the robustness of the instruments, given the difficulty of maintaining and repairing space telescopes. The JWST, launched with a decade of delay, is an excellent example of such a challenge. Furthermore, space-based telescopes are around an order of magnitude more expensive than groundbased ones and take far longer to be in operation. Ground-based and space-based telescopes hence are complementary: where ground-based telescopes bring resolving power, space-based bring spectral coverage, and contrast limits of both types of telescopes are complementary, as Figure 1.17 shows.

Chapter 2

Instrumentation for exoplanet imaging Astronomy has always been intrinsically linked with our understanding of what light is. Since the beginning of humanity, we have questioned the nature of light and the nature of the universe around us. Light is the only source of information for studying extraterrestrial worlds, and its science is encapsulated in the broad field of optics. In fact, as briefly described in Section 2.2, imaging an extraterrestrial world requires overcoming two main challenges. First, as the light comes from the star is impacted by the Earth's atmosphere, which needs to be corrected. Second, once the light is corrected, the main issue is the stellar brightness is far larger than the planet. A coronagraph blocks the starlight, increasing the contrast with the environment and allowing us to image it. This chapter introduces the basic principles of the study of light and astronomical instrumentation, mainly the formalism of how an image forms through a telescope and notions linked to the art of high-contrast imaging. First, I will describe in Section 1 how light from a star through a telescope behaves and the mathematical tools used to understand it. I will then introduce the core of high contrast imaging, which has two aspects: adaptive optics, which is a method aiming at compensating the Earth's atmosphere, necessary for high contrast imaging (Section 2), and coronagraphy (Section 5). Special attention will be given to the non-common path aberrations (NCPA), which I will define in Section 3. Finally, I will briefly describe SCExAO as an example of an extreme AO (ExAO) instrument.

Optics basis 1.Light through a telescope ‹

First, a telescope is an optical system aiming at observing something far. What astronomers consider "far", means infinitely far. Long can be the discussion on what "infinitely" means. Here we will assume that it is far comparatively to what we are used to on Earth. The role of the astronomical telescope is to provide an image of a celestial object, a star, what we will call a "point source", located at an "infinite" distance from us. A point source emits light isotropically 1. Optics basis

Fourier Transform

An introduction ‹

I will now dive into one of the most useful mathematical tools that humans ever invented, and it is present in many fields of science. The Fourier transform. Before getting things complicated, let's give an over-simplistic explanation of what it is and why it is so powerful. The Fourier Transform is a mathematical decomposition of any function of space or time as a sum of different projections onto a set of frequencies. It is a discretization that applies to pretty much any type of signal, from music [START_REF] Wang | An industrial-strength audio search algorithm[END_REF] 1 to comparing DNA sequences [START_REF] Yin | A Novel Method for Comparative Analysis of DNA Sequences by Ramanujan-Fourier Transform[END_REF]. Fourier theory is also very present in optics, and everything related to the study of light: any electromagnetic signal can be decomposed in a series of different frequencies. I will tentatively introduce what happens when light goes through a telescope, although there would be much more to say.

Fourier optics

According to Huygens-Fresnel, when light goes through a telescope, the pupil plane behaves as a secondary source and emits spherical waves, that keep propagating through the telescope: this is the diffraction phenomenon. Then, it becomes possible to describe the wave propagation between the pupil plane and the focal plane, where the equations get simplified through the Fraunhofer approximation. We can then find the electric field amplitude of the focal plane, following the diffraction equation and the Fraunhofer approximation:

E f oc psq9 ż ż r E pup prqe ´2iπ s f . r λ dr (2.3)
where f is the focal length, λ is the wavelength, and s is the position in the focal plane.

We then see that the electric field amplitude in the focal plane corresponds to the Fourier Transform (FT) of the electric field amplitude in the pupil plane, taken between the variables s f and r λ . The amplitude in the focal plane is the FT of the amplitude in the pupil plane: 2.4) This Fourier relationship between the pupil plane and the focal plane is very useful.

E f oc psq " F T pE pup prqq (
One of the powerful applications of Fourier optics is that the focal plane, also called the Fourier plane, is the frequency plane with low spatial frequencies in the center of the PSF and higher spatial frequencies in the outer edge. Thus, this is where the filtering can be done, either in phase or in amplitude. For example, the wavefront component in the pupil plane that will create a pair of speckles in the focal plane is found with the Fourier transform. A speckle is The Strehl ratio is commonly used in astronomical instrumentation. It is however difficult to accurately and objectively measure it [START_REF] Roberts | Is that really your Strehl ratio?[END_REF]. We will later introduce another way to quantify our image quality.

Adaptive optics

Problem description ‹

Let us go back to Figure 2.1, and take a moment to admire how flat the wavefronts are before reaching the telescope. But the reality is indeed very different. Or at least, this is real until the wavefronts reach the Earth's atmosphere. After that, the atmosphere, ultimately impacts the shape of the wavefront, becoming a nightmare for most ground-based astronomers working in visible and NIR wavelengths, especially those interested in high-contrast imaging. It is not nice and flat anymore but aberrated. As a result, the star's light reaching the camera is not an Airy pattern anymore but a scientifically useless blur for exoplanet imaging (but still useful for other astronomical observations such as galaxies). Figure 2.3 shows how much the atmosphere impacts the focal plane image. This is a significant issue in modern astronomy and has opened a whole new field: adaptive optics (AO), or the art of correcting the Earth's atmosphere and all other sources of wavefront errors.

A brief history

Over the last 30 years, adaptive optics instruments have seen tremendous progress in development and scientific use, from the first experiments in astronomy with COME-ON, back in 1989, to the most current advanced systems known as extreme AO (ExAO) systems. There are several types of AO systems, and I will remain focused on the Single conjugate AO (SCAO), considering a single guide star. Many astronomical breakthroughs came from AO instruments, such as the discovery of the supermassive black hole Sgr A* at the center of the Milky Way with the Keck Telescope, leading to a Nobel prize 2020 [START_REF] Ghez | Measuring Distance and Properties of the Milky Way's Central Supermassive Black Hole with Stellar Orbits[END_REF]. Furthermore, AO led to the first direct detection of a planet orbiting a star with VLT/NaCo in 2004 (Chauvin et al., 2004), and the first system with four giant planets, HR8799, discovered in 2008 (Marois et al., 2008). In the following years, the second generation of ExAO systems was developed, allowing them to go much further in performance in terms of Strehl ratio, contrast, and sensitivity. As briefly introduced in Section 2.2, with the scientific goal of directly imaging exoplanetary systems, there was a need for high contrast requirements on AO systems, so that the wavefront could be corrected to an extreme level. The main current ExAO instruments are presented in Table 2.1: SPHERE on the VLT [START_REF] Beuzit | SPHERE: a planet finder instrument for the VLT[END_REF]; GPI, on Gemini South (Macintosh et al., 2014;[START_REF] Macintosh | The Gemini Planet Imager: looking back over five years and forward to the future[END_REF] (currently decommissioned in the process of being upgraded and moved to Gemini North); MagAO-X on the Magellan Clay (Males et al., 2018); and last but not least, SCExAO on the Subaru Telescope [START_REF] Guyon | The subaru coronagraphic extreme AO (SCExAO) system: Wavefront control and detection of exoplanets with coherent light modulation in the focal plane[END_REF]. Those instruments are provided with high-rejection coronagraphs, allowing differential imaging and maintaining a slow temporal evolution of aberrations. The main tradeoff of those instruments is between angular resolution, AO performance, and contrast [START_REF] Milli | Adaptive Optics in High-Contrast Imaging[END_REF]. This first generation of ExAO systems on 8-10-meter class telescopes is precious in benefiting the generation of ExAO instruments on extremely large telescopes.

Atmospheric turbulence

Atmospheric turbulence sets the angular resolution limit without AO correction, with the Fried parameter r 0 defining the seeing quality (cf Figure 2.3). Seeing is defined as λ{r 0 , with r 0 scaling as λ 6 5 . Hence, the shorter the wavelength, the more sensitive we are to the seeing. The correlation time, or the Greenwood time, is defined as τ 0 " 0.314r 0 {v, with v being the mean wind speed weighted by the turbulence profile along the line of sight, as described by [START_REF] Roddier | The effects of atmospheric turbulence in optical astronomy[END_REF] This parameter defines the temporal requirements of an AO system, as it sets the reaction speed of the system to correct the atmospheric turbulence. τ 0 is proportional to λ 6 5 as well. As a result, correcting the atmosphere in the near-infrared is less challenging than in the visible since the turbulence, expressed in a unit of phase, evolves faster in the latter.

AO and its elements: the mind, the heart, the body

AO's challenge is to correct for optical distortions of the light, mainly coming from the Earth's atmosphere. Three main elements are necessary, each having a different and specific role: the wavefront sensor, the real-time control, and the deformable mirror. Figure 2.4 presents a simplistic schematic view of the AO system, which operates as a loop. I will describe the three elements of AO using an analogy to human beings, with the three centers that make us humans: the mind, the heart, and the body. And, just like humans again, AO is pretty much all about control.

Adaptive optics

The mind: the real-time control

Once measured by the WFS, the wavefront aberrations must be reconstructed, allowing us to estimate the wavefront phase. The information from the WFS is sent to a real-time controller (RTC), the brain of the AO system, that will reconstruct the wavefront phase. The RTC proceeds in a closed loop, and this loop is reiterated continuously at high speed (" kHz rate) to catch up with the rapidly changing optical turbulence of the atmosphere. We will later dive into the RTC world.

The body: the deformable mirror

The RTC calculates what needs to be sent to the deformable mirror (DM), a critical hardware element that adopts the reverse shape of the distorted wavefront to compensate for it. The DM is comparable to the body of the AO system, where mechanical action happens. Most DMs are composed of a thin, flexible reflective membrane, behind which actuators aim to move this membrane. The actuators drive the precision of the DM. So, simplistically put, if the incoming wavefront has a phase of Φprq, then the DM will tend to adopt a shape close to ´1 2 Φprq (half because of the reflexion) -although without ever be able to perfectly adopt it due to errors (see Section 2.8).

Hence, in a closed loop configuration, the wavefront beyond the DM is mainly corrected from its aberrations; although never perfect, there is a residual phase:

Φ Residual " Φ Atmosphere ´ΦDM (2.10)
In a nutshell, the WFS first senses the wavefront, the RTC calculates its phase, and the DM acts accordingly to correct the aberrations. "Feel, think, act cycle".

The pyramid wavefront sensor

There are several types of WFSs, however, one of them has taken a special place in recent years, especially in the field of high-contrast imaging: the pyramid WFS (PyWFS). I will introduce it here because it is the type of WFS in the SCExAO instrument.

History

The PyWFS was first introduced in 1996 [START_REF] Ragazzoni | Pupil plane wavefront sensing with an oscillating prism[END_REF], and has the unique characteristic of being particularly sensitive to low photon noise, comparably to the other types of WFSs. It took nearly a decade before its first use in astronomy, with its first implementation in a very large telescope (VLT), the Large Binocular Telescope (2x8.4m), in 2010 [START_REF] Esposito | Laboratory characterization and performance of the high-order adaptive optics system for the Large Binocular Telescope[END_REF]. The PyWFS is now implemented on-sky on several 8-10 meter class telescopes and has been the design choice of all ELTs' first light instruments. However, the PyWFS linearity and calibration issues remain an active field of research (Deo et al., 2019a;Chambouleyron et al., 2020;Bertrou-Cantou et al., 2020;[START_REF] Weinberger | Exploration of convolutional neural networks to handle non-linearity estimation issues in pyramid wavefront sensors[END_REF]. In fact, the PyWFS non-linearities are non-trivial Chapter 2. Instrumentation for exoplanet imaging to model, and it is far from being mastered and fully understood.

Description of its concept

The concept of the PyWFS is illustrated in Figure 2.6. It relies on the principle of the Foucault knife.

First, let us describe the knife-edge test. This method, described by the French physicist Léon Foucault2 , was initially described in 1858 to measure the conic shapes of optical mirrors. So, to view the shape of a concave mirror, a mask occulting half of the plane -the knife edge -is placed before its focal plane; the pupil's image of the mirror is then reconstructed. The pupil's image appears evenly lighted if the mirror's shape is perfectly concave and spherical. On the contrary, if the mirror has optical defects, then the pupil's image presents the aberrations in a magnified way in height. Figure 2.5 illustrates this method.

The PyWFS is a kind of elaborated knife-edge test to measure wavefront aberrations. The pyramid plays the role of a double knife edge (in the case of a 4-sided pyramid), with its apex located on the focal plane. The sensor behind the pyramid is located on a pupil plane downstream, conjugated with the DM. Hence, if the incoming wavefront is aberrant, some of the light rays do not focus precisely on the focal plane anymore, which is the apex of the pyramid, and the light ends up in one of the four faces of the pyramid.

Each side of the focal plane, labeled A, B, C, and D in Figure 2.6, refracts the light in a given direction. The pupil imaging lens then reimages the light coming from each quarter of the focal plane in a quadrant, which is a translated pseudo-image of the pupil, with their respective intensities described by the functions Aprq, Bprq, Cprq and Dprq, with r referring to the Cartesian coordinates in the detector plane. Hence, if the incoming wavefront is aberrated, it does not perfectly focalize on the apex of the pyramid but spreads over its sides, as in Figure 9 of Figure 2.5. The uneven intensity received on each of the quadrants of the detector in the pupil plane can then be used to measure the wavefront aberrations. For example, based on Figure 2.6, positive x slopes will move light toward the quadrants B and D; likewise, positive y slopes will move light toward the quadrants A and B. Hence, the wavefront measurements S, sometimes referred to as "slopes"3 , are defined for the x and y axis as follows: However, when the camera's exposure time is very fast, and the guiding star is very faint, it might occur that the denominators of these Equations 2.11 and 2.12 equal zero, which, well,

S x prq

Modal description of the wavefront

Studying analytically and numerically the phase of the wavefront requires being able to describe it in a discreet way. An efficient way to do so is to project the optical aberrations of the phase of the wavefront over a modal decomposition. The wavefront can be decomposed on a modal basis as a sum of orthogonal functions:

Φprq " `8 ÿ i"0 a i Φ i prq (2.16)
with the Φ i being the multiple sub-wavefronts, of infinite number but ordered, and the a i the corresponding factors. An orthonormal modal basis is a good choice as it allows getting the variance of the phase, by summing the modes of interest:

σ 2 Φ " `8 ÿ i"0 a 2 i (2.17)
An example of an orthonormal modal basis is the Fourier modal basis, following the Fourier decomposition as described in Section 1.2. Another remarkable and famous one is the Zernike modal basis, based on the Zernike polynomials [START_REF] Zernike | Diffraction theory of the knife-edge test and its improved form, the phase-contrast method[END_REF], Figure 2.8 shows the first Zernike modes.

Elements for control

Algebra is at the base of AO control. Interestingly, the literal translation of the Arabic word "Algebra" means "reunion of broken parts", introduced by the Persian mathematician Muhammad ibn Musa al-Khwarizma around 820 AD in his book "The Science of Restoring and Balancing". An etymological origin that perfectly fits AO, as well as the human analogy. The three centers must be balanced to make a healthy human being.

Response matrix

The response matrix (RM) is simply the linear relationship between the WFS measurements s and the DM commands c: s " Rc (2.18) with R being the response matrix. It is usually measured by simply poking the DM with a combination of modes and recording the response on the WFS.

Control matrix

Once the relationship between the WFS and the DM is acquired with the RM, to estimate the DM commands to compensate for the measured WFS signal, we must compute the control matrix, which is the pseudo-inverse of the response matrix: C " R `. However, some modes applied on the DM during the RM acquisition have a weak signal on the WFS. These modes Wavefront control (WFC) refers to everything aiming at correcting for phase aberrations, as well as optimizing the light to deepen contrast. In ExAO, WFC is at the heart of the field, given exquisite correction must be achieved. Besides the RTC, several WFC techniques are being developed, some including the use of coronagraph. NB: a flat wavefront is not necessarily the ideal solution. For example, the wavefront creating a dark hole is not flat (Potier et al., 2020b).

Error budget in AO

Several remaining sources of error have a considerable impact on the final performance on the science camera. They are characterized by the error variance they leave on the final phase, and the total variance of the residual phase corresponds to the sum of the individual variances, defining the error budget. Below is a list of the sources of wavefront error in an AO system, with σ representing the variance of the full wavefront.

-the temporal error, linked with the lag between the measurement of the phase and its correction on the DM;

-the fitting error, due to the DM shape, which can correct modes up to a limit defined by the projected distance between the actuators in the pupil, d act . The residual phase will hence have uncorrected high spatial frequency modes, which is the fitting error. It is defined as:

σ 2 f itting " k ˆdact r 0 ˙5{3 (2.22)
with k=0.23 for a DM with a squared meshing. The smaller d act is, the better the DM will correct higher frequencies, and the smaller the fitting error will be.

-the aliasing error: aliasing is a crosstalk between spatial frequencies, fundamentally different from fitting error. Frequencies above Nyquist are aliased to low order it is linked to the sampling of the WFS: the wavefront will sample the wavefront up to a limit, which is defined by the size of the sub-aperture of the WFS, d W F S , which is the pixel size; spatial frequencies that are greater than the Nyquist frequency of the WFS, defined by 1/(2d W F S ), will experience the aliasing effect. The frequencies above the Nyquist limit will be aliased to low orders.The PyWFS is less sensitive to this effect. For a Shack-Hartmann WFS, it is defined as [START_REF] Rigaut | Analytical model for Shack-Hartmann-based adaptive optics systems[END_REF]:

σ 2 alias " 0.08p d W F S r 0 q 5{3 (2.23)
-the noise error, which is of two different types: the readout noise of the sensors, which is electronic noise, and the photon noise. The photon noise depends on the number of received photons throughout a single frame.

Except for the aliasing, these errors are greater closer to the center of the image, in a HCI configuration; Figure 2.11 presents the contrast distribution of these terms. There are other sources of errors, induced by the optics beyond the AO loop, the non-common path aberrations, 3. The non-common path aberrations calibrate. This is especially problematic for HCI of exoplanets as they induce speckles in the science image that mask and mimic exoplanet signals, as described before and seen in Figure 2.12 and 1.8. Furthermore, speckles resulting from NCPA are different from the ones induced by the atmospheric residuals: they do not average out to a spatially smooth halo as fast as atmospheric speckles, making them even more planet-like.

NCPA and WFS non-linerarities

NCPA are usually corrected by introducing an offset in the WFS signals corresponding to the aberration to correct. However, this assumes the WFS is linear, which isn't the case for the PyWFS, and the calibration with the DM is performed with a previously calculated control matrix, which is true to some extent but mainly wrong, as described earlier. As a result, the problems of NCPA and the non-linearity of a PyWFS are intrinsically linked, since the response of the PyWFS is different depending on the amplitude of the incoming wavefront. Thus, even if we understand what the NCPA are and update the reference of the WFS, there will be a wrong understanding of the NCPA from the DM because of this non-linearity, therefore a wrong command on the DM, therefore a wrong correction of the NCPA. Adding to that the fact that the NCPA are dynamic, the problem reaches another level of complexity.

Different methods for NCPA correction

Post-processing methods have been developed to minimize speckles' intensity in scientific images and analyze the data after the observations. That includes a variety of algorithms, described in Galicher et al., 2018; describing them in detail is out of the scope of this thesis. However, these post-processing methods are limited by several aspects. For example, angular differential imaging (ADI) is limited by self-subtraction effects. Furthermore, with long exposure times of the science images, NCPA are smoothed without being corrected, limiting the performances of post-processing techniques to the photon noise induced by these speckles. Hence, over the last decade, more active methods arose to correct aberrations in the images, during the observations, improving image qualities for the post-processing steps. These methods often rely on using the focal plane for wavefront sensing and control. I will present here some examples of methods to correct NCPA. This list is, however, not exhaustive.

Phase diversity

The basic idea of this method is to create diversity in the phase, by acquiring at least two images (typically one in focus, and one out of focus), to estimate the phase of the electric field from intensity measurements, through an iterative optimization algorithm (Gonsalves, 1982;[START_REF] Paxman | Joint estimation of object and aberrations by using phase diversity[END_REF][START_REF] Blanc | Marginal estimation of aberrations and image restoration by use of phase diversity[END_REF]. In fact, from just a single focal plane image, we only have information about the amplitude of the electric field in the focal plane, and the corresponding phase is degenerate. There is not enough information from the focal plane intensity alone to recover the wavefront; a second defocused image provides sufficient information to recover it. Hence, using the focal plane with phase diversity allows recovery of both the phase and the amplitude, allowing to correct for static NCPA. This method only corrects the low-order aberrations, and works mainly on non-coronagraphic images. There are several phase diversity algorithms, based on different ways to generate this diversity, such as through a Fourier-base modal basis. Several WFC algorithms are based on phase diversity, that have also been developed for coronagraphic images, such as the COFFEE technique [START_REF] Sauvage | Coronagraphic phase diversity: a simple focal plane sensor for high-contrast imaging[END_REF], which was used on SPHERE to calibrate quasi-static aberrations [START_REF] Paul | Compensation of high-order quasi-static aberrations on SPHERE with the coronagraphic phase diversity (COFFEE)[END_REF]. However, a coronagraph filters out the low-order modes, making this method less efficient for coronagraphic images [START_REF] Leboulleux | Experimental validation of coronagraphic focal-plane wavefront sensing for future segmented space telescopes[END_REF].

Electric field conjugation

The goal of electric field conjugation (EFC) is canceling speckles by adding in the focal plane the opposite electric field than what the speckles are. Here, "opposite" means the same amplitude, but with 180 degrees off phase [START_REF] Give'on | Pair-wise, deformable mirror, image plane-based diversity electric field estimation for high contrast coronagraphy[END_REF]. This can be done by DM actuation, because the speckles (what we want to cancel) and the added pattern (what we put with DM actuation) are both starlight, so they are mutually coherent. To do this, we need to measure the complex amplitude of the speckles, which requires DM modulation to "probe". Positive and negative probes are added to the DM, which results in adding a known complex amplitude to the focal plane camera. The speckles can then be removed, by subtracting the two images resulting from the positive and negative probes in the DM, as these images are linearly proportional to the electric field in the focal plane.

This result comes from the Fourier transform again, given the DM is on a pupil plane conjugated to the focal plane. Using modes to probe the DM allows for measuring the speckles' complex amplitude. Using the DM to probe speckles in the focal plane has then been extensively used in different ways, with different names, such as "speckle-nulling", which consists of probing the DM to destructively interfere speckles, creating a dark hole in the focal plane [START_REF] Martinache | On-Sky Speckle Nulling Demonstration at Small Angular Separation with SCExAO[END_REF][START_REF] Pogorelyuk | Dark Hole Maintenance and A Posteriori Intensity Estimation in the Presence of Speckle Drift in a High-contrast Space Coronagraph[END_REF]Potier et al., 2020b). This consists in first probing the DM over the focal plane, and then use a high-order DM to minimize the contrast inside a specific area of the focal plane: the dark hole. The EFC is often combined with other methods, such as pair-wise probing for inducing a phase diversity [START_REF] Potier | Exoplanet direct imaging in groundbased conditions on THD2 bench[END_REF], and linear dark field control (Miller et al., 2017;Ahn et al., 2022).

Self-coherent camera

The self-coherent camera (SCC) is a focal plane science camera designed to measure the speckles' complex amplitude. EFC uses temporal modulation requiring multiple images, while the SCC performs the measurement in the spatial dimension on the detector. They are two different approaches to get the same measurement. The SCC is based on the same interference principles as first demonstrated by Young's double slit experiment, introduced by Thomas Young in 1801 [START_REF] Young | The Bakerian Lecture: Experiments and Calculations Relative to Physical Optics[END_REF], which consists in interfering light coming from the same source and going through two holes, or slits4 . Figure 2.13 presents the principle of the SCC: the starlight and the (the PSF core), and the aberrations therein the system. The detector is located on a pupil plane. The ZELDA was initially inspired by the phase-induced amplitude apodization coronagraph (PIAAC) concept [START_REF] Guyon | Exoplanet Imaging with a Phase-induced Amplitude Apodization Coronagraph. I. Principle[END_REF]. This method has been applied on the SPHERE instrument, resulting in an estimation of the NCPA to be of "50 nm RMS [START_REF] Vigan | Calibration of quasistatic aberrations in exoplanet direct-imaging instruments with a Zernike phase-mask sensor. IV. Temporal stability of non-common path aberrations in VLT/SPHERE[END_REF]. The Zernike phase mask has been used to measure phase discontinuities in segmented apertures and low-wind effects [START_REF] Janin-Potiron | Fine cophasing of segmented aperture telescopes with ZELDA, a Zernike wavefront sensor in the diffraction-limited regime[END_REF]Bertrou-Cantou et al., 2020). ZELDA has to be deployed before the coronagraph, hence it misses some of the NCPA.

Photonic lantern wavefront sensing

This new type of WFS is based on a photonic lantern (PL) located at the focal plane, instead of a pupil plane, allowing to eliminate parts of the non-common path and hence the associated aberrations [START_REF] Norris | An all-photonic focal-plane wavefront sensor[END_REF]. Similarly to ZELDA, the PL will require its own optical path as it has to be before the coronagraph; hence it has the same NCPA limitation as ZELDA. The light in the PL is first received through a multi-mode fiber at its input, and has multiple singlemode outputs. The interference inside the multi-mode part encodes the upstream wavefront complex amplitude.

Optical gain adaptation

With the methods mentioned above, the assumption has been that NCPA would be measured from the focal plane and then corrected by offsetting the upstream pupil-plane WFS. In this configuration, the non-linearity of the PyWFS is a concern, as it is hard to offset by a known amount. Indeed, as mentioned in Section 2.5.3, the non-linear behavior of the PyWFS makes it challenging to accurately correct NCPA with typical focal plane WFC techniques. [START_REF] Esposito | Non common path aberration correction with non linear WFSs[END_REF] have been pioneering the way to deal with NCPA with non-linear wavefront sensors, mainly the PyWFS. They suggest a solution to the problem by adapting the optical gain with a tracking loop, thanks to a sinusoidal signal added on the DM, to have a modulation and demodulation allowing to derive the value of the optical gain. Several other studies (Deo et al., 2019a;Chambouleyron et al., 2021) look into this solution of using the OG to adapt for the PyWFS.

Several other WFC methods have been developed, using coronagraphs [START_REF] Bos | Focal-plane wavefront sensing with the vector-Apodizing Phase Plate[END_REF], and using deep learning algorithms to retrieve and correct NCPA, or to make other algorithms faster to converge and correct them (Orban de [START_REF] Orban De Xivry | Focal plane wavefront sensing using machine learning: performance of convolutional neural networks compared to fundamental limits[END_REF][START_REF] Quesnel | A deep learning approach for focal-plane wavefront sensing using vortex phase diversity[END_REF]. Some of these methods mentioned above are compatible with one another, improving the capabilities of NCPA correction (Potier et al., 2020a). The use of the focal plane for wavefront sensing and control is necessary to correct NCPA; however, retrieving their phase and amplitude remains a challenging task. Several of these methods are invasive in the ExAO system, requiring further hardware, or are problematic to implement during on-sky observations, as they can be conflicting with the requirements of the science data (for example, the phase diversity needs a defocused image, which cannot be used for science).

Smarter adaptive optics control

In present-day conventional AO systems described above (including the current generation of extreme-AO systems), the RTC follows a well-defined linear control scheme: input measurements from a single WFS are multiplied by a control matrix to produce an output DM control command. Thanks to recent high-performance computing capabilities and new algorithms allowing greater computation speed and power, powerful extensions to this framework are now emerging:

Sensor fusion techniques can ingest measurements from multiple WFSs in the AO system, aiming to improve the correction's sensitivity, completeness, and robustness. Sensitivity is improved by combining WFSs that, together, collect more starlight than an individual WFS would. Completeness is improved by gathering information from WFSs that are complementary to the measurements they perform. Robustness gains result from eliminating measurement ambiguities.

Predictive control greatly improves the sensitivity and time response of the AO correction. It is the solution to the most fundamental limit: the trade-off between flux and correction speed. In a conventional AO system, the WFS measurement must be sufficiently fast to catch up with rapidly changing turbulence, but sufficiently slow to average photon noise. The conventional RTC operates at a speed that is a painful compromise between time lag and measurement noise. With predictive control, the time lag is eliminated and replaced by a much smaller temporal prediction error. Recent measurements can be extrapolated in a way that offers the noise-reduction benefits of time averaging without incurring the temporal lag cost (Guyon et al., 2017a). Several studies on predictive have recently been published on that topic [START_REF] Van Kooten | Robustness of prediction for extreme adaptive optics systems under various observing conditions. An analysis using VLT/SPHERE adaptive optics data[END_REF][START_REF] Wong | Predictive control for adaptive optics using neural networks[END_REF][START_REF] Fowler | Battle of the predictive wavefront controls: comparing data and model-driven predictive control for high contrast imaging[END_REF].

Non-linear control extends the range of WFS solutions to include focal plane images, in which information about optical aberrations is encoded with high sensitivity, but for which the relationship to measurements is highly non-linear.

Self-calibration is essential for the robust operation of the above techniques. In conventional AO, calibration is performed offline prior to running the AO system. Typically, a response matrix will be measured by actuating individual DM actuators and recording the corresponding linear response in the WFS. This approach cannot measure the actual on-sky system response which evolves due to variations in conditions, and it cannot extend to the sensor fusion, predictive control, and non-linear control schemes described above. Instead, the calibration needs to be continuously derived from recent (" < 10 mn for predictive control) on-sky measurements. Without spoiling anything, self-calibration is exactly what we will focus on in Chapter 3.

Motivation ‹

Once atmospheric turbulence has been corrected, delivering a wavefront closer to being flat, another major issue to address in HCI when trying to image exoplanets is the star-to-planet contrast. In fact, the star is at least 10 6 times brighter than the planet, in the case of a young giant Jupiter-like planet. For a Jupiter-like (older) planet, the contrast is 10 9 . It is estimated that for observing an earth-like planet in the habitable zone of a Sun-like star, the star-to-planet contrast is about 10 10 in the visible, meaning we receive ten billion photons from the star for a single photon coming from the planet (as introduced in Section 2.2). To put it into human scales, that would correspond to trying to look at a firefly by a lighthouse in Hilo, Hawai'i, from San Francisco, California 5 . Quite a challenge, right? Hence, it is necessary to block out the light from the star, which is possible via a coronagraph, aiming at suppressing the starlight while transmitting the off-axis exoplanet signal.

Coronagraphs present interesting optical properties in the context of exoplanet imaging, thanks to the reduction of bright diffraction structures from the star. They are extremely powerful in achieving high contrasts and have a wide diversity of designs having a different impact on the goal of direct imaging [START_REF] Guyon | Theoretical Limits on Extrasolar Terrestrial Planet Detection with Coronagraphs[END_REF].

Some definitions

Inner working angle: in a unit of λ{D, the inner working angle (IWA) corresponds to the closest angle at which a faint source can be imaged from the star. It is defined at the 50% peak throughput point, where the source throughput is 50% of the maximum throughput;

Transmission: it quantifies the coronagraph throughput as a function of angular separation close to the optical axis.

Contrast: the contrast is the amount of residual starlight in the focal plane after the coronagraph, expressed in a unit of surface brightness relative to the unocculted PSF core.

Null order: it expresses the degree of attenuation of a point source as a function of the source offset to the optical axis. It is quantified by expressing transmission as a polynomial function of this angle and reports the degree of the dominant term. For example, 4th order means transmission goes as x 4 , with x being the distance to the optical axis. This is important to quantify how sensitive the coronagraph is to small pointing errors, and to the stellar angular size. It is used mainly in interferometry with dark fringes.

5.

Assuming there is no curvature between Hilo and San Francisco

Types of coronagraphs

There are several coronagraph types, presenting different optical properties for different use. Describing coronagraphy in detail is out of the scope of this thesis, so I will here give a brief description. Coronagraphy is a very active field of research with new recurring ideas. Coronagraphs can be mainly separated into several categories, I will focus on three types here:

-In focal-plane coronagraphs, a mask is placed on-axis in the focal plane. They block and/or diffract (away from the downstream pupil aperture) the starlight, with amplitude and/or phase. The classic focal plane coronagraph is the Lyot one, introduced by Bernard Lyot in 1939 to observe the sun [START_REF] Lyot | The study of the solar corona and prominences without eclipses (George Darwin Lecture[END_REF], turned to a stellar coronagraph later on, adapted to point sources. The first focal plane phase mask, which induces a difference in the complex amplitude of the image to create (destructive) interferences, was developed in 1997 for the purpose of exoplanet imaging [START_REF] Roddier | Stellar Coronograph with Phase Mask[END_REF]. Downstream the focal-plane coronagraph, in the pupil plane, resides an additional Lyot stop to block the residual starlight that is mostly outside, or at the outer edge of the pupil. As the exoplanet light is off-axis, it misses the focal plane mask and is transmitted toward the detector, and not diffracted outside the pupil. There have been several technological developments in focal plane coronagraphs, both in phase and amplitude. To name two, there is the Four-Quadrant Phase-Mask coronagraph (4QPMC, [START_REF] Rouan | The Four-Quadrant Phase-Mask Coronagraph. I. Principle[END_REF] and the Annular Groove Phase Mask (AGPM, [START_REF] Mawet | Annular Groove Phase Mask Coronagraph[END_REF].

-Pupil-plane coronagraphs shape the PSF to create high-contrast (dark) areas in the focal plane. The region of canceled starlight is called a dark hole. Two pupil-plane coronagraphs are worth citing, the Phase-induced Amplitude Apodization Coronagraph (PIAAC, [START_REF] Guyon | Exoplanet Imaging with a Phase-induced Amplitude Apodization Coronagraph. I. Principle[END_REF] and the vector Apodizing Phase Plate coronagraph (vAPP, Snik et al., 2012).

-Combination of pupil plane and focal plane: further optics, such as an apodizer, can be added in the pupil plane ahead of the focal plane to improve the stellar rejection. An example of such a type of coronagraph is the Apodized Pupil Lyot Coronagraph (APLC, [START_REF] Soummer | Stellar coronagraphy with prolate apodized circular apertures[END_REF].

Contrast curves

The quality of a high-contrast instrument is measured in contrast. Contrast curves provide insight into the instrument's capabilities. Contrast can refer to the raw contrast, which is a property of the coronagraph, or the detection contrast, which is a property of the HCI system, including image processing. Figure 1.7 presents different science cases for different contrasts, and Figure 1.17 shows a combination of contrast curves for different ground and space-based telescopes.

The Subaru Coronagraph Extreme Adaptive Optics instrument 6.1 Introduction

In Chapter 1, I introduced the science goals of DI, and a few of the post-processing methods. In this chapter, I introduced the basics of AO and high-contrast imaging. It goes without saying that a lot is going on, with many ongoing instrumentation developments (Bos et al., 2020;[START_REF] Vievard | Focal Plane Wavefront Sensing on SUBARU/SCExAO[END_REF][START_REF] Lozi | AO3000 at Subaru: combining for the first time a NIR WFS using First Light's C-RED ONE and AL-PAO's 64x64 DM[END_REF]Deo et al., 2022;Ahn et al., 2022;[START_REF] Steiger | Probing Photon Statistics in Adaptive Optics Images with SCExAO/MEC[END_REF]. And yet, imaging extraterrestrial worlds is already within reach, with many directly imaged exoplanets and over 300 circumstellar disks 6 . In this section, I will present the Subaru Coronagraph Extreme Adaptive Optics (SCExAO) instrument at the Subaru Telescope in Hawai'i. The goal here is to sum up with a concrete example all the aspects previously introduced for the direct imaging of exoplanetary systems. SCExAO is also unique worldwide as it offers a platform for both instrumentation development and scientific observations, with, on average, " 40 nights on sky per year, with roughly 3/4 for science observations and 1/4 of engineering nights. Instrumentation development makes SCExAO a system-level demonstrator of the Planetary Systems Imager (PSI), the HCI of the TMT [START_REF] Lozi | Status of the SCExAO instrument: recent technology upgrades and path to a system-level demonstrator for PSI[END_REF]Fitzgerald et al., 2019b). SCExAO is furthermore a flexible bench and open to the international community, making it an excellent, unique, and fruitful collaborative platform (Bos et al., 2020;[START_REF] Norris | Demonstration of a photonic-lantern focal-plane wavefront sensor using fiber mode conversion and deep learning[END_REF], leading to fruitful science results [START_REF] Steiger | SCExAO/MEC and CHARIS Discovery of a Low-mass, 6 au Separation Companion to HIP 109427 Using Stochastic Speckle Discrimination and High-contrast Spectroscopy[END_REF]Currie et al., 2022b;[START_REF] Kuzuhara | Direct-imaging Discovery and Dynamical Mass of a Substellar Companion Orbiting an Accelerating Hyades Sun-like Star with SCExAO/CHARIS[END_REF]. Much of my thesis work has been developed for SCExAO, which I will describe in Chapter 3.

Figure 2.14 presents a schematic view of a two-stage ExAO instrument, such as SCExAO.

Description of the ExAO instrument

SCExAO is located on the infrared Nasmyth platform of the Subaru Telescope, an 8.2meter diameter telescope. It is a second-stage AO system located downstream from the AO188 instrument (Minowa et al., 2010). AO188 performs the first stage of AO with a 188-actuator DM; it corrects the low orders of the aberrations before sending the light to SCExAO, and provides a pre-correction with a SR in H-band of " 20-40% [START_REF] Lozi | AO3000 at Subaru: combining for the first time a NIR WFS using First Light's C-RED ONE and AL-PAO's 64x64 DM[END_REF]. SCExAO is designed to observe exoplanets and circumstellar environments around nearby stars (Jovanovic et al., 2015), and regularly reaches SR above 90% in H-band (Lozi et al., 2019). Figure 2.15 presents the PSF with and without AO188 and SCExAO, and Figure 2.16 presents a simulated perfect PSF on SCExAO.

SCExAO performs the second-stage AO thanks to a visible pyramid WFS, operating in the 600-950 nm wavelength range (Lozi et al., 2019). It controls a 2000-actuator MEMS DM from Boston Micromachines. There are 45 actuators across the pupil, giving a control region of ˘22.5 λ{D squared. The Compute And Control for Adaptive Optic (CACAO) software manages the real-time control (RTC) of the AO system (Guyon et al., 2018), I will describe it in Section 4.1. We use the CACAO software to interact with the system and implement the 6. Source: https://www.circumstellardisks.org

The Subaru Coronagraph Extreme Adaptive Optics instrument

The scexao2 computer deals with managing everything linked with the mechanics of the bench. It controls the following aspects:

-the calibration sources -the different filter wheels, including the coronagraphs -the PyWFS hardware -the NIR cameras (Palila and C-RED ONE) -motors in the IR and visible benches Several scripts allow for easier alignments, such as the "hot spot align" module (performed with CTRL+H) on the camera.

The data storage computer:

The scexao3 computer is the data beast: this is where the database and backups are.

The data acquisition computer:

The scexao5 computer is linked to the cameras and collects their data, before sending them to the RTC computer through a dedicated fiber link.

The RTC computer:

The scexaortc, also known as scexao6 computer is the beast of the SCExAO computers, with the most demanding high-performance computing requirements. It has two AMD Epyc 7763 processors with 128 cores total, 1TB RAM, PCI Gen 4, 5 GPUs (A6000, 3080Ti, 2080Ti), and 600TB+ of storage, including 20GB/s+ temp storage SSDs. scexao6 is operating a fast 100Gbps downlink from the instrument (located in the IR Nasmyth platform) to the server room without data collisions and without introducing too much timing variability. It deals with managing everything linked with the RTC, and controls the following aspects:

-the PyWFS data processing to drive the ExAO loop; -the DM display and control; -the Tip-Tilt (TT) loop; -the astrogrid status; -the low-order WFS loop.

In Section 4.1, I will describe the CACAO RTC.

The science instruments and their capabilities

I briefly mentioned in Section 6.3 the 5 science instruments downstream SCExAO: CHARIS [START_REF] Groff | The CHARIS IFS for high contrast imaging at Subaru[END_REF], VAMPIRES (Norris et al., 2015), FIRST [START_REF] Huby | FIRST, a fibered aperture masking instrument. I. First on-sky test results[END_REF], REACH [START_REF] Kotani | Extremely high-contrast, high spectral resolution spectrometer REACH for the Subaru Telescope[END_REF], and MEC [START_REF] Mazin | MKIDs for Direct Imaging of Exoplanets[END_REF]. Table 2.2 presents a brief description of the characteristics of these instruments. There are two other instruments currently in development and not used for science observations yet: GLINT [START_REF] Norris | An all-photonic focal-plane wavefront sensor[END_REF], and RHEA [START_REF] Rains | Precision single mode fibre integral field spectroscopy with the RHEA spectrograph[END_REF]. NB: FIRST is not proposed as a science instrument yet, but it will soon be. A paper is about to be published with scientific results (Vievard et al., in review).

FoV

As of fall 2022, SCExAO provides the following key capabilities, presented on the SCExAO website:

-Extreme-AO correction providing high SR in near-IR and diffraction-limited imaging in visible light;

-Coronagraphic starlight suppression in near-IR;

-Near-infrared (0.95-2.4 µm) integral field spectroscopic imaging (R=20-70) with the CHARIS instrument;

-Near-infrared (0.95-1.7 µm) high frame rate (kHz) imaging and polarimetric differential imaging (FastPDI);

-Near-infrared (Y and J bands) photon-counting energy-resolving imaging (MEC);

-Near-infrared (0.97-1.75 µm) high resolution (R=100,000) spectroscopy with the REACH spectrograph;

-Visible light (0.6-0.9 µm) imaging, with polarimetric and spectral differential imaging with the VAMPIRES instrument;

-Visible light (0.6-0.9 µm) interferometry and polarimetric interferometry with the VAM-PIRES instrument.

Chapter 3

The DrWHO algorithm

The previous chapters set the scientific and instrumentation grounds for the general context of this PhD thesis. I described the exoplanet context and the main instrumentation tools for the direct imaging of exoplanets. I introduced what adaptive optics systems are, and the basic description of the NCPA problem. As a reminder, the goal is to improve observations of exoplanet worlds, by improving the contrast to image fainter exoplanets, understanding the conditions during their formation and acquiring high signal-to-noise spectra at high spectral resolution.

Speckle control is a considerable step to overcome for that goal, and NCPA have become one of the main limitations to reaching it. I present in this chapter a detailed explanation of the NCPA problem, especially in the field of HCI. I will then offer a suggested solution, one of the main topics of this thesis: the Direct Reinforcement Wavefront Heuristic Optimization (DrWHO) algorithm. I first tested this algorithm on simulations, and then with the SCExAO instrument on sky. The main results of my work are presented in a peer-reviewed paper presented in Section 5. This chapter provides more detailed explanations and additional work. I will conclude this chapter by describing a suggested upgrade of this algorithm, on which I started to work. The reader should keep in mind that this is ongoing work.

Road-map to the speckle noise 1.A challenge with many layers

I introduced in Sections 2.2.2 and 2.7 the challenges with the speckle noise in the context of HCI. 10-m-class telescopes are achieving the required sensitivity for the DI of young giant exoplanets (Marois et al., 2008). While such planets on wide orbits (>"10-15 AU) are relatively easy to image with current instruments (for example, HR8799's planets at >0.4" separation), inner planets (< 10AU) are mostly out of reach due to poor instrument contrast at small angular separation.

1. Road-map to the speckle noise orders of magnitude worse than the photon noise at a small angular separation. Using the focal place as a WFS for WFC brings down the photon noise limit, as there is a clean signal to measure speckles, and more photons are received, allowing a gain of one order of magnitude in contrast.

Furthermore, the aberrations introduced by atmospheric turbulence and instrument optics lead to different types of speckles with different lifetimes, from static to slow and fast. Minimizing the atmospheric residuals have been a focus in the last decade of wavefront control techniques [START_REF] Guyon | Extreme Adaptive Optics[END_REF][START_REF] Singh | Active minimization of non-common path aberrations in long-exposure imaging of exoplanetary systems[END_REF]Vigan et al., 2019;Potier et al., 2020b). Yet, NCPA being slow and static aberrations remain a critical limiting factor for exoplanet detection (Vigan et al., 2018). As mentioned in Section 3 and seen in Figure 2.12, the WFS does not see NCPA, hence the difficulty in correcting them. Using the focal plane for WFC becomes crucial.

Figure 3.1 presents a summary of the challenges faced for HCI of exoplanetary systems as described until this point. With all of these elements put together, there is considerable room for improvement in wavefront sensing techniques for calibrating speckle noise. Currently, the best raw contrast with SCExAO at this angular separation is 10 ´4, and after post-processing, the contrast can get down to 10 ´6 with conventional speckle calibration techniques. However, the goal is to reach the photon noise limit, which is the fundamental limit. The current fundamental photon noise limit without using the focal plane is 2.35 ˆ10 ´9 (1-σ), for one hour of exposure time at 30% efficiency. As mentioned above, the goal is to use use the focal plane as WFS to bring down this limit, and if so, the raw contrast would become 10 ´5, and the photon noise limit becomes 7 ˆ10 ´10 (1-σ). There is hence great interest in using the focal plane, with the potential of improving the contrast limit by " 400 times.

An example: the star ǫ Eri

Hence, by improving AO performances and operate at the photon noise limit, planets in HZ could almost be within reach on the best stars with an 8-meter telescope such as Subaru. Realistically, this is not really achievable, it however illustrates the potential gain of >2 order of magnitude with instrumentation development. Some of it is achieved by improving the raw contrast (from 10 ´4 to 10 ´5) and some of it achieved by calibration of residual speckles which allows us to operate at the photon noise limit. My PhD work is mostly about the first part, but provides encouraging evidence for the second part as well, proving that we are able to accurately derive the speckle field from WFS telemetry.

The DrWHO algorithm lengths;

-choice of optimal wavefront state, with different WFC methods. For example, the dark hole technique, aiming at cancelling static diffraction features, may seek to drive the AO to a non-flat wavefront state [START_REF] Potier | Increasing the raw contrast of VLT/SPHERE with the dark hole technique. II. On-sky wavefront correction and coherent differential imaging[END_REF].

These effects have timescales slower than millisecond-level, which is semi-static compared to the atmospheric turbulence timescale. In this chapter, I will generalize and refer to these effects as NCPA, noting that this term usually only refer to the differential optical effects between the AO loop and the science camera, as seen in Figure 2.12.

These NCPA present challenging characteristics to correct; below is a brief and non-exhaustive summary of these different aspects:

-NCPA induce speckle noise in the focal plane, which is especially problematic as that mimics exoplanet signal;

-NCPA span a wide range of temporal stability, from quasi-static to fast-varying, they can't be corrected once and for all before observations on-sky;

-NCPA are not seen by the WFS, they are not corrected by a conventional adaptive optics control loop, although indirect ways have been developed;

-the focal plane image is highly sensitive to speckles.

I presented in Section 3.4 a few methods that have been developed for NCPA correction. As mentioned, these methods present some down sides, sometimes being invasive to the AO instrument with the need of additional hardware, or are conflicting with on-sky observations. Most of the methods mentioned are not designed to run during the observations, hence their incapacity to correct the quasi-static NCPA that evolve throughout the observations. There is a need to correct for these quasi-static speckles, in a way that is not invasive to the system.

Optimizing image quality: a reference issue

Let's first define the reference of the WFS. It is especially important as it drives the point of convergence of the whole AO loop. The reference of the WFS is the phase that is subtracted from the WFS measurement before measuring the correction that needs to be sent to the DM. It could be compared to the "tare" button on a scale. I described in Section 2.6.3 the different steps performed by the RTC to go from the WFS measurements to the DM commands. Once the WFS measurements are acquired, the RTC subtracts the measurements from the reference of the WFS. Figure 3.3 presents an updated version of the Figure 2.9, including the subtraction of the WFS reference before the measurement is taken into account.

The main question of any AO system is "what is the WFS ideal reference?", in other words, what reference gives a "flat" wavefront in the sense of Strehl maximization, corrected from the 2. The DrWHO algorithm the algorithm is rewarded when choosing the best PSF and self-optimizes itself by updating the reference at each iteration of the algorithm, converging towards compensation of the aberrations. Therefore, as the algorithm proceeds, the WFS is continuously rewarded for high-quality PSF; thus, the PSF quality improves and converges towards better quality.

Algorithm 1 presents the steps of DrWHO, as well as Figure 3.4. First, the focal plane and WFS data must be acquired to create two synchronized data blocks. The size of the block depends on the length of the DrWHO loop, of a few seconds -let's consider 30 seconds (which corresponds to 60,000 images if the loop is running at 2kHz). Then, out of the focal plane data block, DrWHO measures a quality criterion -a score -for each image and selects a fraction of the best images in the 30-second data block-let's consider 10%. This score can be the Strehl ratio, the contrast, the intensity, or any quality criteria desired. Then, the next step is to take the corresponding WFS images of the best 10% selected focal plane frames. Out of these related WFS images, the new reference is calculated by averaging these 10% of the 30 seconds. The new reference is then applied to the WFS, changing the AO loop's convergence point. It can be interesting to see that DrWHO can be approximated as a kind of reinforcement learning approach, which is a data-based machine learning method, rewarding desired behaviors and rejecting undesired ones, as shown in 3.5. The agent is here the algorithm DrWHO, the 3. DrWHO on COMPASS coronagraph. This is currently under development.

Steps of DrWHO on COMPASS

I used ADOPT to run DrWHO, which is a user-friendly interface of COMPASS, developed by Fabrice Vidal at LESIA, and is coded with Python.

Running DrWHO on simulations requires several steps. First, the simulation is started by running a parameter file, simulating the characteristics of SCExAO and the Subaru telescope, including the pre-correction from AO188. This is presented in Table 1 in Skaf et al., 2022b. Algorithm 2 shows the steps needed to run DrWHO on COMPASS. First, a modal basis must be computed, allowing a response matrix to be acquired (based on the push and pull of the modes of the previously computed modal basis), for having a command matrix. The initial reference of the PyWFS must be set to zero, making sure the noise has been removed -a luxury offered by simulations.

Before running DrWHO simulations it is important to verify that the initial reference is indeed the correct one, to avoid biasing the results. Then, the NCPA are added to the wavefront after the AO loop, and included in the PSF computation. The NCPA correspond to a random combination of the first 10 Zernike modes: Figure 2 of Skaf et al., 2022b presents the NCPA phase in the pupil plane and its corresponding PSF in the focal plane. In fact, it is expected that NCPA are mainly composed of low-order aberrations, which motivated our choice to limit the NCPA at the first 10 Zernike modes. The amplitude of the NCPA is an input argument of the function. Typically, I would set an NCPA amplitude of 0.04µm RMS, corresponding to the expected NCPA on SCExAO given the ones measured on SPHERE (Vigan et al., 2019). Another luxury offered by the simulations is that the WFS and PSF frames are synchronized: the AO loop can run at the desired frequency (for us 2kHz, to match SCExAO), and the PSF frames too.

Then, the DrWHO function comes into play, having several input arguments, that can be separated into two categories: the AO loop simulations arguments, and the ones specific to DrWHO. The AO loop arguments are:

-the gain of the AO loop (typically set at 0.3); -the Fried parameter value, r 0 (typically set at 0.16); -the noise; -the choice of modal basis.

The DrWHO arguments are:

-the number of iterations of the AO loop within the DrWHO loop Nbuffer;

-the number of iterations of DrWHO loop Nloop; -the weight w, for applying an integrator filter on the new reference. This function is the algorithm's core, calculates the score -here the SR -for each frame, and computes the new reference.

NB: Because simulating the atmosphere and the RTC is time-consuming, even with GPU, I would typically do my tests with Nbuffer on the order of " 2000 loop iterations, meaning 2000 phase WFS measurements and PSF, per DrWHO iteration.

COMPASS is provided with a GUI interface, offering visibility on anything desired. Figure 3.6 shows a typical example of a simulation running on COMPASS.

Data:

-WFS frames

ImageStreamIO

ImageStreamIO3 allows the use of the data streams in shared memory image format. This deals directly with the camera FITS files, allowing to read and write data streams, at low latency and a high throughput input/output (I/O) of data. There are two main scripts for data conversion, either converting from shared memory to FITS files (shmim2fits) or converting from FITS files to shared memory (Fits2shm).

CACAO architecture

The architecture of the CACAO software4 is made of several steps. It offers several ways to run the AO control loop, whether one wants to run in a closed loop, or a pseudo-open loop, and computes predictive control. The telemetry is systematically saved. I will dive here into a more advanced description of the control loop running SCExAO, based on Figure 3.11 (sensitive souls and non-AO specialists can skip this section).

The figure starts on the bottom left side, where the WFS images are acquired. There are two possibilities from there, either the zonal reconstruction or the modal reconstruction:

-zonal reconstruction: the fastest way to write on the DM is to multiply the WFS image by the control matrix, and send the command to the DM;

-modal reconstruction: the WFS modes are computed from the WFS images (pink box in the figure).

If the modal reconstruction is chosen, the next step is modal filtering (bottom right side of the green area), leading to corrected and filtered modes, that can be sent to the DM for a modal correction.

The is the possibility to run the loop in a pseudo-open loop, meaning part of the correction is in a closed loop, simply sending the correction to the DM from the WFS measurements. The other part goes through further computation to perform different types of correction, in this case, predictive control, as described in Guyon et al., 2017b. The ratio sent to predictive control is done with the ARPF (auto-regressive predictive filter) gain. The pseudo-open loop reconstruction extracts the open-loop WFS modes and computes predicted mode coefficients (top left green area). Telemetry is saved, and predictive filter blocks are computed (top right grey boxes) to send the predicted mode coefficients to the DM.

The different DrWHO scripts

Description

Five main bash scripts run the DrWHO algorithm, and three call other functions. I will call these scripts in letters, from A to E to make it easier. by sending deformable mirror commands and monitoring when they affect the data in the stream.

For example, the NIR camera "Palila" 6 , a cooled InGaAs camera (model CRED2 from First Light Imaging), runs at 1kHz, the PyWFS camera, "Pueo", an EMCCD (model Ocam2k from First Light Imaging), runs at 2kH. I want both streams to be synchronized at a frequency difference of 3kHz. The first step is to wait for the data files to appear on the hard drive, the fits cubes, and the timing files, which will be read and re-sampled to the same time baseline. If there are missing frames, or if the timing is not continuous, the script is designed to handle it appropriately: for example if the operator desires a 1ms frame, and yet there is a half Ocam image, and half the other Ocam image, the script will perform the weighted average of the two halves. Then, the script creates another data stream (which appears on the disk), with data cubes of the length corresponding to the time span of the DrWHO iteration. This process is not appropriately real-time, as there is a latency to it, however the script will provide nearly real-time synchronized fits files with the sampling and the timing information. NB1: it often takes some time for the script to catch up on the data files at the beginning if data were saved for a while, as the script needs to reach each timing files. NB2: the synchronized data cubes are saved in the directory where the script was started.

Evaluation mode

The evaluation mode as presented in Table 3.1 corresponds to the quality criteria, also called the score in Skaf et al., 2022b. It appears in the script cacao-selectWFSframes, where the function at the core of the DrWHO algorithm is called. There are currently three different types of evaluation modes:

-0: maximizes the flux concentration; -1: maximizes the flux; -2: minimizes the flux.

In the case of non-coronagraphic PSF, it is the score of choice for accurately observing the evolution of the PSF. In the case of coronagraphic focal plane images, the goal is (usually) to increase the contrast. Hence, the appropriate quality criteria becomes to minimize the flux over the image. The evaluation mode is flexible, and the user is free to introduce any quality criteria.

The flux concentration

The flux concentration (FC) is described in detail in Section 5.1 in Skaf et al., 2022b. I remind here what it is. As its names suggests, the FC describes the concentration of flux over the pixels. It has been introduced as the quality criteria for quantifying the evolution of the PSF, for the DrWHO runs. It is defined as: FC "

ř i px α i q p ř i x i q α , (3.2)
with x i being the value of the (focal plane) pixel i, and α ą 1 -we will use α = 2, as higher values of α favor the brightest pixels. If some pixels have a negative value following a dark subtraction due to camera readout noise, then the pixel value is set to zero. This quantity is independent of absolute flux since it is normalized by the total flux as seen in the denominator of equation 3.2.

The FC can be normalized by the FC of a simulated perfect PSF -which we will call FC 0computed for the pupil of the telescope (cf Figure 2.16), as the FC is a relative number. This new quantity is referred to as the normalized FC (nFC): nFC = FC / FC 0 .

DrWHO on SCExAO

Running DrWHO steps on SCExAO

General instructions

I described in Section 4.2 the structure of the DrWHO algorithm. To run DrWHO on SCExAO, one must first ensure that the two data streams -WFS and focal plane -are being saved in their respective directories. Then, after measuring the time lag between the camera streams, one must set the input parameters in runDrWHO, depending on the conditions and desired settings.

Bench tests

For testing DrWHO with the internal source, here is how to proceed:

-add atmospheric turbulence: one channel of the DM is for that purpose, this is set via the GUI of the control loop, -add NCPA: this is done by adding a phase map on one channel of the DM (cf Figure 2.17), a combination of the first Zernike modes. Then, we measure the WFS reference after the NCPA are added, such that NCPA are not corrected by the loop. Hence, the DM channel with the Zernike modes is considered as NCPA. It computes an offset based on the continuous components, and because it is in a closed-loop configuration, the optical gain does not impact it.

-dark management: removing the dark is optional, although highly recommended. The dark must be saved in the folder of the data streams, in the format "streamWFS.dark.fits" or "streamPSF.dark.fits" for the WFS and the focal plane camera respectively. The dark subtraction happens during the stream synchronization step, in the cacao-syncStreams script.

Optimizing DrWHO parameters

We need DrWHO to converge the fastest way and, therefore to figure out what is the best selection fraction rate of the best focal plane images, and the best length of the DrWHO iteration, depending on the stellar brightness and seeing conditions. Tests are still on-going.

Main on-sky results

Skaf et al., 2022b presents on-sky results of a DrWHO run in visible light with the VAM-PIRES instrument, in Sections 6.2 and 6.3, for PSF quality evolution and WFS reference evolution respectively. I will show here only the evolution of the PSF, before the DrWHO run, at the first iteration, and at the last iteration, see Figure 3.13, please refer to the paper for further results.

Mapping between WFS and PSF

DrWHO requires a one-to-one mapping from WFS to PSF to work. However, there is a degeneracy of the wavefront: two different wavefronts may lead to the same PSF, as is the case

Introduction

Over the past 30 years, Adaptive Optics (AO) instrumentation has undergone extensive development in terms of its sophistication and scientific capabilities. Compared to the first astronomical AO experiments with the COME-ON system consisting of a 19actuator deformable mirror (DM) driven at several hundred Hz [START_REF] Kern | New Technologies for Astronomy[END_REF]Rousset et al. 1990), current leading extreme AO (ExAO) systems consists of ≈2000-actuator DMs driven at over 1 kHz speeds (e.g., Macintosh et al. 2014;Beuzit et al. 2019). The high-contrast imaging enabled by these new AO capabilities has led to key scientific breakthroughs, including the first direct image of a planet-mass companion (Chauvin et al. 2004) and the first imaged system of jovian exoplanets (Marois et al. 2008).

Some of the current generation of ExAO systems, such as the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) at the Subaru Telescope (Jovanovic et al. 2015) and MagAO-X on the Magellan Clay Telescope (Males et al. 2018), are spurring further achievable levels of performance; for instance, in terms of Strehl ratio (SR), contrast, and sensitivity (e.g., Vigan et al. 2015;Currie et al. 2020). These also serve as technology prototypes for ExAO instruments on 25-40 m extremely large telescopes (Kasper et al. 2021;Fitzgerald et al. 2019;Close et al. 2020).

The ExAO loop corrects wavefront aberrations measured by the WFS, ideally approaching an aberration-free image. However, the ExAO loop convergence point, defined by the WFS reference, may not correspond to the optimal image quality. Reasons for such a discrepancy include several aspects. First, there are the non-common path aberrations (NCPAs) due to optics located after the beam splitting between WFS and science paths, inducing differential aberrations between the science camera and the WFS, as seen on Fig. 1. In a high-contrast imaging system, these aberrations may include coronagraph optics defects. These aberrations can also vary with temperature and mechanical deformation at timescales from minutes to hours, or with the positioning errors of moving optics, making them particularly challenging to calibrate. They are typically of the order of tens of nanometers, enough to lead to static and quasi static speckles in coronagraphic images (Sauvage et al. 2007;Vigan et al. 2019). These speckles are also present in non coronagraphic images but these are less concerning because they do not contribute significantly to the SR, as they are usually beneath the camera contrast limit for unsaturated images. In addition, discrepancies may come from WFS calibration errors due, for example, to a non-flat wavefront used to acquire a calibration. Then, the chromaticity for systems where the wavelength of the WFS and the scientific camera are different. Finally, there myst be a choice of optimal wavefront state: the goal of the AO system may not always be to produce a flat wavefront. For example, in a HCI, cancellation of static diffraction features (airy diffraction rings, telescope spiders), such as dark hole techniques (Potier et al. 2020), may be aimed at driving the AO loop to a non-flat wavefront state.

The phenomena responsible for the above effects exhibit timescales smaller than the millisecond-level atmospheric turbulence timescale and can be (nearly) static. In this paper, we refer to all discrepancies between WFS reference and optimal image wavefront as NCPAs, noting that in previous publications it usually only refers to differential optical defects.

NCPAs affect all AO systems, but they are particularly acute in high-contrast imaging where small wavefront errors can easily mask faint exoplanet images (cf. Fig. 1). Furthermore, quasi-static aberrations do not average out to a spatially smooth halo as fast as the atmospheric speckles, leaving structures in the coronagraphic image that resemble planets -unlike the speckles that are generated by atmospheric turbulence alone.

The most reliable approach to measure and correct optical misalignments is to use focal plane images (Gonsalves 1982). In the particular case of NCPAs, these images are ideally generated by the science detector. Several solutions have been suggested for static NCPAs (Paxman & Fienup 1988;Frazin 2018;Vigan et al. 2018;Vievard et al. 2020;Bos et al. 2020;Potier et al. 2020;Codona & Kenworthy 2013), the quasi-static part is shown to be particularly challenging to measure and correct. The evolutionary timescale of the aberrations with respect to the frequency of the correction is a main difficulty in this regard.

In a closed-loop AO system, NCPAs are usually compensated by subtracting a biasing reference signal in the WFS reference corresponding to the aberration to correct. Doing so requires good WFS response knowledge and stability, so that the adequate offset can be applied and maintained. Ideally, this offset should be updated in nearly real-time due to optical and mechanical variations in the instrument, however, in practice it is typically updated on a daily or weekly basis. Finding the adequate offset requires focal plane images to update the reference and this can furthermore be particularly challenging if the WFS exhibits a non-linear response that must be accounted for, as is the case in some high-performance WFSs such as the Pyramid WFS (PyWFS) (Esposito et al. 2020;Deo et al. 2019;Chambouleyron et al. 2020Chambouleyron et al. , 2021)).

In this paper we present the DrWHO algorithm, a model-free focal plane wavefront sensing approach that is aimed at finding the offset mentioned above to correct slow and static wavefront aberrations, including the NCPAs, on a timescale of a few seconds. We present our discussion in Sect. 2 and we describe the algorithm in Sect. 3. Numerical simulations with the COMPASS software (Ferreira et al. 2018) are presented in Sect. 4. In Sect. 5, we show the results of the algorithm as obtained on-sky with SCExAO. Section 6 presents the main results of the on-sky validation, in terms of PSF and WFS reference evolution. In Sect. 8, we review the characteristics of the algorithm and describe further implications for use in HCI.

Pursuing a good WFS reference

In a closed-loop AO system, each WFS measurement is compared to a WFS reference (usually by subtraction after flux normalization) to isolate residual wavefront errors that must be corrected by the DM. The real-time controller performs the wavefront reconstruction, thus bringing the WFS signal to a point where it gives a flat wavefront, such that the WFS reference defines the convergence point of the AO control loop.

The WFS reference can be measured with an internal light source inside the instrument, before on-sky observations. This can be done as a standalone step or by averaging the WFS signal when taking a response matrix, corresponding to the WFS signal when there is no aberration induced. However, in reality, the "ideal" WFS reference may be different from the internal source WFS reference due to optical illumination discrepancies. The WFS reference is also not static, constantly evolving due to quasi-static aberrations and wavefront chromaticity. The accurate calibration of the WFS is therefore a significant challenge for any AO system. A continuous way to measure the "ideal" reference is therefore required for high accuracy wavefront correction. Finding this "ideal" reference is particularly critical to A170, page 2 of 10 N. Skaf et al.: On-sky validation of image-based adaptive optics wavefront sensor referencing ExAO systems, where a slight deviation can introduce slow or static speckles that appear similar to a planet image.

Algorithm description

Since the goal is to ensure the AO loop converges to the "ideal" reference, the "actual" reference should be updated continuously. To do so, DrWHO regularly re-estimates this reference, chosen by selecting the WFS images corresponding to the best PSF image quality. The algorithm thus comprises a lucky imaging selection of the PSF leading to the selection of the best WFS images.

The algorithm first requires the focal plane PSFs and WFS frames streams to be synchronized in time, as described in Appendix B. The algorithm furthermore requires that there be a one-to-one mapping provided from PSF to WFS images, which is explored in Sect. 7.

The quality metric (hereafter, "the score") for the PSF is flexible as far as it optimizes the PSF quality (cf. Sect. 7): this can be the SR, contrast, minimum of intensity, etc. The algorithm proceeds as follows: on a defined timescale (set arbitrarily at 30 s), the algorithm first selects the best PSF frames according to a score metric and a predefined selection fraction (arbitrarily set to 10%). Then, out of those 10% frames, the corresponding WFS raw frames are extracted from the AO telemetry and averaged; the resulting WFS frame replaces the WFS "actual" reference and the algorithm is iterated to continuously optimize the WFS reference.

As the algorithm proceeds, the AO loop point of convergence removes NCPAs and other slow aberrations. Thus, the PSF quality improves, and converges towards a better score. The temporal frequency of the aberrations that DrWHO can correct depends on the timescale of one iteration of the algorithm (for a timescale of 30 s, the algorithm will be able to correct dynamic aberrations up to 0.03 Hz).

We present the procedure step by step of DrWHO with the description in Algorithm 1.

Validation via numerical simulations

This section presents the AO simulation set up with the COM-PASS simulator (Ferreira et al. 2018). COMPASS is a versatile AO simulator that was designed to meet the need of high-performance for the simulation of AO systems, modeling several kinds of AO features, including several types of WFS, atmospheric simulations, DMs, telescopes, and RTCs. It offers a suitable environment for simulating Single Conjugate Adaptive Optics (SCAO), for 8-m class telescopes and 30-m class telescopes as described in Vidal et al. (2018). Simulations of DrWHO on the COMPASS software were first implemented to explore the algorithm feasibility and potential.

Extreme AO simulation

The first step was to simulate an ExAO on COMPASS. We looked for simulating an AO close to the SCExAO instrument, which is a high-order AO system mounted behind Subaru's facility adaptive optics AO188 (Minowa et al. 2010) that provides a first level of correction (woofer) using a 188-actuator DM and a curvature WFS.

SCExAO performs high-contrast imaging thanks to a second level of correction (tweeter), using a 2000-actuator DM and a visible PyWFS. We simulated a simplified ExAO tweeter system inspired by SCExAO, without trying to be an exact copy. Table 1 synthetizes the parameters used in the COMPASS simulations.

The simulation is idealized, with no source of noise other than the photon noise on both the WFS and the science detector (observing mR = 7 with 50% efficiency), and does not take into consideration the telescope spiders. Furthermore, we considered a PyWFS with a higher sampling than on the SCExAO instrument (64 pixels over the PyWFS pupil diameter, versus 50 pixels), hence higher performance than achieved on-sky. The PyWFS is working in the visible at 750 nm, and the detector in the infrared at 1650 nm (cf. Table 1). Finally, the COM-PASS simulation allows us to have synchronized exposure times, which is not the case on SCExAO (cf. Appendix B).

The quality criteria used for quantifying the PSF on COM-PASS is the SR.

DrWHO on COMPASS

We implemented the DrWHO algorithm as described in Algorithm 1. Results are presented for a case with 15 DrWHO iterations, each consisting of 10 000 AO loop iterations (corresponding to 5 s at 2 kHz). The number of AO loop per DrWHO iteration was constrained by simulation time. Henceforth, the focus remains on the low order modes.

The NCPAs, corresponding to a linear combination of the first 12 Karhunen-Loève modes (which is the linear and orthogonal modal basis used for computing the response matrix), with randomized amplitude, were applied on the science path (not visible to the WFS), with a total amplitude of 30 nm rms (cf. Fig. 2). Such amplitude for the NCPAs is slightly greater than what is A170, page 3 of 10 observed a nearly perfect compensation of the added NCPAs at the first iteration.

For the on-sky test, we combined the PyWFS measurements and the focal plane images in visible from the VAMPIRES module. When DrWHO was running, the PSF significantly improved (15.7% relative improvement in flux concentration) over 20 iterations of 30 s, for a total of 10 min. The best PSFs have a sharper increase over the run of the algorithm, reaching 48% of the simulated ideal PSF flux concentration. The visible improvement in the image quality was confirmed with the calculation of the MTF before and after the DrWHO run. The data on this run were used to explore the mapping from PSF to WFS images, as a one-toone mapping is a necessary condition for DrWHO to converge to the goal PSF image. We established the uniqueness of the mapping in the case where the selection metric is optimal for the aberration-free PSF.

This shows that DrWHO is able to improve the wavefront quality arriving on the science camera, and partially correct for the static and quasi-static NCPAs, over a relatively short period of time of a few seconds. We show that the algorithm converges rapidly, with about half of the correction achieved by the first iteration. This has been observed in simulation and on-sky. Furthermore, the correction of the NCPAs is effective even if it is considerably smaller than the dynamic of the atmosphere.

The characteristics of DrWHO are enumerated in Sect. 8. The main strong points are the robustness of the algorithm, its independence from any model, making it compatible with other wavefront control methods, and that it does not rely on any linear assumption, thus it is particularly fit for a PyWFS. In fact, some other techniques for compensating NCPAs mentioned in Sect. 1 usually work independently from the WFS. They do their own correction based on a model, for example, by applying probes on a DM channel that is parallel to the AO loop DM channel. DrWHO combines focal plane wavefront sensing and the WFS. Furthermore, there is a natural extension of this technique in high contrast imaging in the IR, to be more efficient by parallelizing the algorithm in terms of spatial frequencies, which would allow to correct speckles individually and to observe fainter targets.

This paper is the first proof of concept of the algorithm and presents some first results of its PSF quality and stability enhancement. DrWHO shows a wide potential of improvement, which will be presented in future work. A170, page 9 of 10 6. DrWHO parallelization in spatial frequencies

DrWHO parallelization in spatial frequencies

DrWHO, as described above could be optimized in several possible ways. I presented in Skaf et al., 2022a a suggested improvement. I will remind here what was presented in the conference proceeding, with further explanations. I did preliminary simulation tests, this is however still under development.

Principle

I introduced in Section 1.2 how Fourier transforms are a powerful mathematical tool and how beneficial it is regarding their characteristics linking the pupil plane and the focal plane. In fact, one of the powerful applications of Fourier optics is that the focal plane, also called the Fourier plane, is the frequency plane with low spatial frequencies in the center of the PSF, and higher spatial frequencies in the outer edge. Thus, this is where spatial frequencies are decomposed, either in phase or in amplitude. In that respect, the PyWFS is particular as it does preserve spatial frequencies, making it especially suitable for the DrWHO upgrade described below. In our particular context of DrWHO for direct imaging of exoplanets, asking what the contrast will be at a specific place in the focal plane is equivalent to asking what is the pupil plane phase aberration at the corresponding spatial frequency. Therefore, we decompose the aberration in a sum of sinusoids corresponding to the Fourier decomposition in modes. As described in Section 1.2, the phase aberration in the pupil plane that will create a pair of speckles (two Diracs) in the focal plane can be traced back thanks to FT, to find the corresponding sine wave. The wavefront can be decomposed into a sum of sine waves through Fourier filtering, leading to speckle patterns in the focal plane. This correspondence between focal plane position and pupil plane spatial frequency allows us to consider an improved version of DrWHO, by running parallel optimizations of the algorithm for improved convergence speed, and individual quasi-static speckle correction. There are several possible ways to work in the separation of spatial frequencies. I will present here two ways, first, a separation of the focal plane image in concentric rings, and second a separation in smaller zones (of « 1λ{D). In both cases, two approaches can be explored: (1) the use of FT to link focal plane position to WFS modes, or (2) the use of the response matrix, which we have, to explicitly identify the WFS response to sine waves on the DM.

Zonal DrWHO with concentric rings

Given the physical relationship between the focal plane and pupil plane, the first optimization for the upgrade of DrWHO is to take advantage of the difference in spatial frequencies in the PSF: the inner part is mainly composed of low orders, while the outer part is mainly higher orders. A possibility is to separate the PSF in different concentric circular zones, each zone being the starting point for an independent DrWHO optimization loop, leading to as many loops as there are zones.

DrWHO parallelization in spatial frequencies

Φ Ref " ř N i"1 a i Φ Ref,i
, with each of the Φ Ref,i spanning a limited set of spatial frequencies. The splitting of spatial frequencies among the Φ Ref,i will depend on the choice of our PSF regions. A given region will be associated to a given set of reference Φ Ref,i 's. For a first approach with three regions as shown in Figure 3.15, the core and the rings, we simply have the reference corresponding to the sum of the references of each zones, such as:

Φ Ref " Φ core `ΦC1 `ΦC2 (3.3)
However, the core being this special place where the light goes as the aberrations decrease, by minimizing the flux in the rings, we necessarily increase the flux in the core. This works only because you set the inner zone to be very small, such that flux maximization is almost equivalent to SR optimization. Hence, one can only focus on minimizing the flux in the circles. Then, we can generalize Equation 3.3, and we have:

Φ Ref " N ÿ i"1 Φ Ref,i (3.4)
with N being the number of concentric circles dividing the focal plane image, Φ Ref,i the references for each zone, and Φ Ref the final reference applied to the WFS.

Once the focal plane image is separated, one needs to find the corresponding frequencies in the WFS plane. This can be done from knowledge of the focal plane camera plate scale and WFS pupil scale, or by using the Fourier control modes if available. Doing so via the modal basis is an option, given the control matrix gives access to modes, and hence the frequencies. This only works with the modal basis is itself derived from Fourier modes, or encodes spatial frequencies. This works on SCExAO because we use Fourier domains to create the control modes. Figure 3.16 presents a preliminary simulation test, with three DrWHO iterations, each having 500 loop iterations, and with two zones: the core, and one ring. There was then two DrWHO loops running in parallel: DrWHO loop on the core was maximizing the SR, while the DrWHO loop on the ring was minimizing the flux intensity. This figure shows how they mirror each other almost perfectly, confirming there is no need to have a DrWHO loop on the core when there is a DrWHO loop minimizing the intensity on the outer ring.

NB: I did simulation tests on COMPASS with several zones. However, I faced again the same problems described in Section 3.2, preventing me to have relevant results. Writing the code for SCExAO is the next step.

Zonal DrWHO for individual speckle treatment

The focal plane images can be separated into several different zones, ideally of size « 1λ{D. For each of those zones, we apply the chosen quality criteria (the flux miminization, for example). As the DrWHO loop is running one iteration, for each zone of the focal plane, we take the best 10%. With DrWHO being demonstrated on sky, the next step is to add it as a functionality of the AO control GUI. Although there are several parameters to set ahead of running the algorithm, only one script starts it, making it accessible to being added to the control GUI, and used by support astronomers during science observations with SCExAO. There is furthermore ongoing work for demonstrating DrWHO on IR-coronagraphic mode. Several on-sky engineering data are patiently waiting to be analyzed. I started simulation work for zonal DrWHO, which need further work.

Advantages Drawbacks

Robust

Conclusion

In Section 3.4, I reviewed a few different previously proposed approaches for NCPA correction. These methods have advantages and limitations. Mainly, they either require additional hardware, or are invasive to the AO loop. Furthermore, the correction speed is usually slower than the lifetime of NCPA. For these reasons, I looked into developing the DrWHO algorithm.

I demonstrated the efficiency of DrWHO on-sky, and published the results in Skaf et al., 2022b. Unlike some other methods to correct NCPA, DrWHO is entirely transparent to the AO loop, and only updates the reference of the WFS. Doing so changes the point of convergence of the AO loop, which then includes NCPA. Furthermore, DrWHO works for non-linear WFSs such as the PyWFS, as it does not rely on any model nor linear assumptions. It is compatible with other NCPA methods. However, DrWHO needs a fast focal plane camera close to the science camera, something that most ExAO instruments do not have. DrWHO offers numerous

Conclusion

promising ways of improvement. The ambition is to upgrade the algorithm to treat static and quasi-static speckles individually, using a very fast and very sensitive camera such as a photon counting camera. Doing so would allow to see on-sky which zone(s) of the focal plane image do(es) not decrease, indicating of the presence of a planet.

Chapter 4

The β Pictoris system

This chapter presents a paper on the first ExAO-assisted MIR observations at high contrast of the β Pictoris system. The paper is in Section 5. I will here introduce this system and a few of its characteristics in Section 5, including the motivations to perform HCI observations of this system in the MIR. I will introduce the NEAR instrument, in Section 2. I will further describe some steps of the data analysis not presented in the paper and summarize the main results in Sections 3.2 and 4 respectively.

1 The case of β Pictoris 1.1 The historical adventure ‹ β Pictoris is an emblematic system, discovered nearly 40 years ago. The research on it has been a unique, fascinating, and inspiring historical rollercoaster. In this section, I will first describe this system and briefly walk back to the human journey behind scientific discoveries. I will not be exhaustive; much more remains to be shared about it.

β Pictoris is the second brightest star in the Pictor (Latin word for "painter") constellation. Visible to the naked eye from the southern hemisphere (although visible from Hawai'i), its apparent magnitude is 3.85 in V and is located at 63.9 light years, or 19.6 pc (Gaia Collaboration et al., 2021). " 23 million years old [START_REF] Miret-Roig | Dynamical traceback age of the β Pictoris moving group[END_REF], this A5V type star has entered the main sequence stage of its evolution. Young and active, its mass is nearly twice as much as our Sun's, yet nearly nine times more luminous.

This star became a symbol of DI and HCI and has been extensively studied, triggered by the observation of a 400 AU-wide circumstellar disk in the 80s [START_REF] Smith | A Circumstellar Disk around β Pictoris[END_REF] with structures in it [START_REF] Telesco | Mid-infrared images of β Pictoris and the possible role of planetesimal collisions in the central disk[END_REF]. This was indeed the first circumstellar disk ever resolved.

This started a series of decadal milestones for this system, punctuated by periods of impatient waiting, preparations, and different observations.

In 1988, spectroscopic observations of the star led to the understanding that a large amount of gas falls into the star, at high velocities: exocomets were discovered for the first time (Lagrange-1. The case of β Pictoris [START_REF] Lagrange-Henri | The beta Pictoris circumstellar disk. VI. Evidence for material falling on to the star[END_REF][START_REF] Beust | The beta Pictoris circumstellar disk. X. Numerical simulations of infalling evaporating bodies[END_REF].

A decade later, in 1997, only two years after the first exoplanet detection with the RV method, observations of the inner parts of the disk showed a distortion -a warp -spanning up to 70 to 80 AU, and inclined of "3-5 degrees. There, were the first indications of a possible giant planet orbiting the system: this warp located around 70-80 AU was interpreted as resulting from the gravitational perturbation of a " 10 M J planet, located at " 10 AU [START_REF] Mouillet | A planet on an inclined orbit as an explanation of the warp in the beta Pictoris disc[END_REF].

At the same period of time, the adaptive optics revolution in astronomy started, and the very large telescopes in Chile saw their first lights. There were observations of the β Pic system with VLT's NaCo instrument in 2003, which were later analyzed in 2008: the data provided images of what clearly seemed to be this giant planet expected from the warp, on the North-East side of the disk, but weren't published until 2009: further observations were needed to definitely confirm this planet β Pic b.

Lecavelier Des Etangs et al., 1995 published a photometry monitoring over several years and suggested a transit in 1981. It was then suggested that the planet could be transiting after the 2003 observations. In fact, regular RV observations of the star started around 1986. The 2003 data were published in early 2009 [START_REF] Lagrange | A probable giant planet imaged in the β Pictoris disk. VLT/NaCo deep L'-band imaging[END_REF], after several years of suspense and patient hard work to improve instrumentation and post-processing methods. In this study, the authors predict the planet will become visible again at the end of 2009. Then, the star was observed again with NaCo, and the planet was indeed detected as expected, this time on the South-West side of the disk. Sure enough, a year later, in 2010, the star was re-observed, with NaCo again: they detected a faint point-source, located at " 8 AU -the planet β Pictoris b was finally confirmed (Lagrange et al., 2010).

A couple of years later, the planet was confirmed with other instruments, such as NICI on Gemini South [START_REF] Boccaletti | Independent confirmation of β Pictoris b imaging with NICI[END_REF]. The planet was regularly observed with NaCo and SPHERE, until November 2016, and the time of transit of the planet (if happening) was predicted in 2017. But the monitoring of the star never showed any transit. The astrometric observations of the planet show that it does not transit, but its Hill sphere, might. Figure 4.1 shows the image combination of the disk, as well as the first observations of the directly imaged planet b. Back then, observing a directly imaged planet, within a circumstellar disk, was revolutionary in the field. Specific workshops focused on β Pic were organized, gathering experts on DI instrumentation, observations, and planet formation. The global scientific and human collaboration behind the interest in this system grew substantially, leading to fruitful results. In 2014, the planet was expected to disappear again behind the star sometimes in " 2017, leading to the design of a dedicated space mission to observe the possible transit of β Pic b: the nanosatellite PicSat [START_REF] Nowak | Reaching sub-milimag photometric precision on Beta Pictoris with a nanosat: the PicSat mission[END_REF]. Launched in 2018, PicSat stopped communicating soon after its orbit insertion, until June 2022, emitting signal and telemetry again.

Further observations of the system continued, leading to a plethora of papers. Almost a decade after the detection of β Pic b, in 2019, years-long RV observations with the HARPS instrument concluded on the presence of another planet, β Pic c [START_REF] Lagrange | Evidence for an additional planet in the β Pictoris system[END_REF], making β Pic the first multi-planetary system observed in a circumstellar disk (along with the HR8799

β Pictoris in the NIR: main results

β Pictoris was extensively observed at different wavelengths, from UV to radio [START_REF] Ballering | A Comprehensive Dust Model Applied to the Resolved Beta Pictoris Debris Disk from Optical to Radio Wavelengths[END_REF]. The planet b was detected in the NIR, with NaCo (VLT) (Lagrange et al., 2010), allowing then to constrain the orbital characteristics on the planet [START_REF] Chauvin | Orbital characterization of the β Pictoris b giant planet[END_REF], and determine its temperature, being at 1650K˘150 (Bonnefoy et al., 2014). The first trials of atmospheric characterization were then achieved, giving indications on its surface gravity log(g) (3.8˘0.2), its radius (" 1.5˘0.2R J ), its mass ("7˘4M J ), and its absolute luminosity (Bonnefoy et al., 2013;Currie et al., 2013). Soon after performing their first lights, the first XAO instruments, SPHERE and GPI, imaged β Pic b with deeper contrast, allowing them to better determine the planet's characteristics (Macintosh et al., 2014;Bonnefoy et al., 2014;Baudino et al., 2015). More recent interferometric studies with Gravity have allowed putting better constraints on the bulk parameters of the planet (cf Table 4.1) and measured an eccentricity of e " 0.15 `0.05 ´0.04 . They extracted a spectrum of the planet, presenting a low C/O ratio, suggesting that if the star has a solar metallicity, the formation process of the planet is through core accretion with strong planetesimal enrichment (Gravity Collaboration et al., 2020).

β Pictoris in the MIR

The first MIR observations of the system, in the 90s, concluded in an asymmetry in the disk [START_REF] Lagage | Dust depletion in the inner disk of β Pictoris as a possible indicator of planets[END_REF]. Later, [START_REF] Telesco | Mid-infrared images of β Pictoris and the possible role of planetesimal collisions in the central disk[END_REF] observed the disk at different MIR wavelengths, finding the disk has a brightness asymmetry at shorter wavelengths, with the south-west wing being much brighter than the north-east one, especially at 12µm, while at about 25µm the disk brightness is symmetric. They discovered a clump of gas and dust on the south-west side of the disk, located at "52 AU. They witnessed that the color, between 10 and 25µm, is not the same in the disk and the clump. They interpreted this difference and this asymmetry with the possible destruction by the collision of a planetesimal, generating in the clump smaller grains than in the rest of the disk.

Motivations to observe β Pictoris in HCI in the MIR

Observing a system such as β Pic at different wavelengths allows us to better understand the dynamics of the disks. I described in Section 2.3 the considerable benefits of MIR observations. However, MIR observations of exoplanets from the ground have not been possible because of various limitations. Mainly, the thermal background contamination is such that it would be comparable to trying to observe the star in the daytime in the visible.

There have been observations of the disk in the far-IR wavelengths with Herschel [START_REF] Cataldi | Herschel/HIFI observations of ionised carbon in the β Pictoris debris disk[END_REF] and mm wavelengths with ALMA [START_REF] Matrà | Exocometary gas structure, origin and physical properties around β Pictoris through ALMA CO multitransition observations[END_REF]; they provided information on the structure and composition of the disk: mainly C, O, and CO detections, which are indicators of the formation processes (Öberg et al., 2011). There have been MIR observations from the ground with T-ReCS [START_REF] Telesco | Mid-infrared images of β Pictoris and the possible role of planetesimal collisions in the central disk[END_REF][START_REF] Li | The Mineralogy and Structure of the Inner Debris Disk of β Pictoris[END_REF], providing information on the disk structure, yet none in HCI.

As for NIR observations of β Pic, which are mainly focused on planet b and not the disk, there are synergies with MIR observations and benefit from being completed by increasing the spectral coverage. This significantly improves model fitting of the atmosphere, and provides better determination of the atmospheric parameters, allowing us to perform a much more precise atmospheric characterization of planet b. In fact, recent spectroscopic observations with Gravity [START_REF] Lacour | First direct detection of an exoplanet by optical interferometry. Astrometry and K-band spectroscopy of HR8799 e[END_REF] at a resolution of 500 will benefit a posteriori from MIR observations to constraint the Spectral Energy Distribution of β Pic b and achieve higher precision on atmospheric parameters in the retrieval process.

In addition, the Rayleigh-Jeans law indicates that a planet flux in the MIR linearly depends on the effective temperature, as opposed to the NIR. MIR observations can hence provide in turn a better measurement of planet radius, whose estimation is sometimes poorly constrained, being unreasonably too small or too large at shorter wavelengths [START_REF] Patience | The highest resolution near infrared spectrum of the imaged planetary mass companion 2M1207 b[END_REF]. HCI in the MIR provides a unique chance to constrain the Spectral Energy Distribution of β Pictoris b and to investigate the relative planet-disk flux in preparation for new and future facilities like MIRI on JWST, and METIS on the E-ELT.

The NEAR program 2.1 The α Centauri context ‹

In the search for life in the Universe, one of the first places to look at is our closest stars.α Centauri is our closest neighbor, a triple star system located at "4.2 light years. It is composed of two stars relatively similar to our Sun, α Cen A, and α Cen B, nicknamed Toliman. A third star, α Cen C, also known as Proxima1 , is a smaller red dwarf star, on a wide orbit around alpha Cen A and B [START_REF] Kervella | Proxima's orbit around α Centauri[END_REF]. This nearby system has caught the attention of astronomers looking for life in the universe for several reasons. Many astronomy-enthusiasts got a heartbeat skipped learning the discovery in 2012 of an Earth-mass planet orbiting α Cen B through the RV method, located at 0.04 AU and with an orbital period of 3.2 days [START_REF] Dumusque | An Earth-mass planet orbiting α Centauri B[END_REF]. Later, in 2016, a 1.3 Earth-mass planet orbiting Proxima was detected with the same method, located at 0.05 AU and with a " 11.2 days orbit [START_REF] Anglada-Escudé | A terrestrial planet candidate in a temperate orbit around Proxima Centauri[END_REF]. The enthusiasm around this system went far beyond the astronomy community, generating a plethora of art and science-fiction stories -see Figure 4.2 for an artistic poster on Proxima b.

α Cen has motivated numerous technological and instrumentation developments to observe it at different wavelengths, and with different methods. In fact, the first developments for HCI of a multi-star system were indeed motivated by α Cen observations [START_REF] Thomas | Techniques for High-contrast Imaging in Multi-star Systems. I. Super-Nyquist Wavefront Control[END_REF]. Several ongoing space mission concept studies exclusively focused on α Cen observations, such as Breakthrough's ambitious Starshot project [START_REF] Parkin | The Breakthrough Starshot system model[END_REF], and the Toliman space astrometric

Instrument science goal and description

NEAR was a 100-hour long observation campaign to observe α Cen. The instrument was designed to image Neptune-sized planets in the habitable zone. Although such a planet was not detected, the experiment improved the sensitivity of state-of-the-art exoplanet imaging mass detection limits by one order of magnitude. It also proved the detection capabilities of Earth-like planets in the habitable zone of the α Cen binary is within reach with 8-meter class telescopes in the MIR [START_REF] Kasper | NEAR: First Results from the Search for Low-Mass Planets in α Cen[END_REF]Wagner et al., 2021a).

The one-year-long NEAR program was an upgrade of the VLT Imager and Spectrometer for mid-Infrared (VISIR) and was performed in 2019. The VISIR instrument commissioned in 2004 on the VLT UT3, is a MIR imager observing three atmospheric windows: in M-band at 5µm, in N-band between 8 and 13µm, and Q-band, between 17 and 20µm [START_REF] Lagage | Successful Commissioning of VISIR: The Mid-Infrared VLT Instrument[END_REF]). VISIR's science camera started with a pixel scale of 0.075 arcseconds per pixel and has been upgraded to a pixel scale of 0.0453 arcseconds per pixel. VISIR was moved to the VLT UT4 and upgraded for NEAR [START_REF] Kasper | NEAR: Low-mass Planets in α Cen with VISIR[END_REF]. These upgrades included:

-use of the adaptable secondary mirror and its AO capabilities; -configured in N-band, with 10-12.5µm filter centered at 11.23 µm;

-an angular groove phase mask (AGPM) coronagraph [START_REF] Mawet | Annular Groove Phase Mask Coronagraph[END_REF].

In this respect, the NEAR project has made VISIR a high-contrast imaging instrument, allowing a boost in sensitivity, angular resolution, and hence contrast. Such an upgrade offers the potential to open a new window into young giant planets' physics. The success of NEAR motivated further MIR observations and HCI instrumentation development, such as the LBT Exploratory Survey for Super-Earths/Sub-Neptunes Orbiting Nearby Stars (LESSONS) observational program [START_REF] Wagner | Imaging low-mass planets within the habitable zones of nearby stars with ground-based mid-infrared imaging[END_REF].

Further details on the instrument are found in Section 2.1 of the paper, presented in Section 5 of this chapter, and in [START_REF] Kasper | NEAR: Low-mass Planets in α Cen with VISIR[END_REF][START_REF] Kasper | NEAR: First Results from the Search for Low-Mass Planets in α Cen[END_REF]. VISIR has since been moved back to VLT/UT3 and to its previous configuration.

Motivations for β Pic observations with NEAR

A proposal to observe β Pic with NEAR was granted time in December 2019 and January 2020 (PI: A. Boccaletti). Some of the elements presented below are from this proposal.

Although designed to probe the presence of planets in the habitable zone around α Centauri, NEAR is also a powerful facility to detect warmer planets [START_REF] Pathak | High contrast imaging at 10 microns, a search for exoplanets around: Eps Indi A[END_REF], which are easier targets. NEAR can furthermore detect planets that previous surveys have already identified in the NIR. By performing the first attempts to observe giant planets in the MIR, NEAR became a key instrument in preparing science programs with MIRI/JWST and METIS/ELT.

Performance analysis of NEAR for several targets was assessed; see Figure 4.3. As seen in this figure, β Pic b, corresponds to a particular regime of contrast, angular separation, and 2. The NEAR program sensitivity, making it an ideal emblematic target to demonstrate the capabilities of NEAR. Given the angular separation of β Pic b (" 0.3"), the use of the coronagraph is necessary to ensure that, once the sensitivity is achieved (set by the thermal background), the contrast floor will be set by speckle residuals and not by the diffraction pattern. Ammonia (NH 3 ) has an absorption feature at 10µm, but this molecule has not been detected in K band (Hoeijmakers et al., 2018), giving hope that the planet MIR flux would be close to a black body.

While β Pic b is an easy target in terms of contrast and sensitivity (as demonstrated in Figure 4.3, right), it was expected that the disk could hamper the planet detection. In fact, it is reasonable to assume that disk contamination will happen for many systems that JWST and METIS will observe. Therefore, to counteract that, it was argued the planet could be revealed through disk subtraction, as done in L' band by [START_REF] Milli | Very deep images of the innermost regions of the β Pictoris debris disc at L[END_REF]. The intention was to detect the planet and characterize its atmosphere, by measuring its true photometry. This was part of the road map to prepare the efficient exploitation of future instruments, to perform the analysis of disk features like the clump observed by [START_REF] Telesco | Mid-infrared images of β Pictoris and the possible role of planetesimal collisions in the central disk[END_REF], and the orientation of the warp, which differs from NIR to MIR [START_REF] Pantin | View of Beta Pictoris by the VLT[END_REF]. In that respect, high SNR images of the disk were necessary for disk characterization and subtraction. As a byproduct, the data was expected to allow us to address whether the clump structures, observed in MIR [START_REF] Telesco | Mid-infrared images of β Pictoris and the possible role of planetesimal collisions in the central disk[END_REF], are due to mean motion resonances, meaning the clump rotating with the disturber inducing the resonance, or due to collisions -in which case the clump would be seen as static. The intention was furthermore to take advantage of synergies with NIR data (SPHERE, Gravity), to achieve better characterization, as well as synergies with future instruments, such as MIRI and METIS, to initiate their science programs. Finally, observing β Pic with NEAR offered a performance demonstration of this instrument, and quantifying the benefit resulting from the use of HCI technologies in MIR wavelengths from the ground.

For these reasons, NEAR observing time was provided to β Pic. It was observed in December 2019, providing the first -and thus far unique -observations of this system in HCI in the MIR. NB: At the time of the observations, it is important to note that the preliminary reduction of the NEAR program on α Centauri did not reveal any planets, and had some limitations to achieve the very high sensitivity needed by co-adding several nights. Observations of β Pictoris and other targets became a point of focus to use NEAR to characterize a planet in the MIR in HCI, before JWST observations.

Photometric study of β Pic NEAR data

Planet detection?

At the same time as NEAR observations of β Pic, this system was observed with SPHERE, and detected a planet at a separation of 0.3" [START_REF] Lagrange | Unveiling the β Pictoris system, coupling high contrast imaging, interferometric, and radial velocity data[END_REF]. I describe in Section 3.1 of the paper the search for planet b in the NEAR data.

The planet is not detected in the reduced images. To accurately measure the SNR and calculate the upper detection limit, a method is to perform fake planet (FP) injection in the disk, at the expected separation, at different contrast, and measure the corresponding SNR. As mentioned earlier, the transmission of the coronagraph must be taken into account, which is 30% at this separation [START_REF] Maire | Design, pointing control, and on-sky performance of the mid-infrared vortex coronagraph for the VLT/NEAR experiment[END_REF]. As a result, we get a contrast curve as a function of the separation, equivalent to a 5 σ detection.

The contrast measurements described above and shown in Figure 4.6 present a 5σ contrast detection limit of 5.10 ´3 at 0.3".

We must go through the star's flux to get the corresponding flux. In fact, as mentioned earlier in Chapter 2, the contrast is defined as :

C " planet flux stellar flux (4.1)
We used the stellar flux presented in Bonnefoy et al., 2013, which was in erg.s ´1.cm ´2.A ´1, that I converted to W.m ´2.µm ´1. I then extracted the stellar flux at NEAR's wavelength. The 3. β Pic through NEAR's lens closer to the planet, receive further heat from the planet itself. This is shown in Figure 4 of the paper: the equilibrium temperature from the planet decreases as the distance increases, up to a shifting point at "100R J , where the stellar's equilibrium temperature takes over the planet's. This figure was obtained by combining the equilibrium temperature linked to the planet, and the one linked to the star. The dust distance was varied, considering only the albedo of the planet, which led to this curve.

Then, we calculated the flux emitted by one grain. We assume the dust is distributed as an optically thin shell, as seen in Figure 4.8, so all grains are at the same distance from the planet. We varied this distance between two extreme positions:

-the Roche radius: minimal limit at which a satellite can be formed nor exist, and would be destroyed by tidal effects. This does not mean there cannot be dust closer than the Roche radius, but it is a fair minimum radius to consider for our case;

-the Hill radius: it is the influence sphere of the planet, depending on the star-to-planet distance, as well as the mass; the further away from the star the planet is, the bigger its Hill sphere. The Hill radius is defined as:

R Hill " a planet ˆˆM planet 3M ‹ ˙1{3 (4.2)
with a planet the planet's semi-major axis, M planet the planet mass, and M ‹ the mass of the central star.

We assume furthermore that flux is linearly proportional to dust concentration because optically thin. In other words, if we multiply by 100 the number of dust grains, we multiply by as much the flux, emitted by all these grains. We also assumed we see the emissions of all the grains. Another hypothesis on the dust grain is regarding its emission: we considered a black-body emission, weighted by an absorption coefficient Qabs.

Then we assumed the density of astrosilicates grains, which is 2.7g.cm ´3.

Finally, given these hypotheses, we can come back to our main question presented in 2. at the beginning of this section, formulated differently: how many dust grains do we need to reproduce the flux upper limit given by the image? And the corresponding total mass of dust and the size of the hypothetical parent body producing these particles.

The flux radiated by one dust particle follows Planck's law:

F pT dust , λq " Q abs 2πhc λ 5 1 e hc{kT dust λ 4πs 2 dust 4πd 2 pd (4.3)
with d pd being the distance planet to dust, c being the speed of light, h being the Planck constant, and k being the Boltzmann constant.

Considering the flux upper limit and in the optically-thin hypothesis, we then derive, at each radial distance from the planet, the maximum number of 2 µm-size dust particles as N dust " the paper. The SW clump is again observed in our data, as seen in Figure 4.5 on the right-hand side. Other unexpected clumps are clearly visible in these images: there is at least one obvious clump on the NE side, which I labeled C2 in the paper, and two other clumps, labeled C3 and C4 in the paper. The SW clump is labeled C1, I will stick with it for the following.

A way to study the disk dynamics is to measure the exact positions of the clump along the disk at different epochs. To accurately do so, I looked at the surface brightness of the images, which requires to perform three steps:

1. measure the intensity (in arbitrary unit), by summing up the pixel counts perpendicularly to the spine of the disk in a box of 20 pixels of width (with a pixel scale of 0.045mas/pixel), and along the x-axis;

2. convert the image from pixel to AU or arcsecond;

3. convert the image in pixel counts to an image in Jansky per arcsec 2 , through the following equation:

Im Jy{arcsec 2 " Im pixel ppix_scale 2 ˚photometric_calibrationq (4.7)
From previous calibration of the stellar flux in and out of the coronagraphic mask we estimated the conversion factor to be 1.1e6 ADU/Jy for coronagraphic images (E. Pantin, priv. comm.). Measuring the position of these clumps was performed with Gaussian fits along the x-axis. Section 5.2 details the methods to accurately measure the positions, and estimate the error bars, Section 6 gives the results of the position measurements for C2, C3, and C4.

Combining other MIR data

Between 2003 and 2019, there have been five MIR observations in the N-band of β Pictoris, including the NEAR observations. Table 4.2 presents these observations, indicating the instrument used during these observations as well as the telescope, the central wavelength of the filter, and the HCI set-up. Two of these data sets are from the VISIR instrument, these data had never been previously published. These five data sets are introduced in Section 2.2 of the paper. Regarding the T-ReCS data, the surface brightness was extracted from the figures presented in [START_REF] Li | The Mineralogy and Structure of the Inner Debris Disk of β Pictoris[END_REF] Regarding the VISIR data, I used the same method as described in [START_REF] Li | The Mineralogy and Structure of the Inner Debris Disk of β Pictoris[END_REF]: I performed a centro-symmetrical subtraction of the image, to reveal the presence of the clumps. The error bar estimation on the position of the clump C1 in VISIR's 2004 and 2015 data is described in Section 5.2 of the paper. We then plotted, for each projected separation, including the error bars, and the rotation speeds of the clump, with three scenarios: Keplerian motion or resonance 2:1 or 3:2. The result of these curves is in Figure 12 of the paper.

As a conclusion, by studying the behavior of the clump C1 over the 16-year baseline of observations, we found out this clump is likely orbiting at a Keplerian speed around the star.

We can now discuss the consequences of the hypothesis of the clump's origins, I summarize here what is presented in Section 7:

-Giant impact: [START_REF] Telesco | Mid-infrared images of β Pictoris and the possible role of planetesimal collisions in the central disk[END_REF] suggested the clump could result from a giant impact. [START_REF] Jackson | Debris froms giant impacts between planetary embryos at large orbital radii[END_REF] describe that it is the case if the structure is fixed with the observer, which is not our case, as we have a clear motion. Hence, C1 does not result from a giant impact.

-Resonance with an inner planet: if there is a resonance, then the rotation speed is non-Keplerian. Here, Figure 12 clearly shows a Keplerian motion. C1 is not in resonance with another object in the system.

-Planet's Hill sphere: the clump could be hiding a yet-to-be detected planet, having a mass of "2.5M J .

- [START_REF] Li | The Mineralogy and Structure of the Inner Debris Disk of β Pictoris[END_REF], and the 2015 VISIR data. Their data analysis varies from the one we undertook: they first convolved the image of the disk with the PSF, and then integrated the flux vertically, resulting in a 1D observable. They then looked at the relative displacement of the clump from one data set to another. They looked at the disk as a whole, not focusing on the peak. While in our case, we looked at the surface brightness for each data set, determined the position of the clump by fitting a Gaussian on the peak, where there is a maximum of intensity, and looked at the positions. In fact, the profile of the clump evolves with time, that is why we focused on the peak. They conclude the clump is likely stationary, which is a conflicting result with our study. The different data analysis is at the origin of this conflict.

Conclusion

Main results

Here I present a summary of the results of this study, presented in the paper's conclusion. 131 Chapter 4. The β Pictoris system -We studied unique MIR data of β Pic in HCI; -The planet b was not detected, but we put constraints on possible dust around the planet:

we find that at the Roche radius, the flux upper limit corresponds to the total mass that is equivalent to an asteroid of 5km in diameter;

-Several structures in the disk are visible, including the previously observed clump on the South-West side, labeled C1 in Figure 4.5. We detected three new clumps labeled C2, C3, and C4, located at ´35. -the Hill's sphere of a yet-to-be-detected planet with a maximum mass of 2.5M J ; -a vortex of gas and dust.

Perspectives

Observations of the β Pic system in the MIR in high contrast with AO and a coronagraph have been a success, providing data that allowed us to know more about planet b and the disk. This shows the power of HCI in the MIR from the ground, which was never performed before NEAR. The MIRI instrument onboard the JWST will perform observations of β Pic. The NEAR study is an excellent preparation for the JWST ones, which are impatiently awaited. Planet b will likely not be detected either, however, we expect the disk images to be very well resolved. This will tell us more about the different clumps observed with NEAR. MIRI data will provide temporal follow-up of the clumps and greater precision on their location and motion. The precision will allow the search for potential fainter structures in the disk, and provide color hints, or even spectroscopy. This will allow for determining the optical properties of the grains within the disk structures. Furthermore, detecting the planet with MIRI is of high interest to refine the measured temperature, independently of clouds that bias the photometry in NIR [START_REF] Carter | The JWST Early Release Science Program for Direct Observations of Exoplanetary Systems I: High Contrast Imaging of the Exoplanet HIP 65426 b from 2-16 µm[END_REF].

Along with further MIR observations, it would be of great interest to study the disk at different wavelengths, to have a global understanding of the disk and compare that with evolution models.

As mentioned in Section 3.2.2, several spectra of β Pic b were observed with SPHERE at different epochs. These spectra show some differences from one epoch to another, which requires to be looked into. These differences could be coming from instrumentation artifacts or could be resulting from atmospheric variability. Further work is needed to say more...

Introduction

Exploring the diversity of planetary systems requires a broad spectral range tuned for detecting various components in these environments: gas, dust, planetesimals, and planets. The past two decades have seen the development of extreme Adaptive Optics (AO) on monolithic telescopes, a technology that allows to perform high angular resolution and high contrast imaging at both visible and near IR wavelengths. Instruments like the Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE, Beuzit et al. 2019) are sensitive to the thermal emission of young giant planets, as well as the scattered light from dust particles. At the same time, the Atacama Large Millimeter/submillimeter Array (ALMA) has revolutionized observations of the thermal radiation emitted from gas components and millimeter dust grains in both debris disks and gas-rich protoplanetary disks (e.g., ALMA Partnership et al. 2015). The intermediate spectral range, the mid-IR, has so far received much less attention, primarily because of the high thermal back-⋆ Based on data collected at the European Southern Observatory under programs 60.A-9107(K), 095.C-0425(A), and 60.A-9234(A). ground contamination in ground-based observations. However, this paradigm is about to change thanks to the James Webb Space Telescope and its Mid-Infrared Instrument (MIRI, Rieke et al. 2015;[START_REF] Wright | The Mid-Infrared Instrument for the James Webb Space Telescope, II: Design and Build[END_REF] and references there-in), and later in the decade, thanks to the upcoming Mid-infrared ELT Imager and Spectrograph (METIS, Brandl et al. 2018).

In the meantime, the New Earths in the α Centauri Region project (NEAR, [START_REF] Kasper | NEAR: First Results from the Search for Low-Mass Planets in α Cen[END_REF]) was installed at the VLT to perform a deep observing campaign of α Centauri [START_REF] Wagner | Imaging low-mass planets within the habitable zone of α Centauri[END_REF], and being part of the Breakthrough Initiatives Foundation, offered an upgrade of the existing VLT spectrometer and imager for the mid-infrared instrument (VISIR, [START_REF] Lagage | Successful Commissioning of VISIR: The Mid-Infrared VLT Instrument[END_REF], which operates in the L, N and Q bands. VISIR was moved to UT4 for a period of time to benefit from the Adaptive Optics Facility on the secondary mirror (Arsenault et al. 2017), and an annular groove phase mask (AGPM) coronagraph [START_REF] Mawet | Annular Groove Phase Mask Coronagraph[END_REF][START_REF] Delacroix | Society of Photo-Optical Instrumentation Engineers[END_REF]) was installed, operating in a single broad filter covering from 10 µm to 12.5 µm, with the filter centered at 11.25 µm [START_REF] Maire | Design, pointing control, and on-sky performance of the mid-infrared vortex coronagraph for the VLT/NEAR experiment[END_REF]. We took advantage of the NEAR Science Demonstration program to observe the β Pictoris system.

Article number, page 1 of 15 A&A proofs: manuscript no. output β Pictoris is a young (∼ 18.5 +2.0 -2.0 Myr, Miret-Roig et al. 2020) and bright Main Sequence pulsating star. Since the discovery of its debris disk by [START_REF] Smith | A Circumstellar Disk around β Pictoris[END_REF], this system has been extensively observed to search for signs of planets. First indirect clues of a planet were brought by the detection of stargrazing comets falling onto the star [START_REF] Lagrange-Henri | The beta Pictoris circumstellar disk. VI. Evidence for material falling on to the star[END_REF], and of a warp in the disk attributed to the gravitational interaction between an unseen massive body (planet, brown dwarf) on an inclined orbit and the planetesimals in the disk [START_REF] Mouillet | A planet on an inclined orbit as an explanation of the warp in the beta Pictoris disc[END_REF]. According to surface brightness measurements, the planetesimals are distributed within ∼120 au, while the inner part inside ∼80 au is warped (Augereau et al. 2001). In scattered light, small dust particles, blown by the stellar radiation pressure, are observed at even larger projected separations (Janson et al. 2021).

Years after, observations with AO of the NaCo instrument at the VLT led to the detection of the thermal emission from the giant planet β Pictoris b [START_REF] Lagrange | A probable giant planet imaged in the β Pictoris disk. VLT/NaCo deep L'-band imaging[END_REF](Lagrange et al. , 2010)). Finally, in 2019, a second planet β Pictoris c, has been identified via radial velocity as a result of nearly ten years of monitoring the host-star with the High Accuracy Radial velocity Planet Searcher (HARPS) instrument [START_REF] Lagrange | Evidence for an additional planet in the β Pictoris system[END_REF]). The planet c was then confirmed with long-baseline optical interferometry (Nowak, M. et al. 2020;[START_REF] Lagrange | Unveiling the β Pictoris system, coupling high contrast imaging, interferometric, and radial velocity data[END_REF].

The β Pictoris system is certainly unique to probe the mechanisms of planetary formation. A large fraction of the previous studies focused on the characterization of the disk, and in particular on the possible interaction between planets with the dust and gas components by identifying the different features in various spectral regimes, and spatial scales. In that respect, Apai et al. (2015) provided a comprehensive analysis of the system by using data obtained in various spectral bands: optical, near IR, mid-IR, and sub-millimeter. Asymmetries, especially between the northeast and the southwest arms of the edge-on disk, are reported at all wavelengths both in scattered light, tracing the submicronsize grains, and in emission, through the analysis of micron-size and sub-millimeter-size grains. A striking feature in the mid-IR is the clump identified in the southwest by [START_REF] Telesco | Mid-infrared images of β Pictoris and the possible role of planetesimal collisions in the central disk[END_REF], located at a projected separation of 52 au. The clump was confirmed by [START_REF] Pantin | View of Beta Pictoris by the VLT[END_REF], and recovered by [START_REF] Li | The Mineralogy and Structure of the Inner Debris Disk of β Pictoris[END_REF] with a small offset, which was interpreted as orbital Keplerian motion. In addition, this asymmetric feature appears at ∼ 10 µm and fades away at ∼ 20 µm, indicative that its flux is dependent on either temperature, grain size, composition, or a combination of these three effects. [START_REF] Telesco | Mid-infrared images of β Pictoris and the possible role of planetesimal collisions in the central disk[END_REF] argued that this clump could be the result of either collisions among planetesimals trapped in resonance, or the dismantling of a more massive object. Finally, Okamoto et al. ( 2004) reported amorphous silicates peaks at about 6, 16, and 30 au of radial distance from the central star, and a recent study revisited Spitzer data identifying various rings based on amorphous silicates peaks (Lu et al. 2022).

In addition to the dust clumps observed in the mid-IR, ALMA identified the presence of both a CO (Dent et al. 2014;[START_REF] Matrà | Exocometary gas structure, origin and physical properties around β Pictoris through ALMA CO multitransition observations[END_REF]) and neutral carbon (Cataldi et al. 2018) gas spatially extended features. The CO clump can be readily explained because CO would be mainly produced in the brightest dust clump and is overabundant there. Indeed, CO would not have time to spread around its orbit and become axisymmetric because the photodissociation timescale is much smaller than the orbital timescale, and CO cannot complete a full orbit. Hence when observed edge-on it still looks like a clump similar to the dust clump. For what concerns carbon, a clump is much more complicated to explain with current models as carbon gas is ex-pected to survive over Myr timescales [START_REF] Kral | A self-consistent model for the evolution of the gas produced in the debris disc of β Pictoris[END_REF], and to quickly become symmetrical in azimuth because of collisions with ambient gas (even if it were produced in an asymmetric clump initially).

In this work, we analyze for the very first time the mid-IR images of β Pictoris obtained using Adaptive Optics technology, which enables us to reach an unprecedented angular resolution and contrast at this wavelength on this emblematic system. Furthermore, we revisit former VISIR data to perform a multi-epoch comparison. As a result, we provide important constraints on the planet and the disk structures.

The paper is organized as follows: Section 2 presents the context of the observations, as well as the data reduction and post-processing. We discuss the non-detection of the planet b in section 3 and we put some constraints on the presence of dust material around the planet in section 3.3. In section 4 we analyze the disk structures, and measure the variations of the southwest clump position to better constrain its orbital radius in the system, blackwhich is described in section 5. Section 6 discusses the other clumps detected in the disk. Finally, we discuss the implications of these observations in section 7, and we conclude in section 8.

Observations and data reduction

VISIR NEAR science demonstration data

Project description

The VLT mid-infrared imager, VISIR, has been modified in the framework of the NEAR project [START_REF] Kasper | NEAR: First Results from the Search for Low-Mass Planets in α Cen[END_REF]) for an observation campaign of the α Centauri system aiming at detecting terrestrial planets. NEAR is supported by ESO and the Breakthrough Initiatives Foundation. The project was designed to push VISIR N-band performances to their limit, in terms of sensitivity and contrast. To that aim, VISIR was equipped with phase mask vortex coronagraphs (AGPM) [START_REF] Mawet | Annular Groove Phase Mask Coronagraph[END_REF][START_REF] Delacroix | Society of Photo-Optical Instrumentation Engineers[END_REF]) optimized for the 10 -12.5 µm band. The control of the centering of the star into the coronagraph was performed with the quadrant analysis of coronagraphic images for tip-tilt sensing estimator (QACITS, Huby et al. (2015); [START_REF] Maire | Design, pointing control, and on-sky performance of the mid-infrared vortex coronagraph for the VLT/NEAR experiment[END_REF]). NEAR has also been coupled to a visible wavefront sensor that controls the deformable secondary mirror (DSM) of the adaptive optics facility (UT4), allowing access to extreme adaptive optics regime, and reaching Strehl ratios higher than 90% at 12 µm.

Observing setup

β Pictoris was observed with NEAR on the 12th and the 15th of December 2019 (program ID 60.A.9107 (K), P.I. NEAR team). Coupling NEAR with the DSM of the VLT allowed the use of AO without increasing the number of warm optics that would add to the thermal background. The NEAR spectral filter transmits light from 10 to 12.5 µm and the full width at half maximum (FWHM) is ∼ 0.28 ′′ , or ∼ 6 pixels. The Cassegrain instrument was fixed in pupil-stabilized mode during the observations. To suppress the large thermal background, a chopping frequency of 8.33 Hz has been adopted, and a chop throw of 4.5 ′′ . This relatively high frequency allowed to significantly decrease the lowfrequency noise excess of the Aquarius type detector (Ives et al. 2014), and reach background limited sensitivity performances. To compensate for the difference in optical path induced by the chopping, the nodding was performed by slightly slewing the telescope every minute. The subtraction of the chopping yielded to have two images of the star taken at different positions, one coronagraphic, and the other off-axis, non-coronagraphic image. As a result, there are two negative images of the star on the side of the central coronagraphic image.

The detector integration time was set to 6 ms, to avoid saturation in the background. Ten frames were acquired and stacked in each DSM chopper position, out of which the 2 first were discarded to suppress any PSF smearing due to the DSM settling time. The recorded data have thus a time frame of 160 ms. Simple chopping leaves some low spatial frequency residuals due to inhomogeneities of the thermal footprint. Nodding was thus also applied to calibrate these residuals. The nodding offset was parallel and of the same amplitude as the chopping so that the target was always kept within the detector's field of view. A temporal binning of chopped-nodded frames was performed to produce a data cube in which each frame corresponds to an integration time of about 5s. The data from the 12th and the 15th were combined corresponding to 2442 s and 3180 s on source respectively. During these observations, the seeing ranges were 0.7 -0.9 ′′ and 0.55 -0.80 ′′ on the 12th and the 15th respectively, and the coherence time was ∼5 ms and ∼4 ms respectively, and the precipitable water vapor (PWV) was ∼5 mm and ∼3 mm respectively, as well.

Post-processing

After the observations, frame selection was performed on the data cubes, based on criteria of residual flux behind the coronagraphic mask. The 10% worst frames, for which the star was slightly off-centered, were rejected because otherwise resulting in poor stellar subtraction during the next step. After frame selection, the remaining on-source telescope time (behind the mask) is about 5060 s. We took advantage of the SPHERE Calibration Tool, SpeCal (Galicher et al. 2018), which can be easily adapted to any instrument by providing minor modifications of the input data to match the SpeCal format. SpeCal has been developed to accurately detect the faintest point sources in high contrast imaging data, offering several types of algorithms for data analysis, such as angular differential imaging (ADI, [START_REF] Marois | Angular Differential Imaging: A Powerful High-Contrast Imaging Technique[END_REF]) combined with principal component analysis (PCA, Soummer et al. 2012) or TLOCI [START_REF] Lafrenière | A New Algorithm for Point-Spread Function Subtraction in High-Contrast Imaging: A Demonstration with Angular Differential Imaging[END_REF]). The simplest processing provides a direct stacking of frames once compensated by the field rotation. This is the classical averaging described in Galicher et al. (2018, ClasImg, for classical imaging) . Figure 1 presents the resulting images, after a ClasImg and PCA reduction.

VISIR archival data

Non-coronagraphic observations of β Pictoris were obtained with VISIR on 2004 (program ID 60.A-9234(A) and 2015 (program ID 95.C-0425(A), with the VLT. The observations were performed in a standard chopping-nodding mode. The data were reduced by combining all the chop-nodded frames into a single one. Each observation was typically 1 hour long. The data were consequently flux calibrated by observing with the same settings an infrared standard (HD 42540, spectral type K2/3III, J=2.90, H=2.24, K=2.09) just before β Pictoris observations. The reduced data are further examined in Section 5 to perform a comparison with the NEAR observations.

Searching for β Pictoris b

A non-detection at mid-infrared wavelengths

Using various SpeCal's algorithms we performed several tests to reduce the stellar contribution, and allow us to reveal the expected planet. We compared the contrast curves provided by the cADI, ClasImg, PCA, and TLOCI algorithms: we found that the PCA reduction provides the deepest contrast curves at the expected separation of the planet. All the assessments provided a non-detection outcome, preventing us to identify the giant planet β Pictoris b within the NEAR data. Observations obtained at a similar epoch with SPHERE yielded an angular separation of 301 ± 4 mas with respect to the star [START_REF] Lagrange | Unveiling the β Pictoris system, coupling high contrast imaging, interferometric, and radial velocity data[END_REF]. At such a distance, which corresponds to 1 × λ/D at this wavelength (λ = 11.25 µm), the AGPM coronagraph would transmit only 32% of the flux of a point-source (see Figure A.1). Taking this parameter into account, we further explored the sensitivity to point sources by injecting fake planets built from the noncoronagraphic star's image at various contrasts, and processed with a set of ADI algorithms. We concluded that the PCA algorithm is providing the best contrast with 10 modes removed.

One of the SpeCal output provides an estimation of the azimuthal contrast level for each angular distance. Therefore, we estimated the limit of detection in the PCA image. We note that the disk itself and the background are the major contributions to the noise, far beyond the speckle noise. The transmission curve of the coronagraph was computed by comparing the maximum intensity of the coronagraphic image at an increasing separation from the center, normalized to the PSF (non-coronagraphic) maximum intensity (Figure A.1,in Appendix). Figure 2 shows the 5σ contrast curve corrected from the coronagraphic transmission. The contrast at the expected position of the planet β Pic b, at 0.3", is 5.10 -3 . method to measure the PA in the VISIR data of 2004 and 2015, leads to ∼ 33.3 • ± 1 • and ∼ 34.4 • ± 1 • respectively. As a reference, the most accurate value measured in scattered light owing to precise astrometric calibration is 29.2 ± 0.2 • [START_REF] Chauvin | Orbital characterization of the β Pictoris b giant planet[END_REF]. The notable difference of several degrees with the NEAR 2019 data could be related to the lack of an astrometric calibration procedure attached to these data, especially since VISIR was moved to the VLT UT4 for the NEAR experiment. However, this mismatch has no impact on the following analysis.

We note that in scattered light images, the midplane and the warp are observed as two distinct components owing to the edge-on orientation combined with the radiation pressure effect (Golimowski et al. 2006;[START_REF] Chauvin | Orbital characterization of the β Pictoris b giant planet[END_REF]. [START_REF] Milli | Very deep images of the innermost regions of the β Pictoris debris disc at L[END_REF] is also referring to a warp in the L band while in fact the disk image shows a single component with a very similar trend to the one observed in the mid-IR: a single disk component with a misalignment of the two sides. Moreover, a larger PA in the mid-IR has also been reported by [START_REF] Pantin | View of Beta Pictoris by the VLT[END_REF], both in the N and Q bands. A possible interpretation resides in temperature effects. Grains that are closer to the stars, hence located inside the warp ( 80 au), dominate the global emission. In addition, the warp can be collisionally more active than the outer part of the disk due to the planet's gravitational influence, β Pic b, onto the planetesimals, with a larger rate of small grains released, the latter being efficient emitters. As a result, the mid-IR image of the disk would be essentially oriented along the warp.

A clumpy structure

To analyze the clumpy structure of the disk, we converted the images to intensity units in Jy/arcsec 2 , by taking into account the pixel area (a dilution factor of 2.10 -3 corresponding to 1/pixel_scale 2 ), and a photometric calibration which gives a total flux in the coronagraphic image of 1.1 × 10 6 ADU for a point source of 1 Jy. The surface brightness of the disk is obtained by integrating the intensity values for each pixel slice, of 12 pixels wide (0.54 ′′ ), encompassing the disk thickness, and perpendicular to the mid-plane.

Figure 7 presents the resulting intensity profile along the disk for the ClasImg and PCA processing. The clumps C1 and C2 can be identified in the surface brightness profiles, both in the ClasImg and PCA case. To a lower extent the hypothetical structures C3 and C4 are barely visible in the surface brightness. As visible in Figure 1, the PCA reduction considerably attenuates the stellar contribution, impacting the photometry of the disk due to self-subtraction, with a stellocentric dependence. We note that the clumps, in particular C1 and C2, are very elongated and that being seen edge-on there is an obvious degeneracy between radial and azimuthal extension (or possibly both). C1 has a projected width of ∼30 au as seen in Figure 11, with a sharper width of ∼10 au, corresponding roughly to the width of the peak in the PCA profile.

Temporal evolution of the southwest clump C1

The β Pictoris system has been observed in the mid-IR on several occasions with 8-m class telescopes since Dec. 2003, when C1 was first identified by [START_REF] Telesco | Mid-infrared images of β Pictoris and the possible role of planetesimal collisions in the central disk[END_REF]. Given the 16year baseline with respect to our NEAR observations, the study of its evolution becomes relevant and can potentially allow us to address the question about its origin. Table 1 presents the data available in the mid-IR that we used for comparison with our data set. Both [START_REF] Telesco | Mid-infrared images of β Pictoris and the possible role of planetesimal collisions in the central disk[END_REF] and [START_REF] Li | The Mineralogy and Structure of the Inner Debris Disk of β Pictoris[END_REF] located the position of C1 by performing a centro-symmetrical subtraction of the disk image, subtracting the emission in the fainter NE wing from the SW wing, and vice-versa. This yielded a residual emission, which was then assumed to be the main contribution of the clump. Indeed, in images without AO, the resolution is such that it is difficult to isolate the clump without this specific processing. For consistency reasons, we processed the 2004 and 2015 VISIR data similarly (Figure 8). In comparison, in the 2019 data, C1 is unambiguously detected and resolved, as seen in Figure 1, without any particular processing. This emphasizes furthermore the efficiency of the use of AO and a coronagraph.

Impact of the centro-symmetrical subtraction

Measuring the exact position of C1 from the intensity profile is not straightforward, given the width of the clump of several au. In the following, we assume that the position of C1 is driven by the intensity peak of this structure, and we did not make any assumption on whether it is radially or azimuthally extended. Furthermore, as we use either PCA or centro-symmetrical subtraction, any stellar residuals or the main disk emission itself do not impact the determination of the C1 position. In order to verify that the centro-symmetrical subtraction does not impact the position of C1, especially given the presence of the clump C2 and that the stellar contribution is substantial, we performed a measurement in the ClasImg 2019 image after applying the same centro-symmetrical subtraction.

We found that the results of the two methods (centrosymmetrical subtraction in ClasImg vs. PCA ADI) are consistent within ±0.1 au (corresponding to approximately ±0.1 pixel), confirming the accuracy of the former method, as seen in Figure 9. Hence, we did not apply the centro-symmetrical subtraction to determine the location of C1 in the 2019 data.

Position and error bar estimations

We consider the following sources of uncertainty in measuring the position of C1, and describe the resulting errors for each of these contributions to the 2019 data.

(a) Position of the star in the image: it was estimated by doing a Gaussian fit of the center of the image in the ClasImg process, compared to the center of the image. The residual error is coming from the derotation of the images in the ClasImg process, when assuming the star is centered in the image. We estimated a resulting 0.2-pixel error corresponding to the cumulative error in the ClasImg sequence. This includes QAC-ITS pointing control error, which centers the star on the coronagraph within ∼ 0.02 λ/D. (b) Orientation of the disk: repeating the process of measuring the clump position for the range of PA (30 • ± 0.5 • ), we found a dispersion lower than 0.3 pixel. (c) Gaussian fitting of the clump: To accurately measure the position of the clump we limited the range of distance from the star where we fit a Gaussian profile (from around 2 ′′ to 4 ′′ , centered approximately on C1, as seen in Figure 10). The resulting error is 0.1 pixel. (d) Data reduction method: first, the PCA reduction introduces a bias leading to a photometric error; furthermore, the centrosymmetrical subtraction performed for the 2004 and 2015 data adds up. To estimate the bias introduced by the PCA reduction, we compared the position of C1 with the one found with the ClasImg reduction (by performing a centrosymmetrical subtraction), resulting in a shift of 0.1 pixel.

Article number, page 7 of 15 possible (reduced minimal χ 2 ν = 1.4) given the error bars. Still, the scenarios with resonances are significantly worse than when assuming the local Keplerian orbit (reduced minimal χ 2 ν = 0.22, Figure 12). Note that, for this 3:2 resonant scenario, any new observation of the clump location should easily settle the validity of this hypothesis.

Planet's Hill sphere or trojans

The most likely hypothesis we are left with is thus that of a dust clump that orbits at the expected local Keplerian speed and should be relatively long-lived in order to be observed. If this clump is linked to the presence of a yet-undetected planet, then it could be either circumplanetary material within the planet's Hill radius or Roche lobe or, alternatively, material trapped in the corotating L4 or L5 Lagrangian points, in a Trojan-like configuration. [START_REF] Telesco | Mid-infrared images of β Pictoris and the possible role of planetesimal collisions in the central disk[END_REF] estimate the total mass of dust in the clump to be around 4 × 10 20 g, which is much less than the estimated mass of the Jupiter Trojans, ∼ 6 × 10 23 g (Jewitt et al. 2000). However, 4 × 10 20 g is the estimated mass of dust (typically ≤ 1 mm) whereas the estimated mass of Trojans is that of ≥ 1 km objects. If we assume that the observed dust is produced by a collisional cascade starting at ∼ 1 km object with a differential size distribution following a power law of index q = -3.5, then we get an extrapolated total mass of ∼ 4 × 10 23 g, which is roughly comparable to the mass of km-sized Jupiter Trojans. There is, however, a potential issue with this scenario if the dust clump has the same radial extent as that of the clump seen in CO. The relative radial width of the stable region around the L4-L5 points should indeed not exceed ∼ 10% (Liberato & Winter 2020), whereas it is at least ∼ 50% for the observed CO clump [START_REF] Matrà | Exocometary gas structure, origin and physical properties around β Pictoris through ALMA CO multitransition observations[END_REF]. As discussed in Sec. 6, the correspondence between the dust and CO clumps is a complex issue that is left to future investigations. We here remain careful and stress that the Trojan scenario might be challenged by a radially broad dust clump.

Another possibility is that the clump is confined within the Hill sphere surrounding a planet. In this case the minimum mass of the putative planet can be derived from the size of the clump using Equation 5and assuming that the clump is smaller than R Hill . For a typical clump size of ∼10 au, the mass of the planet having a Hill sphere of this size is of the order of 3M J . The problem is that, at a distance of ∼ 50 au, such a massive planet would have had a 99% probability of having been detected by [START_REF] Lagrange | Unveiling the β Pictoris system, coupling high contrast imaging, interferometric, and radial velocity data[END_REF] with a combination of radial velocity and imaging. This problem could be overcome if the clump is optically thick (τ > 1) and thus hide the planet's photosphere. For a 10 au wide clump made of the smallest possible grains (∼ 2µm), the τ > 1 criteria would lead to a minimum clump mass of ∼ 5 × 10 25 g, which corresponds to the mass of a Moon-sized object.

A vortex

In the hypothetical case that the gas and dust clumps are colocated, a scenario that could allow for a somewhat large radial extent (as deduced from observations of the gas velocity [START_REF] Matrà | Exocometary gas structure, origin and physical properties around β Pictoris through ALMA CO multitransition observations[END_REF] while explaining that the gas orbits at the local Keplerian velocity is that of a vortex. Vortices have been extensively studied, both analytically and numerically, in the context of younger protoplanetary disks, yet they have never been proposed as an explanation for clumps in debris disks. There are several ways to generate vortices in disks, but large-scale vortices are most often thought to arise from the Rossby-Wave In-stability (RWI). This instability can set in when there is a radial minimum in the gas potential vorticity, which in practice can be when there is a radial maximum in the gas pressure (see, e.g., the review by Lovelace et al. ( 2013)).

Radial pressure maxima could well occur in debris disks. The pressure maximum could be related to 1) a Saturn-like planet or more massive creating a gap with a natural pressure maximum at its outer edge (just like in a gas-rich protoplanetary disk; see, e.g., Hammer et al. 2021), 2) the presence of a clump of solids -similar to that observed in β Pic -that releases gas and naturally creates a pressure maximum. Large-scale vortices can also survive for thousands of orbits, i.e. millions of years at > 50 au (Hammer et al. 2021), making it not unlikely to be observed in a ∼20 Myr old system. Note, however, that the typical lifetime of vortices depends, among other things, on the gas turbulent viscosity, with smaller turbulent viscosities favoring longer-lived vortices (see, e.g., the discussion in Sect. 4.2 in Baruteau et al. 2019). The amount of turbulence in debris disks is not yet observationally constrained but it could be very high in low-gas mass ionized systems and lower in more massive disks (Kral & Latter 2016).

According to current RWI models, the smallest dust with a Stokes number of ∼1 (∼ µm dust) should tend to concentrate near the center of the vortex but the effect of radiation pressure, which cannot be neglected in debris disks, has not been taken into account in RWI models and may alter this conclusion. We also note that when the dust-to-gas mass ratio in the vortex becomes greater than 0.3-0.5, the vortex may be destroyed (Crnkovic-Rubsamen et al. 2015). In the case of β Pic, [START_REF] Kral | A self-consistent model for the evolution of the gas produced in the debris disc of β Pictoris[END_REF] calculated that the dust-to-gas mass ratio is greater than 1 beyond 20 au so this effect of dust feedback on the gas vortex may be relevant here.

The presence of a vortex would also solve another still unexplained phenomenon, namely that the neutral carbon gas observed with ALMA is not axisymmetric as predicted by the models but clumpy similar to CO (Cataldi et al. 2018). Indeed, according to current models, CO should photodissociate in less than one orbit, which may explain why it is clumpy [START_REF] Matrà | Exocometary gas structure, origin and physical properties around β Pictoris through ALMA CO multitransition observations[END_REF]), but the carbon that is created due to the photodissociation of CO should instead become axisymmetric rapidly on a time scale of a few orbits. On the contrary, if the gas forms a vortex, both the carbon and CO are indeed expected to be clumpy. The large width of the clump is also in line with the idea of a vortex in the gas. An RWI-induced vortex has indeed a radial width that is typically twice the local pressure scale height (Baruteau et al. 2019) and can thus reach tens of au as observed for β Pic.

We also note that a significant brightness asymmetry is observed in the near IR (e.g. Apai et al. 2015) and a clump in the mid-IR [START_REF] Telesco | Mid-infrared images of β Pictoris and the possible role of planetesimal collisions in the central disk[END_REF], and this study) but not in the mm (Matrà et al. 2019). This could also be explained by the presence of a vortex trapping only the smallest µm-sized grains (with a Stokes number 1), while the largest mm-grains would remain unperturbed by the vortex and retain a near axisymmetric spatial distribution. These statements should be further analyzed via numerical simulations in a dedicated study.

Although further numerical simulations for the specific case of debris disks are needed to strengthen our conclusions, vortices are compelling contenders to explain observations and deserve more attention for β Pic as this would allow us to explain for the first time the observations of CO and carbon gases as well as the observations of dust in the near-, mid-IR and in the mm. For all these reasons, we suggest that it is a viable scenario that needs further theoretical and observational testing.

If we expect C1 to be caused by a vortex formed at the outer edge of the annular gap of a planet, we could give an idea of where the planet would be located according to its mass. A vortex formed at the outer edge of a planet's gap is typically located within a few (5)(6)(7)(8)(9)(10) Hill radii of the planet. For a Jupiter-mass planet around a Sun-mass star, the vortex will have a semi-major axis ∼ 1.5 a (see for instance Figure 2 by Baruteau et al. 2019). In our case, the hypothetical planet would be located around 37 au (assuming a dust clump centered at ∼50 au), which is between C3 and C1.

Conclusion

This paper presents the first high contrast imaging data in the mid-IR of the β Pictoris system, observed with NEAR. We summarize here the main results of our analysis of these data, and their comparison with previous observations.

• The planet β Pictoris b was not detected with NEAR. However, by taking into account the transmission of the coronagraph, we derived the planetary flux upper limit from the contrast curve at 5σ. We collected spectro-photometry from different instruments, and presented a combined spectrum the first spectra of β Pictoris b acquired with SPHERE during several epochs. The upper limit of the NEAR data does not allow to put meaningful constraints on atmospheric scenarios. • Given the planetary flux upper limit, we investigated which corresponding amount of dust, present around the planet, could reproduce such a limit. Although this quantity scales with the distance to the planet, we concluded that the presence of a dust cloud around the planet was unlikely. If dust particles were located at the Roche radius, it would correspond to the collisional debris of a 5 km size asteroid. • The disk is uniquely resolved in these mid-IR data, allowing us to identify structures that were never observed prior to those observations. The southwest clump, previously reported in the literature, is distinctively detected in the NEAR data set, at 56.1 +0.3 -0.3 au. On the northeast side of the disk, there is a clear detection of a new clump at -35.2 +0.3 -0.3 au. We note the possible presence of two other clumps at 29.3 +0.3 -0.3 au at -15.2 +0.3 -0.3 au. Further observations will be required to confirm their existence.

• The southwest clump was observed several times since its discovery in 2003, with T-ReCS and VISIR. The 16-year baseline of observations, with five observing sequences, allowed us to assess the motion of the clump over time, and to confirm a Keplerian behavior. This result is based on the assumption that the clump has a circular orbit, which would be challenged in the case of an elliptical orbit. • We investigated qualitatively different origins for the southwest clump, in particular the possibility that it could be the Hill sphere of a yet-to-be detected planet with a maximum mass of 3M J . Given it is in motion we ruled out the scenario that this clump is the result of a giant impact. We provided arguments for a scenario where the clump would be a dust-trapping gas vortex, based in particular on the possible superimposition of the southwest clump and the CO clump seen with ALMA.

The β Pictoris system has been extensively studied at different wavelengths, and is an archetypal system for our understanding of planet-disk interactions and planet formation. This study shows that the use of adaptive optics along with a coronagraph in N band does bring a considerable improvement to the data quality. NEAR data have allowed us to put constraints for the first time on the presence of circumplanetary material around a directly imaged planet. We could indeed expect giant planets to have circumplanetary disks, as all the giant planets in our solar system have some. Similarly, we detected disk structures that were never observed before. Further observations are needed to confirm some of those structures, and understand their origin. Likewise, further observations of C1 are needed to track its evolution and confirm its origin, and put better constraints on the evolution of the size of the clump. The James Webb Space Telescope will provide unique mid-IR data, that will significantly help us in our understanding of the famous β Pictoris system.

Chapter 5

Exoplanet atmospheric characterization

This chapter presents a collaborative work that I led following a summer school. The Ariel Retrieval of Exoplanets School (ARES) happened during the first week of my PhD, in early October 2019, in Biarritz, France. Five papers were published after this school. I will first present the framework of this summer school and then present in Section 2.4 the paper I led.

Summer school objectives

As described in Section 4, up until the operation of JWST, the current spectral coverage provided by the available instruments was not wide enough to allow us to break degeneracies in studying the spectra of exoplanet atmospheres. A wider spectral coverage is necessary to break these degeneracies and shed light on exoplanets' diversity, formation, and evolution processes. ESA's next M4 mission, Ariel [START_REF] Tinetti | Ariel: Enabling planetary science across light-years[END_REF], is designed to study 1000 exoplanets' atmospheres, with a wide spectral coverage spanning continuously from 0.5 to 7.8 µm through three spectrometers and three photometric channels. It is aimed to launch in 2029. The summer school, open to PhD and post-docs, was aimed at preparing for the Ariel data by first teaching on exoplanet atmospheres, then on studying publicly available data with open source codes. The school started a momentum that continued for several months, leading to the five papers, all led by school attendees. This summer school was divided into three main parts: first, we learned the basics of exoplanetary atmospheric physics. Then, we learned how to get Hubble's Wide Field Camera 3 (WFC3) data from the public archive. We learned to use the Iraclis pipeline1 to reduce the data (Tsiaras et al., 2016). Finally, we learned how to analyze the reduced spectra, with the TauREx retrieval code2 (Waldmann et al., 2015b). We looked at unpublished public data from HST. I focused on data of WASP-127b, which is a sub-Saturn mass and super-Jupiter radius hot Jupiter. It is the least dense exoplanet discovered to date, and is located in the short-period Neptune desert, also called the photoevaporation desert (Mazeh et al., 2016). The few planets 2. Characterising the Hot Jupiters WASP-127 b, WASP-79 b and WASP-62 b with HST in this location have a complex formation history, and studying their atmosphere is crucial to understand their origins. Other students of the summer school studied two other hot Jupiters, WASP-79b and WASP-62b, from the public archive of HST/WFC3. The data of this paper were public for a couple of years before we analyzed them (from 2017 and 2018) 3 . This paper was a collaborative work with the other students of the summer school. I will present in this section the main steps of the work that led to the paper, which is presented in Section 2.4. Given the paper is long and describes in detail the work that was done, and given that both software used, TauREx and Iraclis, are open source and well documented, I will here focus on presenting the main steps of the method, and will present the main results.

Target description

The Wide Angle Search for Planets (WASP) [START_REF] Pollacco | The WASP Project and the SuperWASP Cameras[END_REF] is an array of robotic telescopes located in the Canary Islands (Spain) and South Africa, which survey the entire sky to detect transiting planets. The array is composed of 8 telescopes of 200 mm in diameter, open at f1.8, giving a sky covering of 490 square degrees. WASP detected and published its first planets in 2007 [START_REF] Collier Cameron | WASP-1b and WASP-2b: two new transiting exoplanets detected with SuperWASP and SOPHIE[END_REF]; since then, nearly 200 planets have been detected with it. WASP-127 b (Lam et al., 2017), WASP-79 b [START_REF] Smalley | WASP-78b and WASP-79b: two highly-bloated hot Jupiter-mass exoplanets orbiting F-type stars in Eridanus[END_REF] and WASP-62 b [START_REF] Hellier | Seven transiting hot Jupiters from WASP-South, Euler and TRAPPIST: WASP-47b, WASP-55b, WASP-61b, WASP-62b, WASP-63b, WASP-66b and WASP-67b[END_REF] are three hot jupiters detected with WASP. These three planets are inflated with low eccentricity orbits. The planets' parameters are presented in Table 5.1. Table 5.2 presents the HST/WFC3 observations summary. The three planets were observed with HST/WFC3, with the G141 grism (1.088 -1.68 µm). WASP-127 b, located at 520 light-years from Earth, is the most inflated known exoplanet with its unusually low density (super-Jupiter radius and sub-Saturn mass), making it an ideal target for spectroscopy. It is located in the short-period Neptune desert, where it is expected that planets do not survive photo-evaporation (Mazeh et al., 2016;[START_REF] Owen | The Evaporation Valley in the Kepler Planets[END_REF]Owen et al., 2018). Its unusually large radius raised several questions on the origins of its inflation. There have been several observations of this planet to better understand its atmospheric composition and its formation, with different instruments and telescopes, such as TESS, HARPS, ESPRESSO, and the Gran Telescopio Canarias (GTC) [START_REF] Seidel | Hot Exoplanet Atmospheres Resolved with Transit Spectroscopy (HEARTS). VI. Non-detection of sodium with HARPS on the bloated super-Neptune WASP-127b[END_REF][START_REF] Allart | WASP-127b: a misaligned planet with a partly cloudy atmosphere and tenuous sodium signature seen by ESPRESSO[END_REF]Chen, G. et al., 2018). Regarding WASP-79 b and WASP-62 b, they both present photo-evaporation signs of their atmospheres, at a mass loss rate estimated to be " e 11 g.s ´1 (Bourrier et al., 2015). WASP-127 b planet raised an interest beyond the scientific community. Figure 5.1 presents an artist's impression of this planet. If you are into American rap, you may have heard the attempt from Lil Uzi vert to buy WASP-127 b, and become its legal owner. I won't comment 2. Characterising the Hot Jupiters WASP-127 b, WASP-79 b and WASP-62 b with HST and 1.9 R J . We used the method of this study as a benchmark for our paper. We used the same baseline for the three planets, for both the data reduction and calibration.

HST/WFC3 data reduction

The data reduction process of the HST/WFC3 data with Iraclic is described in Section 2.2 of the paper. The resulting white and spectral light curves for WASP-127 b are presented respectively in Figures 1 and2 of the paper.

Retrieval analysis

The reduced spectra were analyzed with TauREx 3 (Al-Refaie et al., 2019), which is a retrieval framework, as described in Section 4.4.1. Our analysis is described in Section 2.3 of the paper. To run a retrieval, we must provide a parameter file with different parameters, and their respective range of variability, for the retrieval to explore the different scenarios in the forward models. For consistency, we used the same general setup for all three planets. This is described in Section 2.3.1 of the paper. Below is a list of this general setup:

-Plane-parallel approximation to model the atmospheres; -100 atmospheric layers; -Pressures ranging from 10 ´2 to 10 6 Pa; -Rayleigh scattering; -Collision-induced absorption (CIA) of H 2 -H 2 and H 2 -He (Fletcher et al., 2018;[START_REF] Abel | Infrared absorption by collisional H2-He complexes at temperatures up to 9000 K and frequencies from 0 to 20 000 cm-1[END_REF];

-Grey cloud model: fully opaque layer below the cloud top pressure, considered at 10 6 Pa.

Below is a list of the parameter bounds, which have been applied to the three planets as well:

-Molecular abundances profiles were allowed to vary between 10 ´12 and 10 ´1 in volume mixing ratio;

-The molecules explored were: H 2 O, CH 4 , CO, CO 2 , NH 3 , and FeH;

-The planetary radius was set to vary within 50% of the reference radius as found in the literature (cf Table 5.1, which is assumed to be the radius at 10 6 Pa pressure;

-The cloud top pressure ranged like the pressure, from 10 ´2 to 10 6 Pa;

-The planetary temperature was set to vary from 400 to 2500 K, to accommodate the wide equilibrium temperature ranges between the three planets.

Figure 5.2 presents the main choices of this baseline model for the parameters files for the TauREx retrievals of all three planets. These retrievals were the first ones to consider the iron hydrate molecule, FeH (Dulick et al., 2003), in an exoplanet atmosphere. 5.25 1.10 0.88 ,withan extended cloudy atmosphere. We also detected water vapor in the atmospheres of WASP-79 b and WASP-62 b, with best-fit models indicating the presence of iron hydride, too. We used the Atmospheric Detectability Index as well as Bayesian log evidence to quantify the strength of the detection and compared our results to the hot Jupiter population study by Tsiaras et al. While all the planets studied here are suitable targets for characterization with upcoming facilities such as the James Webb Space Telescope and Ariel, WASP-127 b is of particular interest due to its low density, and a thorough atmospheric study would develop our understanding of planet formation and migration.

Unified Astronomy Thesaurus concepts: Exoplanet astronomy (486); Exoplanet atmospheres (487); Astronomy data analysis (1858); Hubble Space Telescope (761)

Introduction

The currently known exoplanet population displays a wide range of masses, radii, and orbits. Although many planets have been detected and it is thought that they are common in our Galaxy (Cassan et al. 2012;W r i g h te ta l .2012; Batalha et al. 2013;Dressing & Charbonneau 2013;H o w a r d2013),o u r current knowledge of their atmospheric characteristics is still very limited. Examining the atmospheres of exoplanets further unveils their planetary properties, with their study made possible by various methods, including transit spectroscopy (e.g., Tinetti et al. 2007;Swain et al. 2008). Facilities such as the Hubble Space Telescope (HST) and the Spitzer Space Telescope, as well as some ground-based observatories, have provided constraints on these properties for a limited number of targets and, in some cases, have identified the key molecules present in their atmospheres while also detecting the presence of clouds and probing their thermal structure (e.g., [START_REF] Brogi | [END_REF];M a j e a u et al. 2012; Stevenson et al. 2014;S i n ge ta l .2016;F ue ta l . 2017; Hoeijmakers et al. 2018;Tsiaras et al. 2018Tsiaras et al. , 2019;;Pinhas et al. 2019;Edwards et al. 2020a;Ehrenreich et al. 2020).

This paper presents the analysis of data from Hubble's public archive for the exoplanets WASP-127 b, WASP-79 b, and WASP-62 b. They are all inflated, with low eccentricities and short orbital periods around bright stars. Table 1 presents the stellar and planetary parameters for each of these targets.

WASP-127 b is an ideal target for spectroscopic studies, given its unusually low density (with a super-Jupiter radius and a sub-Saturn mass). It is located in the short-period Neptune desert, where it is expected that planets might not survive photoevaporation (Mazeh et al. 2016;O w e n&L a i2018).H o w e v e r , photoevaporation is strongly case dependent, and this planet receives a relatively low extreme ultraviolet flux (Chen et al. 2018). Potential explanations for its inflation include tidal heating, enhanced atmospheric opacity, ohmic heating, and reinflation by the host star during inward migration (Batygin & Stevenson 2010;Leconte et al. 2010;Batygin et al. 2011;Rauscher&Menou2013;Lithwick & Wu 2014). Both WASP-62 b and WASP-79 b are believed to have an evaporating atmosphere, with mass-loss rates estimated at ≈11 g s -1 (Bourrier et al. 2015). WASP-79 b, which has a polar orbit, was originally detected through an aberration in the radial velocity due to the Rossiter-McLaughlin effect (Addison et al. 2013).

Allspectraldatapresentedherein were acquired with the G141 grism (1.088-1.68 μm) of the HST/Wide Field Camera 3 (WFC3) camera, and details regarding each observation can be f o u n di nT a b l e1. In Section 2, we detail how the data were reduced with the Iraclis pipeline (Tsiaras et al. 2016b), following the approach described by Tsiaras et al. (2018) and summarized here. In Section 2.3,w ed e s c r i b et h eT a u R E x retrieval code used to analyze the reduced spectra (Waldmann et al. 2015a(Waldmann et al. , 2015b;;Al-Refaie et al. 2019), along with the initial parameters and priors used. Our results can be found in Section 3, followed by a discussion on our findings and the implications they hold for future missions, including simulations of data from Ariel and the James Webb Space Telescope (JWST).

Methodology

HST Observations

Data reduction and calibration were performed using Iraclis, software developed in Tsiaras et al. (2016b) and available on GitHub; 18 it has been used to extract HST spectra in multiple studies, including Tsiaras et al. (2016aTsiaras et al. ( , 2018Tsiaras et al. ( , 2019)). We used the Mikulski Archive for Space Telescopes 19 to assess the spectroscopic observational data of WASP-127 b, WASP-79 b, and WASP-62 b, and information about the observations can be found in Table 2. The WASP-127 b proposal was led by Jessica Spake while David Sing was the PI for the observations of WASP-79 b and WASP-62 b. Although more data are available from additional instruments, we have restricted our study to HST/WFC3 data, in order to maintain consistency in comparing the analysis of the planets.

Data Analysis

The planets in this paper were analyzed to be comparable to the 30 planets studied in Tsiaras et al. (2018). We followed the same methodology as summarized below; differences between our studies are stated explicitly.

Our analysis began with raw spatially scanned spectroscopic images, with data reduction and correction steps performed in the following order: zero-read subtraction, reference pixel correction, nonlinearity correction, dark current subtraction, gain conversion, sky-background subtraction, calibration, flatfield correction, and bad pixels and cosmic-ray correction.

Following the reduction process, the flux was extracted from the spatially scanned spectroscopic images to create the final transit light curves per wavelength band. We considered one broadband (white) light curve covering the whole wavelength range in which the G141 grism is sensitive (1.088-1.68 μm) and spectral light curves with a resolving power of 70 at 1.4 μm. When extracting the spectral light curves, Iraclis accounts for the geometric distortions induced by the tilt of the detector in the WFC3 infrared channel. The bands of the spectral light curves are selected such that the signal-to-noise ratio is approximately uniform across the planetary spectrum. We extracted our final light curves from the differential, nondestructive reads. Prior to light-curve fitting, we chose to discard the first HST orbit of each visit, as these exhibit much stronger hooks than subsequent orbits. Our white-light curves were fit using literature values, and the only free parameters, other than the coefficients for Hubble systematics, were the planet-to-star radius ratio and the transit midtime. This is motivated by the gaps in the observations, caused by Earth obscuration, which often means the ingress and egress of the transit are missed, limiting our ability to refine the semimajor axis to star radius ratio and the inclination of the planet's orbit. The limb-darkening coefficients were selected from the quadratic formula by Claret (2000), using the stellar parameters in Table 1. Figure 1 shows the raw white-light curve, the detrended white-light curve, and the fitting residuals for WASP-127 b while Figure 2 shows the fits of the spectral light curves for each wavelength bin. Similar plots for WASP-79 b and WASP-62 b are shown in Figures 3 and4.

Atmospheric Characterization

The reduced spectra obtained usingIracliswere thereafter fitted using the publicly available 20 Bayesian atmospheric retrieval framework TauREx3 (Al-Refaie et al. 2019). TauREx uses the nested sampling code Multinest (Feroz et al. 2009) to explore the likelihood space of atmospheric parameters and features highly accurate line lists from the ExoMol project (Tennyson et al. 2016), along with those from HITRAN and HITEMP (Rothman et al. 1987(Rothman et al. , 2010)). In our retrieval analysis, we used 750 live points and an evidence tolerance of 0.5. (Rothman et al. 2010),N H 3 (Yurchenko et al. 2011), andFeH (Dulick et al. 2003). In the wavelength range covered by G141, water vapor is the dominant spectral feature, but these other molecules can present detectable signals, particularly FeH (Tennyson & Yurchenko 2018). Clouds are fitted assuming a gray opacity model.

General Setup

In this study we use the plane-parallel approximation to model the atmospheres, with pressures ranging from 10 -2 to 10 6 Pa, uniformly sampled in log-space with 100 atmospheric layers. We included the Rayleigh scattering and the collisioninduced absorption (CIA) of H 2 -H 2 and H 2 -He (Abel et al. 2011[START_REF] Abel | Infrared absorption by collisional H2-He complexes at temperatures up to 9000 K and frequencies from 0 to 20 000 cm-1[END_REF]Fletcher et al. 2018). A summary of the fitted retrieval parameters is given in Table 1. For consistency, the same parameter bounds have been applied for all three planets. Constant molecular abundance profiles were used and allowed to vary freely between 10 -12 and 10 -1 in volume mixing ratio. The planetary radius was set to vary in our models between 0.5 R ref and 1.5 R ref , where R ref is the reference radius from the literature for each planet, as shown in Table 1. This is assumed to be equivalent to the radius at 10 6 Pa pressure.

The cloud-top pressure ranged from 10 -2 to 10 6 Pa, in loguniform scale. We consider a cloud-top pressure of 10 6 Pa to be a cloud-free atmosphere; the gray cloud model used for this study corresponds to a fully opaque layer below the cloud-top pressure.

An isothermal atmosphere was assumed and the planetary temperature, T p , set to vary from 400 to 2500 K; this is to accommodate the wide range in equilibrium temperatures between our three planets, which are between 1400 and 1750 K as shown in Table 1.

Atmospheric Detectability Index

To quantify the detection significance of an atmosphere, we use the Atmospheric Detectability Index (ADI) from Tsiaras et al. (2018), positively defined as the Bayes Factor between the nominal atmospheric model and the flat-line model (i.e., a model representing a fully cloudy atmosphere). For the flat-line model, the only free parameters are the planet radius and temperature, along with the cloud pressure. The nominal model then includes Rayleigh scattering and the CIA of H 2 -H 2 and H 2 -He, as well as molecular opacities. If an atmosphere is detected at the 3σ and 5σ level,s the corresponding ADI will be above 3 and 11, respectively. An ADI below 3 suggests the atmospheric detection is not significant, indicating the spectral feature amplitudes are insufficient given the uncertainty of the data.

To quantify the detection of particular species, we computed the Bayes factor, which is the ratio of the Bayesian evidences of different models. We follow the formalism by Kass & Raftery (1995) for model selection significance as well as translate the Bayes factor to the more traditional σ significance nomenclature following Benneke & Seager (2012).

Ephemeris Refinement

Accurate knowledge of exoplanet transit times is fundamental for atmospheric studies. To ensure the planets studied here can be observed in the future, we used our HST white-light curve midtimes, along with data from TESS [START_REF] Ricker | Proc. SPIE[END_REF],t o update the ephemeris of each planet. TESS data is publicly available through the MAST archive, and we used the pipeline from Edwards et al. (2020b) to download, clean, and fitt h e 2 minute cadence data. WASP-127 b had been studied in Sector 9, WASP-79 b in Sectors 4 and 5, and WASP-62 b in Sectors 1-4 and 6-13. After excluding bad data, we recovered 4, 12, and 60 transits for WASP-127 b, WASP-79 b, and WASP-62 b, respectively. These were fitted individually with the planet-tostar radius ratio R p /R s , reduced semimajor axis (a/R s ), inclination (i), and transit midtime (T mid ) as free parameters. Finally, we fitted a linear period (P) to these midtimes and selected the updated transit midtime (T 0 ) such that the covariance between T 0 and P was minimized. Midtimes were converted to BJDTDB using the tool from Eastman et al. (2010).

Results

Each planet's retrieval produced results consistent with the significant presence of water vapor, with opaque clouds in two of the three planets. While we did attempt to retrieve the carbon-based molecules, CO, CO 2 , and CH 4 , only their upper value could be constrained as they lack strong absorption features in the G141 wavelength range. In each case, our bestfit solution also indicates the presence of FeH, with abundances of log(FeH) between -3.04 and -5.25.

The relatively high water abundances retrieved (10 -2 -10 -3 ) for these three planets can be suggestive of metallicities in the super-solar regime (Madhusudhan 2012;Charnay et al. 2018;Pinhas et al. 2018). However, there are known degeneracies between the the cloud pressure, 10 6 Pa radius, and water abundance retrieved from WFC3 data (Griffith 2014;Heng & Kitzmann 2017). Additionally, due to the restrictions of the WFC3 wavelength ranges, these observations are not generally sensitive to the main carbon-bearing species, and arguments of high metallicities are usually based on retrieved water abundances alone, assuming that half of the oxygen is in H 2 O as expected for a solar C/O ratio at high temperatures (Madhusudhan 2012). Hence, observations covering longer wavelength ranges are needed to further constrain the C/O ratios of these planets, to fully understand their metallicity.

Our findings are shown in Table 3, with Figure 5 showcasing all three retrieved spectra with the corresponding contributions for each opacity source in Figure 6. For WASP-127 b, the posteriors are shown in Figure 7, with equivalent results for WASP-79 b in Figure 8 and for WASP-62 b in Figure 9.

( ) log CH 4 1e-12-1e-1 <-5 <-5 <- 5
( ) log CO 1e-12-1e-1 <-3 <-3 <- 3
( ) log CO 2 1e-12-1e-1 <-3 <-3 <-3 ( ) log NH3 1e-12-1e-1 <-5 <-5 <-5 T p [K] 400-2500

WASP-127 b

As expected given the low density, we retrieved a statistically significant atmosphere around WASP-127 b with a strong detection of water and opaque clouds. The retrieved radius is -+ 1.16 0.04 0.04 R J at a pressure of 10 bar, which is smaller than stated in previous studies (1.37 R J ; Chen et al. 2018). However, our analysis is best fit with high-altitude opaque clouds (log(P clouds )= -+ 1.85 0.66 0.97 Pa), which corresponds to approximately 1.37 R J , thus explaining this difference between the retrieved radius and the radius in the literature.

In terms of chemistry, our best-fit solution indicates significant amounts of water at log(H 2 O)=-2.71 - +

1.05 0.78 and constraints on FeH. FeH produces a flat absorption between 1.2 and 1.3 μm, while deepening the slope in the longer wavelengths (around 1.5-1.6 μm). We also note a correlation between the amount of these two molecules, the radius, and the cloud pressure. For less H 2 O and FeH, the model requires deeper clouds, but a higher base planet radius. In particular, the abundance of FeH can vary from 10 -4 to 10 -7 , depending the complementary contribution of clouds. The posteriors for FeH are, however, always distinct; clouds cannot be used to completely replace the additional visible absorption provided by FeH. A lower metallicity, and larger radius, could be consistent with current data, but is not the bestfit solution. Given the posterior distribution, we do not find a clear correlation between the radius and the water abundance.

WASP-79 b

For WASP-79 b, we get very similar results to those of WASP-127 b, with the exception of the cloud deck. Following our baseline approach, we find a large abundance of water at log(H 2 O)=-2.43 - + 0.76 0.57 and well-defined constraints on the abundance of FeH with log(FeH)=-4.42 - + 1.18 0.91 . The clouds, however, do not impact the model, and we only retrieve a lower limit on their top pressure (P clouds >10 3 Pa). This means that either the planet possesses a clear atmosphere, or that the clouds are located below the visible pressure, at which the atmosphere is opaque due to molecular or CIA. We do not detect signatures of CH 4 , CO, or CO 2 . The retrieved temperature of ∼1000 K is lower than the calculated equilibrium temperature for this type of planet; this was also found in Sotzen et al. (2020) and is discussed further in Section 4.

WASP-62 b

The recovered spectrum of WASP-62 b was flatter than that of the two other planets. However, we found that the data were best explained by the presence of H 2 O and FeH and, for this retrieval, the recovered abundances are log(H 2 O)=-2.03 - + 1.27 0.52

and log(FeH)=-3.04 - + 2.27 2.18 . These results stem from detections in the lower-wavelength spectrum, below 1.5 μm, which guides the retrieval toward non-fully opaque sources, such as clouds and high-radius solutions. Again, the retrieved temperature is lower than the expected 1475 K equilibrium temperature, which is indicative of a large day-night temperature contrast and/or efficient cooling mechanisms. Our analysis indicates that clouds are likely to be present, but the quality of our data means that we cannot completely rule out a clear atmosphere.

The retrieved abundances are very high, but we note that the posteriors allow for a wide range of abundances and present interesting correlations, such as, the lower the abundances of H 2 O and FeH are, the higher in the atmosphere the clouds are located. There is also a negative correlation between the molecular abundances and the temperature and, from the posterior distributions, we see that the data are consistent with abundances of order of 10 -4 in H 2 O and FeH. Finally, we note that given the low spectral variations in this spectrum, the retrieval may lack a scale height constraint, which would provide a relevant baseline in predicting the molecular abundances and temperature more accurately.

Ephemeris Refinement

We found that the observed HST and TESS transits were consistent with literature ephemeris within 1σ. Nevertheless, we refined the period and reference midtransit time for each planet. The updated ephemeris is given in Table 3 while the fitting for the TESS data can be seen in the figures of the Appendix.Thetransit depth and errors of the WFC3 for the three planets are presented in Table 4. The observed minus calculated plots are given in Figure 10, and all transit midtimes used for the fitting are listed in two tables in the Appendix. These have been uploaded to ExoClock, 21 an initiative to ensure transiting planets are regularly followed up, keeping their ephemeris up to date for the ESA Ariel mission (Tinetti et al. 2018).

Discussion

Initially, our baseline model did not include FeH, but these models struggled to fit the data, forcing solutions to lower temperatures and nonphysical values in order to account for the opacity sources at shorter wavelengths with a gray cloud deck. FeH has strong absorption features in the visible and nearinfrared, and can be expected at the temperatures of these planets (Madhusudhan et al. 2016;Tennyson & Yurchenko 2018); hence, we propose it as the possible absorber to suit our spectral features and explore our justifications for FeH over molecules with similar spectral signatures, such as TiO or VO, in this discussion. FeH was not included in the analysis of Tsiaras et al. (2018) and thus, for the hotter planets in that study, retrievals with FeH may alter the retrieved atmospheric characteristics.

Theoretical equilibrium chemistry models predict FeH (Sharp & Burrows 2007;Woitke et al. 2018) to be stable in the gas phase at the temperatures and pressures consistent with the planetary atmospheres considered here. FeH has previously been observed in L and M brown dwarfs at 1800 K (Visscher et al. 2010). In cooler T dwarfs, it has been shown to appear where brown dwarfs have temperatures below 1350 K (Burgasser et al. 2002), with some additional studies [START_REF] Cushing | [END_REF] confirming FeH detection in dwarfs with temperatures of 1000 K. The latter of these detections is at temperatures comparable to the retrieved temperatures of the planets here.

A recent study from Ehrenreich et al. (2020) found atomic iron (Fe) in the dayside of the planet WASP-76 b and not in the terminator, concluding that Fe is condensing on the nightside, then falling into deeper layers of the atmosphere. Furthermore, the results in Pluriel et al. (2020) and Caldas et al. (2019) have investigated how the 3D structure of the atmosphere biases the abundances retrieved with typical retrieval codes, as there is a chemical dichotomy between the day-and nightside that is not considered in a 1D treatment of transit geometry.

We therefore identify three possible scenarios for the detection of FeH in these planets:

• FeH is originating from the dayside where the temperature is much higher and leaks in the nightside before it is able to condense due to circulation processes (Heng et al. 2011). • Atmospheric retrieval studies involve temperature bias due to 3D effects, and we indeed retrieve a cooler temperature than expected; we discuss this in Section 4.1. • A 3D effect is in play, and we retrieve the FeH in the dayside inflated region of the limb (Caldas et al. 2019;Pluriel et al. 2020). Table 5 contains the log evidence of several retrievals for each planet. In all cases, the addition of FeH increases the goodness of fit while also raising the retrieved temperature. We note that all models included clouds. By comparing the log evidence of the models with only H 2 O and the models with H 2 O and FeH, we confirm for all planets that clouds are not a suitable opacity substitute for FeH.

The difference in log evidence for these models ( () ) D E log is 8. 33, 3.39, and 5.37 for WASP-127 b, WASP-79 b, and WASP-62 b respectively (4.48σ,3 . 0 9 σ,and 3.72σ detection of FeH,respectively). This indicates strong to decisive evidence in favor of models containing FeH (Kass & Raftery 1995;Benneke & Seager 2012;Changeat et al. 2019).

While we postulate that our evidence holds for FeH, it is possible that we detect another, yet unidentified, opacity source with absorption characteristics similar to those of FeH over the WFC3 passband. For instance, similar absorption features can be produced with metal oxides such as TiO, VO, and YO. However, we do not expect the presence of these molecules in these planets due to the planets' low equilibrium temperatures. TiO and VO have condensation temperatures of over ∼2000 K (Lodders 2002;Hubeny et al. 2003;Fortney et al. 2008); the highest equilibrium temperature featured of these three planets is WASP-79 b's 1716 K, as referenced in Table 1, thus rendering it less likely that the spectral features are due to TiO and VO compared to FeH. Ultimately, this further exemplifies the need for longer wavelength coverage with JWST or Ariel to confirm the nature of observed absorption in the future.

For each planet, we have calculated the ADI and found significant evidence of atmospheric features for all three. Given the water detection on all three planets, our results support the conclusions drawn by Tsiaras et al. (2018);inflated, hot Jupiterlike planets do not necessarily destroy water in their upper atmospheres.

Retrieved Temperature

For the three planets considered, the temperature retrieved is notably lower than the equilibrium temperature. In Figure 11, we present a plot analyzing the temperatures retrieved for other planets, particularly giving attention to the population paper we based our study on, Tsiaras et al. (2018). Indeed, retrieved temperatures are typically lower than the equilibrium ones, and we derived a best fit of this.

One of the key assumptions leading to this effect is that the equilibrium temperature is usually calculated for the planet dayside and considering a planetary albedo of zero. Considering Note. For WASP-79 b and WASP-62 b, the retrieved temperature is always significantly below the equilibrium temperature for the planet, particularly if FeH is not included as an opacity source. In all cases, a better fit is obtained by including FeH.

WASP-127 b

We used Exo-REM (Exoplanet Radiative-convective Equilibrium Model; Baudino et al. 2015;Charnay et al. 2018), a selfconsistent simulation software for brown dwarfs and giant exoplanets, to calculate the mean temperature profile and the expected abundances of WASP-127 b assuming a solar composition.

The model suggests significant abundances of H 2 O, CO, and Na; though, as stated previously, the WFC3 coverage means our data set is only sensitive to H 2 O.

From Figure 12, we can see that our retrieval is sensitive at pressures between »10 4 and 10 2 Pa. Figure 13 indicates that the retrieved abundances of WASP-127 b are compatible with a solar composition in this pressure range. The mean retrieved abundance of FeH is higher than expected values; however, the error spans three orders of magnitude, allowing for more physical solutions, as discussed at the beginning of this section.

As displayed in Figure 14, the retrieved temperature of WASP-127 b is compatible with the calculated mean temperature profile within our pressure sensitivity range. We can also see that the calculated temperature profile crosses the condensation curves of MnS and Cr between 10 4 and 10 3 Pa. We could therefore expect clouds composed of these species to form at these pressures. 58 is similar to the value retrieved here. Hence, our independent data reduction and analysis of the water content in the atmosphere of WASP-127 b is consistent with these studies. We do not attempt a joint retrieval with this data due to the potential incompatibility between the data sets from different instruments as highlighted in Yip et al. (2019). Given that the planet lies within the short-period Neptunian desert and has large atmospheric features, it will be an intriguing target for further characterization. In our retrievals without FeH as an opacity source, our solution is driven to low temperatures; Sotzen et al. (2020) encountered a similar predicament when attempting to fita chemical equilibrium model to the data. Here, by adding FeH as a retrieval parameter, our recovered temperature increases to While the temperature is still cooler than expected, we note the degeneracy with the 10 bar radius. Our analysis of purely the HST/WFC3 data also favors the presence of H 2 O and FeH. Na does not have features within the WFC3 spectral range, and we do not attempt the addition of other data for the aforementioned reasons.

WASP-62 b

WASP-62 b has demonstrably similar bulk characteristics to HD 209458b; both planets have roughly the same radius and effective temperature, although HD 209458b is ≈20% more massive than WASP-62 b (Bonomo et al. 2017). Given their similarities, we may expect them to exhibit a similar atmospheric chemistry and structure. HD 209458b has been extensively analyzed in the literature, with 3D simulations (Showman et al. 2009) and cloud analysis (Sing et al. 2016), making it ideal to interpret the results on WASP-62 b. We observe a cloud deck located at »2.5 10 Pa

3

. This cloud deck could be explained by the condensation of MgSiO 3 in the atmosphere, as was the case with HD 209458b (Sing et al. 2016).

Using the models of Showman et al. (2009) and Caldas et al. (2019), we may expect the temperature at the terminator to be close to ≈1350 K. This is somewhat hotter than the -+ 891 164 211 K retrieved in our standard setup (2.2σ). However, as seen in the posterior plot in Figure 9, there is a strong correlation between the temperature, the planet radius, and the cloud pressure; thus, the data remain consistent with the expected temperature.

Future Characterization

Upcoming ground and space-based telescopes such as the European Extremely Large Telescope (E-ELT; Brandl et al. 2018), the Thirty Meter Telescope (TMT; Skidmore et al. 2018), the Giant Magellan Telescope (GMT; [START_REF] Fanson | Proc. SPIE[END_REF], the JWST (Greene et al. 2016), Twinkle (Edwards et al. 2018), and Ariel (Tinetti et al. 2018) will characterize the atmospheres of a large population of exoplanets via transit and eclipse spectroscopy at visible and infrared wavelengths. These missions will move the exoplanet field from an era of detection into one of characterization, allowing for the identification of the molecular species present and their chemical profile, insights into the atmospheric temperature profile, and the detection and characterization of clouds (e.g., [START_REF] Rocchetto | [END_REF][START_REF] Rodler | Handbook of Exoplanets[END_REF]Changeat et al. 2019).

Ariel has been selected as ESA's M4 mission adoption candidate for launch in 2028 and is designed for the characterization of a large and diverse population of exoplanetary atmospheres to provide insights into planetary formation and evolution within our Galaxy. Ariel will provide simultaneous photometry and spectroscopy over 0.5-7.8 μm. Each of the planets studied here is an excellent target for atmospheric studies with Ariel (Edwards et al. 2019), and we use ArielRad (Mugnai et al. 2020) to simulate observations of this forthcoming mission. For each of the planets, we take the best-fit solution from the Hubble WFC3 analysis to model Ariel observations at the native resolution of its instruments. Figure 15 highlights the increased wavelength coverage and data quality that will be achieved with Ariel, allowing for a deeper understanding of each of these worlds. WASP-79 b is part of the JWST Early release Science program and will be observed by JWST with several different instruments (Bean et al. 2018). Here, we simulate JWST observations for these planets, assuming NIRISS GR700XD and NIRSpec G395H are used. Again, the increase in data quality is easily discernible and, although it is not a dedicated exoplanet mission, JWST promises to provide exquisite data for atmospheric characterization.

Conclusion

We have presented the analysis of data from Hubble's WFC3 G141 grism for three planets. By using the Iraclis pipeline and fitting the resultant spectra with TauREx, we have characterized the atmospheres of WASP-127 b, WASP-79 b, and WASP-62 b, recovering best-fit models that favor the presence of H 2 O and FeH in each case. This was performed during the ARES Summer School, using software and data publicly available to the community in order to allow for reproducible results.

The properties of WASP-127 b, particularly its extended atmosphere with clouds and large spectral features; the resultant high atmospheric detectability; and its unusually low density; make it an ideal target for further characterization with the next generation of facilities. Large spectral features were also detected in WASP-79 b and WASP-62 b, with clouds in the atmosphere of the latter.

None of the three planets studied have strong features in their spectra that can be linked to NH 3 ,C H 4 ,C O ,o rC O 2 .T h i si s expected, given that their spectroscopic lines do not have major bands in this wavelength range compared to the H 2 Oa n dF e H lines and higher quality data, with a broader spectral coverage, is required to improve constraints on the atmospheric chemistry. Nevertheless, studying the atmospheric composition of these planets has extended the catalog of hot Jupiters studied with WFC3 from those by Tsiaras et al. (2018). The ADI introduced therein has been utilized effectively in this paper to estimate the significance of these atmospheric observations. This was done in order to unify the statistical results between our study and that of further populations studies, which remain fundamental tools in understanding the nature and evolutionary history of planets. Chapter 5. Exoplanet atmospheric characterization where F T ot is the total flux, F Clear is the flux from regions without clouds, F Cloudy is the flux from regions with clouds and x is the fraction of surface area with clouds.

There has been an ambition to apply TauREx to directly imaged spectra; this is, however, ongoing work.

Conclusion

With this study, we increased the number of planets detected with water. When the paper was published, our water detection on WASP-127 b was the best water signal ever found. This is mainly due to the high puffiness of the planet, making the water vapor signal very obvious in the spectra. We attempted to detect FeH, which was the first detection effort of this molecule in a planet's atmosphere, as the ExoMol line list had become available shortly before we started the summer school (Tennyson et al., 2018;Tennyson et al., 2016). Our retrievals statistically favored the presence of FeH in the atmosphere of the three planets (over 3σ). We ran different retrievals for different scenarios and models, and found that clouds alone do not explain the feature seen in the spectra (cf Table 5 of the paper). Further observations of these planets and others to retrieve this FeH result are needed to conclude on the presence of this molecule. Soon after our study was published, another team tried to detect FeH in 12 other transiting giant planets, unsuccessfully [START_REF] Kesseli | A Search for FeH in Hot-Jupiter Atmospheres with High-dispersion Spectroscopy[END_REF], questioning our own detection, but the feature at 1.25 µm still needs to be explained. Furthermore, we studied the correlation between the retrieved temperature and the equilibrium temperature for our three planets and the 30 planets studied in Tsiaras et al., 2018. We observed a global trend that the retrieved temperature is lower than the calculated equilibrium temperature, and derived a best-fit for this trend. This can be indicative of 3D effects (Caldas et al., 2019;MacDonald et al., 2020;Changeat et al., 2020b), and points to the fact that the terminator region, which is the one probed with transit spectroscopy, naturally does not receive direct radiations from the star. Finally, we show in this paper that inflated hot jupiters do not necessarily destroy water in their upper atmosphere at the terminator region, which was a question of the field. I concluded this chapter with discussing the application of the TauREx retrieval code to direct imaging spectra.

Besides the results we obtained, the main outcome of this study is to understand the consequent limitations of studying exoplanets' atmosphere with such a narrow spectral range, such as what HST/WFC3 offers. Combining ground and space-based data has been proven to be tedious (Yip et al., 2019). Hence the need for the JWST and Ariel, offering a wider spectral range, which will be priceless in finally understanding exoplanets' atmospheres.

Chapter 6

Conclusion and perspectives

1 Conclusions ‹ My PhD thesis has been shaped towards a better understanding of exoplanetary systems, and their observations.

There have been three main chapters on different topics.

Instrumentation development with DrWHO: Chapter 3

First, I focused on instrumentation development for direct imaging of exoplanets. Direct imaging is a highly challenging method to study exoplanetary systems, and requires state-ofthe-art extreme adaptive optics (ExAO) instrumentation to correct for atmospheric distortions on the wavefront, as well as coronagraphy, to overcome the high star-to-planet contrast. Downstream of ExAO loop are optics, inducing what we call the "non-common path aberrations" (NCPA). These aberrations are the main limitation in exoplanet imaging, as they induce errors, "speckles", in the science images, that mimic exoplanet signal. They are particularly difficult to correct as the ExAO wavefront sensor (WFS) is blind to them. Furthermore, they evolve with time during on-sky observations. Using the focal plane for wavefront control is thus necessary. In the last decades, there have been several proposed solutions to correct NCPA. Most of these methods are invasive to the ExAO loop or are hardly compatible with on-sky observations. I developed the DrWHO algorithm, which aims at correcting NCPA during on-sky observations, while being transparent to the ExAO system. DrWHO is based on a fast focal plane camera as a wavefront sensor to finds a new reference for the AO loop WFS. To do so, DrWHO uses the diversity of the atmosphere to identify when "by chance" the NCPA in the focal plane are corrected. The algorithm then selects the corresponding WFS state as a new point of convergence of the ExAO loop -the reference, set by the WFS, changes. At each DrWHO iteration, the system is rewarded when the focal plane images are better, hence converging toward an aberration-free state. DrWHO does not make any linear assumption, hence it is compatible with non-linear WFSs such as the pyramid WFS. Furthermore, it is robust, flexible, and does not rely on any Chapter 6. Conclusion and perspectives model; hence it is compatible with other methods. The main downside of DrWHO is that it requires a fast focal plane camera close to the science instrument, something that most ExAO systems do not have.

I have tested DrWHO on simulation with the COMPASS simulation software, then on-sky, on the SCExAO instrument onboard the Subaru Telescope in Hawai'i. I have proven that DrWHO can measure and correct for the NCPA. I demonstrated PSF quality improvement onsky in visible light on the SCExAO system, and published these results in Skaf et al., 2022b. DrWHO has been used in support of science observations, in visible and non-coronagraphic mode, a couple of times, for a total of a few hours. There is a need to improve the infrared and coronagraphic modes before having DrWHO available for scientific observations. There is furthermore a need to understand how the algorithm can be optimized depending on the seeing conditions and the brightness of the target, which rely on the different settings of the algorithms, such as the DrWHO loop length, and the selection fraction of the best focal plane images.

Along with these optimizations, there are several ways to improve DrWHO, which were discussed in the chapter. The next main step for DrWHO is to use a photon-counting fast focal plane camera available on SCExAO, MEC [START_REF] Mazin | MKIDs for Direct Imaging of Exoplanets[END_REF][START_REF] Walter | The MKID exoplanet camera for Subaru SCExAO[END_REF], to correct speckles individually, by applying DrWHO on small zones of size 1λ/D. Doing so would allow us to detect on-sky when a speckle remains, in which case it would indicate the presence of an exoplanet.

DrWHO is a milestone as it is the first time that the focal plane is used in real-time to assist and optimize the AO correction. It is the very first step of using the focal plane at high speed, there is much more to be done as the technology is becoming available, with fast computers, low noise fast cameras, and machine learning algorithms. This first step consists on optmizing the reference of the loop using the focal plane. The next big step is to optimize not just the reference, but the control loop itself, with the response matrix, with reinforcement learning based on real-time PSFs.

β Pictoris with high-contrast imaging in the mid-infrared: Chapter 4

I worked on data analysis of the β Pictoris system in the mid-infrared (MIR), with the NEAR program. NEAR was a one-year-long program in 2019, aiming to do high-contrast imaging observations of the α Centauri system. NEAR was an upgrade of the VISIR instrument with a coronagraph and the use of VLT's UT4 secondary deformable mirror. It was the first MIR high-contrast instrument. The opportunity was taken to observe β Pic with NEAR. I studied the data resulting from these observations. There were several outcomes of this analysis. First, planet b was not detected. The corresponding flux upper limit provided meaningful constraints on its nature. Our MIR observations are sensitive to the thermal emission of dust grains. We used simplified hypotheses, mainly in terms of dust grain sizes and composition, to constrain the presence and distribution of dust around the planet. Our study is the first one to ever put such constraints around an exoplanet, 1. Conclusions ‹ at distances as close as the Roche radius. This analysis could be further developed on β Pic and other planets when more MIR data will become available. In fact, every giant planet in our solar system has rings, hence it is reasonable to expect that there must be rings around the young giant planets detected in direct imaging. Observations with JWST will provide the opportunity to better study disks around planets. In the same way that disks indicate the presence of planets, dust around planets is indirect proof of the presence of satellites.

Regarding the study of the β Pic disk, NEAR provided unique data. We detected several new clumps, along with the southwest clump (C1) previously observed at this wavelength. We studied the evolution of the position of C1 over a 16-year-long baseline with five data sets. We found that the clump is in Keplerian motion toward us. However, another study recently published conflicting results. Their analysis of the C1 position is based on a different method. This emphasizes the difficulty in accurately measuring the position of the clump, especially with data from different instruments and without high-contrast capabilities. There is a need to understand the origin of this discrepancy. The shape of C1's intensity from NEAR data provides a hint that the clump is not homogeneous, but with substructures within it. The radial flux distribution between the inner and outer parts of the clump indicates that the clump's shape evolves throughout time. This was to be expected given the considerable size of the clump, of about 10 AU. There has not been any study considering the distortion of the clump with time prior to ours. Studying the position evolution of C1 and confronting our results to another study emphasizes the need to do a dynamical study of this clump, and simulate its radial and azimuthal spread. These simulations could then be compared with observations. This requires further and frequent observations of the system. The JWST will provide unique data in the mid-infrared to better unveil the mysteries of the emblematic β Pictoris system. I started my PhD working on a project following a summer school, to analyze the atmospheres of three hot jupiters observed with the Hubble space telescope, with transit spectroscopy. These hot jupiters, WASP-127 b, WASP-79 b and WASP-62 b, present comparable characteristics, which is why we published their analysis together. The spotlight was put on WASP-127 b, particularly interesting as it is the puffiest planet detected, with a sub-Saturn mass and a super-Jupiter radius, located in the hot Neptune desert, also called photoevaporation desert. We studied these planets' spectra with the same baseline models for both the data reduction, and the spectra analysis with retrievals. We followed the method indicated in the population study of 30 hot jupiters, from Tsiaras et al., 2018. We detected statistically significant atmospheres on the three planets. We tested several retrievals models with different characteristics in order to test the statistics of our results. For all three planets, we detected water vapor at >5σ significance; we put an upper limit on the presence of carbon-based molecules. Furthermore, we attempted to detect a molecule that had not been observed in exoplanet atmospheres before: iron hydride (FeH). Our analysis statistically favors the presence of FeH; however, the spectral Chapter 6. Conclusion and perspectives feature could be coming from something else. The narrow spectral range is insufficient to confirm or rule out the presence of FeH in these planets. We did not attempt to detect the molecules TiO, VO, and YO, given their relatively low equilibrium temperatures. Furthermore, we found that the retrieved temperature is often lower than the theoretical one. This indicates 3D effects and provides material to better study the energy exchange within hot Jupiters' atmosphere, which is probed with transit spectroscopy.

Atmospheric characterization of WASP

This study emphasized the need for a wider wavelength coverage to study exoplanets' atmospheres. The James Webb and Ariel telescopes promise to provide exquisite data for atmospheric characterization.

Perspectives

Dare to dream, then decide to do " Annette White

Enabling deeper contrast at small angular separations

Using the focal plane with a fast camera provides new opportunities to push the speckle noise toward the photon noise limit. SCExAO and MagAO-X are the first ExAO systems to combine high frame rate focal plane imaging with wavefront sensing, opening new possibilities for speckle calibration, and a new era in high-contrast imaging. Indeed, the AO system can include real-time communication with the focal plane science camera, immediately informing how well the correction is performing. This allows for both real-time optimization of the control loop and calibration of residual starlight from WFS telemetry, potentially operating at the photon noise limit (cf Figure 3.2), yielding deeper contrast closer in where existing image processing techniques provide limited gain. Indeed, detector technology has progressed, now providing fast photon-counting camera options (like MKIDS).

Until now, AO systems correct optical aberrations (atmospheric turbulence + optics) as measured by the WFS, ideally delivering an aberration-free state. But the WFS is not accurate: the point of convergence of the AO loop does not exactly correspond to an image of optimal quality. This is why I developed the DrWHO algorithm, on the SCExAO instrument. Currently, DrWHO successfully sharpens images, but is slow and with limited efficiency as it considers the science image as a whole. The next step will be to divide the image into different zones of size 1λ{D (the resolution limit), to treat speckles individually, and take advantage of the ongoing coronagraph upgrades giving access to as close as 1λ{D. This promising upgrade will sharply reduce speckle noise, allowing us to detect directly, during the observations, which zone might host a planet, increasing our post-processing potential by reducing the photon noise, and achieving unparalleled contrast and inner working angle performances.

Perspectives

From instrumentation to answering astrophysical questions

Unveiling circumstellar disks and forming planets

Direct images of still-forming protoplanets embedded in circumstellar disks offer an unparalleled opportunity for understanding how planets form, in particular Jovian exoplanets. But imaging protoplanets still embedded in gas and dust-rich disks is a significant challenge, mainly in distinguishing between the protoplanet, scattered-light disk features and speckle noise (especially strong at smaller angular separation), requiring several methods of observations. Hα imaging provides a hint on protoplanet accretion [START_REF] Haffert | Two accreting protoplanets around the young star PDS 70[END_REF]. While promising, there is an active debate on whether or not Hα imaging is a sign of forming planet (Currie et al., 2022b;[START_REF] Huélamo | Searching for Hαemitting sources in the gaps of five transitional disks. SPHERE/ZIMPOL high-contrast imaging[END_REF]. This is complicated to answer because in a young system, the star also accretes and presents an Hα emission, that is challenging to untangle from the planet's. More work is needed to address these important questions. During my PhD, I led a successful proposal to observe with SCExAO protoplanetary disks in the NIR and Hα: LkCa 15 and PDS 201. Regarding LkCa 15, there have been claims of protoplanets that have been contested [START_REF] Sallum | Accreting protoplanets in the LkCa 15 transition disk[END_REF][START_REF] Currie | No Clear, Direct Evidence for Multiple Protoplanets Orbiting LkCa 15: LkCa 15 bcd are Likely Inner Disk Signals[END_REF]. New observations with new reduction methods (such as PACO and REXPACO, Flasseur et al., 2021), on both visible and NIR, would be priceless to shed light on the nature of the LkCa 15 system.

Atmospheric characterization of exoplanets

High-contrast imaging and spectral analysis of young giant planets are fundamental to deriving constraints on their atmospheric properties and eventually detecting traces of biosignatures. Furthermore, the chemical diagnostics of the gas giants near the ice line give us clues on their formation and migration history (Öberg et al., 2011). However, existing tools to analyze spectra require development to deal with the complexity of atmospheric physics and the low SNR of exoplanet spectra. I will help to provide better spectra (from the CHARIS and REACH instruments) and contribute to developing tools, such as the TauREx retrieval framework, to mature them for direct imaging, as mentioned in Section 3. Homogeneous population studies of exoplanet atmospheres, such as a recent transmission survey I contributed to [START_REF] Edwards | Exploring the Ability of HST WFC3 G141 to Uncover Trends in Populations of Exoplanet Atmospheres Through a Homogeneous Transmission Survey of 70 Gaseous Planets[END_REF], are key to determining formation pathways. In direct imaging, we have now enough detected planets to conduct a similar study. A possible perspective is to use DrWHO to produce higher SNR spectra. In such a study we would characterize a different population of planets from [START_REF] Edwards | Exploring the Ability of HST WFC3 G141 to Uncover Trends in Populations of Exoplanet Atmospheres Through a Homogeneous Transmission Survey of 70 Gaseous Planets[END_REF] comparing any trends found to those from the transmission data, we will provide new insights into the formation mechanisms of giant planets. In fact, hot jupiters are giant planets that migrated.

Additionally, this may contribute to the design of high-resolution spectroscopy instruments for the next generation of telescopes, guiding target selection by highlighting the successes, and limitations, of currently available datasets.

Personal note

It is not an easy exercise to find relevant words to conclude a PhD thesis. It requires a considerable step back to answer whether the objectives of the thesis have been met, what could have been improved and how. Overall, this PhD ended up being far different than initially expected, and in my opinion, far more exciting. The initial goal was to focus on instrumentation development. The papers on β Pictoris and the atmospheric characterization on the three hot jupiters were not initially planned. In fact, to me, instrumentation on its own takes even more meaning when there is an understanding of the astrophysics it serves. My academic journey until the PhD was equally focused on instrumentation and fundamental physics (cf my resume, in Appendix B). Hence, it seemed to me important to merge both dimensions to my work, instrumentation and astrophysics; this is why I embarked on a journey to analyze data of exoplanetary systems, along with my instrumentation work with DrWHO. Both projects on planet formation and atmospheric characterization seemed to me essential for understanding exoplanetary systems as a whole, especially as this is one of the main focus of direct imaging, which is the focus of my instrumentation work. I wanted to work towards a greater understanding of the connectedness of these different subfields, motivating my work for these three papers. It feels important to me to remind the reader that I have been very lucky in being able to collaborate with people, without whom none of these papers would have been accomplished. Of course, this came with a cost, and much can be shared on how things could have been better. Switching from one project to another has been challenging and not ideal in terms of time and energy management. There has been a lot of geographical movement, between the impact of Covid, the conferences, and the outreach mission in French Guiana. Furthermore, having two PhD supervisors added some difficulty and latency in my productivity. I spent two years of my PhD at the Subaru telescope, in the SCExAO team. A lot of effort has been put into dealing with the technical aspects of a real and complex instrument that is SCExAO. During my time there, I joined (almost) all the science and engineering observations, and contributed as support astronomer to run the RTC. This was extremely rewarding on many levels, among other things I have been added as co-author on several studies, but with a cost to the PhD, delaying some of my work. Along with my main PhD projects, I continued to be involved in studies regarding atmospheric characterization (cf my list of publications, in Appendix C).

To conclude, this PhD has been diverse on many levels, from the different projects I worked on, to the various teams I worked with, and the different work environments. I am grateful to all of those who made this (sometimes complicated) journey possible. , 1996. There are three main phases: Phase I: within the first million years, there is an important terrestrial mass coagulation; Phase II: the solid core will slowly accrete gas along its orbit; Phase III: the body will reach a critical mass, when the solid core and the gaseous envelope will equal each other, leading to a runaway gas accretion in the last million years of the lifetime of the disk.

Abbreviations list

AO

The solid line corresponds to the solid mass, the dotted line is the gaseous mass, and the dot-dashed line is the planet's total mass. . . . . . . . . . . . . . . . . . 1.14 Schematic view of the three formation theories of hot Jupiters: in situ formation (although this is highly unlikely), the gas-disk migration, and the high eccentricity followed by the tidal migration mechanism. Source: and the DM. The grey boxes are processes, linked together with streams, represented in blue boxes. The signaling between streams and processes is achieved through semaphores: a process "waits" to a semaphore, and will start as soon as the semaphore is "posted" to 1, at which point it will decrement the semaphore value back to zero.

INTRODUCTION

Adaptive Optics (AO) instrumentation has undergone extensive growth in sophistication and scientific capabilities over the last 30 years, enabling high-contrast imaging technologies, with extreme AO (ExAO) systems consisting of ≈2000-actuator DMs driven at over 1 kHz speeds. 1, 2 This has lead to key scientific breakthroughs, including the first direct image of a planet-mass companion 3 and the first imaged system of jovian exoplanets, HR8799. 4 Some of the current generation of ExAO systems, e.g. the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) at the Subaru Telescope 5 and MagAO-X on the Magellan Clay telescope 6 are pushing further achievable performancee.g. Strehl ratio (SR), contrast and sensitivity 7-11 -and serve as technology prototypes for ExAO instruments on 25-40 m extremely large telescopes. 12-15 The ExAO loop corrects wavefront aberrations measured by the WFS, ideally approaching an aberration-free image. However, the ExAO loop convergence point, defined by the WFS reference, may not correspond to the optimal image quality. Reasons for such a discrepancy include: that the adequate offset can be applied and maintained. Ideally, this offset should be updated in nearly real-time due to optical and mechanical variations in the instrument, however in practice it is typically updated on a daily or weekly basis. Finding the adequate offset requires focal plane images to update the reference, and can furthermore be particularly challenging if the WFS exhibits non-linear response that must be accounted for, as is the case in some high-performance WFSs such as the Pyramid WFS (PyWFS). 25-28 In this paper we will present the DrWHO algorithm, a model-free focal plane wavefront sensing approach which is aimed at finding the offset mentioned above to correct slow and static wavefront aberrations, including the NCPA, on a few seconds timescale. After stating the issues to be solved in Section 2, we describe the algorithm in Section 3. The application of the algorithm to non-coronagraphic PSF, with numerical simulations and on-sky tests, is presented in Section 4. Section 5 presents the main results of the on-sky validation for coronagraphic images. In Section 6, we review the characteristics of the algorithm and mention further implications for use in HCI.

PROBLEM STATEMENT: DEFINING A GOOD WFS REFERENCE

In a closed loop AO system, the WFS signal corresponds to the WFS measurement subtracted by the WFS reference, to isolate residual wavefront errors that must be corrected by the DM. This reference defines the convergence point of the AO control loop, which brings the WFS signal to where it gives a flat wavefront after the real-time controller performs a wavefront reconstruction. This WFS reference is usually measured with an internal light source, before on-sky observations. In reality, however, the ideal WFS reference is different from the internal source WFS reference due to optical illumination discrepancies. Furthermore, the WFS reference contains a dynamic part, constantly evolving due to quasi-static aberrations and wavefront chromaticity. The accurate calibration of the WFS, through the reference, is therefore a significant challenge for any AO system, on top of the fact that the static part cannot be accurately measured.

Therefore, a continuous way to measure the ideal reference is required for high accuracy wavefront correction.

Finding this ideal reference is especially critical to ExAO systems, where a slight deviation can introduce slow/static speckles that appear similar to a planet image.

ALGORITHM DESCRIPTION

Because the ideal reference changes continuously, the role of DrWHO is to update frequently, on seconds timescales, the actual reference, and ensure the AO loop converges towards a correction of NCPA. In the context of high contrast imaging, the algorithm does so by wisely selecting the WFS images corresponding to the best lucky imaging of coronagraphic or non-coronagraphic images, in terms of contrast or intensity for the former, and Strehl ratio or other metric for the latter. Hence, the WFS and coronagraphic images first need to be synchronized in time.

The algorithm proceeds as follows: on a defined timescale T DrWHO (of the order of tens of seconds for example), the algorithm first selects the best frames according to a score metric, and a predefined selection fraction P, in percent. Then, out of those P% frames, the corresponding WFS raw frames are extracted from the AO telemetry and averaged; the resulting WFS frame replaces the WFS actual reference, and the algorithm is iterated to continuously optimize the WFS reference. Hence, as DrWHO proceeds, the point of convergence of the AO loop includes NCPA and other aberrations of a timescale longer than T DrWHO , which are thus compensated for. The image quality then improves and presents less speckles features. In fact, the frequency of the aberrations that DrWHO can correct depends on the timescale of one iteration of the algorithm, which depends whether there is a coronagraph in place or not, and how good the seeing conditions are.

We present the procedure step by step of DrWHO with the description in Algorithm 1, and a schematic view of the algorithm is in Figure 2.

NON-CORONAGRAPHIC RESULTS

Most of those results have been extensively presented in 29, we present here a summary of those results.

Data:

• WFS frames • fast science camera frames Result: Update the reference of the WFS Initialization: take the reference of the WFS with the internal light source; while AO loop is running do Numerical simulations have been performed with the AO simulator COMPASS. 30 Compass is a versatile AO simulator, designed to meet the need of high performance for the simulation of AO systems, modeling several kinds of AO features, including several types of WFS, atmospheric simulations, DMs, telescopes, and RTCs. DrWHO was first implemented on the COMPASS software, to explore the algorithm feasibility and potential. Table 1 synthetizes the parameters used in the COMPASS simulations.

The simulation is idealized on several aspects. First, it does not take into consideration the telescope spiders. Second, there is no source of noise other than only the photon noise on both the WFS and the science detector (observing mR=7 with 50% efficiency). Furthermore, we considered a PyWFS with a higher sampling than on the SCExAO instrument (64 pixels over the PyWFS pupil diameter, versus 50 pixels), hence higher performance than achieved on-sky. The PyWFS is working in the visible at 750 nm, and the detector in the infrared at 1650 nm (cf Table 1). Because COMPASS does not simulate coronagraphic images, DrWHO was first tested on non-coronagraphic PSF, with the Strehl ration as quality criteria for the image selection.

Simulation results

We performed a test with 15 DrWHO iterations of 10 000 iteration each (corresponding to 5 seconds at 2kHz). The number of AO loop per DrWHO iteration was constrained by simulation time. NCPA were applied on the science path, thus not visible by the WFS. Those NCPA correspond to a linear combination of the first 12 Karhunen-Loève modes (which is the linear and orthogonal modal basis used for computing the response matrix), with a randomized amplitude, and a total amplitude of 30 nm RMS, which is slightly greater to what is expected in reality (approximately 20 nm RMS on SCExAO). DrWHO run were projected over the modal basis with which the response matrix was acquired. Figure 4 shows this modal decomposition along with the ideal NCPA correction, where the opposite of the NCPA was added, to better compare the correction. It appears from the top plot of this figure that, as we previously concluded, the algorithm converges from the first iteration towards a compensation of the NCPA. The average of all those references (minus the reference 0, which is the initial reference) is neighbouring the NCPA aberrations. This proves that DrWHO measured them, with the correct amplitude, and compensated for them. The middle and bottom plots of this figure prove that the algorithm does not diverge at the higher order modes, as confirmed by the increase of SR. The quadratic sum of 12 modes from the mean of all the references from the algorithm corresponds to 36 nm RMS, which is roughly consistent with the amplitude of the NCPA.

To conclude the simulation results, DrWHO on COMPASS improved the image quality in terms of SR, and the NCPA applied over the PSF, were almost totally corrected. Half of the correction has occurred at the first iteration of the algorithm.

Observation setup

DrWHO was tested on-sky on the engineering night of December 8 UT, 2020. 20 iterations of the algorithm were performed, each of 30 seconds. Each iteration entails synchronized data cubes resampled to a common 1 kHz frame rate for both VAMPIRES and PyWFS images, running at 500Hz and 2kHz respectively. 1200 modes were corrected. The observation conditions at that time were a seeing of 0.5", and a wind speed of 4 m/s. The observed target was the star ξ Leo, at an airmass of 1.03. The window size of the image for the selection of the quality criteria was of 70x70 pixels, corresponding to 0.43x0.43 arcsec field of view.

PSF quality evolution

The comparison of the PSFs before, after the fist iteration, and after the last iteration of the DrWHO run is shown in Figure 6. The evolution of the nFC over the 20 DrWHO iterations is shown in Figure 7. We plotted the evolution of the nFC for the 10% best PSFs that were selected by the algorithm for the new reference computation, as well as the nFC for the average of all the PSFs for each iterations. The difference of those nFC is shown in Figure 8. Furthermore, the Modulation Transfer Function (MTF) has been calculated for the PSFs before and after the DrWHO run, and is shown in Figure 9. The MTF of the ideal simulated PSF has been added to the figure. This figure shows as well that most of the correction is done at the first iteration.

Here are the points highlighted in 29:

• After 20 iterations, the PSF visually looks better and more circular, attesting a partial correction of the low orders;

• The major correction is applied at the first iteration, with the nFC jumping from 24.3% to 35%, comparably to simulations;

• The FC keeps increasing throughout the run, as shown by the best linear fit of the two curves, which is something that was not observed in simulations, where the evolution was smoother and reached a plateau ;

• Considering PSFs averaged over each iteration, nFC increases from 28%, to 35% at the first iteration, to then 40%: the overall improvement is 15.7% ;

• The best DrWHO images present a sharper increase than all the images together : Figure 8 presents the difference of these two nFC over the algorithm run. Despite selecting only the best 10% frames, DrWHO seems to be improving both the selected and unselected frames. We note that the algorithm has not fully converged yet and would have performed even better on a longer period of time ;

• Finally, Figures 7 and8 show that even if the PSFs are subject to the variations in seeing over a few minutes, they overall get better in terms of the concentration of flux. Hence, DrWHO corrects the NCPA even if they are not as dominant as the dynamical wavefront residuals from atmospheric turbulence.

WFS reference evolution

Figure 10 compares the WFS reference prior to the DrWHO run, Ref 0, which is simply the WFS mask showing which pixels are active (i.e. respond to DM pokes) in the WFS image, and the average of the last 3 WFS references applied by DrWHO, during the on-sky 10-minute run. The averaging minimises the noise contribution. The difference between the two references is also shown in Figure 10. This difference was then converted to wavefront mode coefficients by multiplication by the control matrix. Modal coefficients are shown in Figure 11 where the first three modes are tip, tilt, and focus and the following modes correspond to orthogonal modes, optimized for SCExAO's AO control law.

The total contribution of all modes is measured to be 116 nm RMS. However, as seen on Figure 11, the high order modes, corresponding to the higher spatial frequencies, seem to be noise more than actual correction, which will be further explored thereafter.

When calculating the total contribution of the modes by removing the modes beyond 900 (roughly where the modes amplitude starts increasing), we compute a correction of 70 nm RMS. Figure 12 (top) shows the first 20 wavefront mode values, excluding tip-tilt. Focus is the dominant contribution to the aberrations, with an amplitude of nearly 14 nm, while the other modes have values below 5 nm. We furthermore note There are numerous ways to improve the algorithm efficiency and convergence speed. For example, a possible extension is to parallelize DrWHO in terms of spatial frequencies. If there is a good understanding of the relationship between the input wavefront and the focal plane, as for example a Fourier relationship, DrWHO can optimize separate spatial frequencies independently.

CONCLUSION

The DrWHO algorithm has first been tested on non-coronagraphic images in the visible, by being initially implemented on an ExAO simulator, then on the SCExAO instrument and tested on-sky, at the Subaru Telescope. Secondly, DrWHO was validated on coronagraphic images in the IR.

Results presented here demonstrate its ability to measure and compensate for NCPA, considered to be a limiting factor in the detection and characterisation of exoplanets in high-contrast imaging observations. To quantify the quality of the PSF, we used the Strehl ratio for the simulations, and the Flux Concentration for the SCExAO run. For coronagraphic images, we used the total intensity of the image, which is correlated with the image contrast. For the simulation, we observed a nearly perfect compensation of the added NCPA, at the first iteration.

For the on-sky test, we combined the PyWFS measurements and the focal plane images in visible from the VAM-PIRES module for non-coronagraphic tests, and from the fast focal plane IR camera for coronagraphic tests. For noncoronagraphic tests, when DrWHO was running, the PSF significantly improved (15.7% relative improvement in flux concentration) over 20 iterations of 30 seconds, for a total of 10 minutes. The best PSF have a sharper increase over the run of the algorithm, reaching 48% of the simulated ideal PSF flux concentration. The visible improvement in the image quality was confirmed with the calculation of the MTF before and after the DrWHO run.

Regarding coronagraphic tests, the preliminary results in relatively bad seeing indicate that DrWHO does improve the image contrast, and the corrected modes are mainly the low orders. Further tests are ongoing to quantify the extent of the potential of the algorithm fully.

Overall, we show that DrWHO can improve the wavefront quality arriving on the science camera, and partially correct for the static and quasi-static NCPA, over a relatively short period of time of a few seconds. We show that the algorithm converges rapidly, with about half of the correction achieved by the first iteration. This has been observed in simulation and on-sky. Furthermore, the correction of the NCPA is effective even if it is considerably smaller than the dynamic of the atmosphere.

The characteristics of DrWHO are enumerated in section 6. The main strong points are the robustness of the algorithm, its independence from any model, making it compatible with other wavefront control methods, and that it does not rely on any linear assumption, thus particularly fit for a PyWFS. DrWHO combines focal plane wavefront sensing and the WFS.

A possible extension of DrWHO is to parallelize it in terms of spatial frequencies, which would allow to correct speckles individually and to observe fainter targets. This paper is the first proof of concept of the algorithm on coronagraphic images, following, 29 and presents some first results of its image quality and stability enhancement. DrWHO shows a wide potential of improvement, which will be presented in future work.

Image-based adaptive optics wavefront sensor referencing for high contrast imaging.

Nour Skaf a,b,c , Olivier Guyon b,d,e,f , Anthony Boccaletti a , Eric Gendron a , Vincent Deo b , Sébastien Vievard b,d , Julien Lozi b , Kyohoon Ahn b , and Thayne Currie b,g

INTRODUCTION

Adaptive Optics (AO) instrumentation has undergone extensive growth in sophistication and scientific capabilities over the last 30 years, enabling high-contrast imaging technologies, with extreme AO (ExAO) systems consisting of ≈2000-actuator DMs driven at over 1 kHz speeds. 1, 2 This has lead to key scientific breakthroughs, including the first direct image of a planet-mass companion, 3 the first imaged system of jovian exoplanets, HR8799, 4 and now ∼20 directly-imaged planets and protoplanets around nearby stars (e.g. 5-11 ).

Some of the current generation of ExAO systems, e.g. the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) at the Subaru Telescope 12 and MagAO-X on the Magellan Clay telescope 13 are pushing further achievable performance -e.g. Strehl ratio (SR), contrast and sensitivity 14-18 -and serve as technology prototypes for ExAO instruments on 25-40 m extremely large telescopes. 19-22 The ExAO loop corrects wavefront aberrations measured by the WFS, ideally approaching an aberration-free image. However, the ExAO loop convergence point, defined by the WFS reference, may not correspond to the optimal image quality. Reasons for such a discrepancy include:

The most reliable approach to measure and correct optical misalignments is to use focal plane images. 26 In the particular case of NCPA, these images are ideally generated by the science detector. Several solutions have been suggested for static NCPA, 25, 27-31 the quasi static part being particularly challenging to measure and correct. The evolutionary timescale of the aberrations with respect to the frequency of the correction is a main difficulty.

In a closed loop AO system, NCPA are usually compensated by subtracting a biasing reference signal in the WFS reference corresponding to the aberration to correct. Doing so requires good WFS response knowledge and stability, so that the adequate offset can be applied and maintained. Ideally, this offset should be updated in nearly real-time due to optical and mechanical variations in the instrument, however in practice it is typically updated on a daily or weekly basis. Finding the adequate offset requires focal plane images to update the reference, and can furthermore be particularly challenging if the WFS exhibits non-linear response that must be accounted for, as is the case in some high-performance WFSs such as the Pyramid WFS (PyWFS). 32-35 In this paper we will reintroduce the basis of the DrWHO algorithm 36 , 37 a model-free focal plane wavefront sensing approach which is aimed at finding the offset mentioned above to correct slow and static wavefront aberrations, including the NCPA, on a few seconds timescale. After stating the issues to be solved in Section 2, we describe the algorithm in Section 3. We will then present an upgrade of the DrWHO algorithm in Section 4. We will here focus on the concept, and will present results of the upgrade in a future study.

PROBLEM STATEMENT: DEFINING A GOOD WFS REFERENCE

In a closed loop AO system, the WFS signal corresponds to the WFS measurement subtracted by the WFS reference, to isolate residual wavefront errors that must be corrected by the DM. This reference defines the convergence point of the AO control loop, which brings the WFS signal to where it gives a flat wavefront after the real-time controller performs a wavefront reconstruction. This WFS reference is usually measured with an internal light source, before on-sky observations. In reality, however, the ideal WFS reference is different from the internal source WFS reference due to optical illumination discrepancies. Furthermore, the WFS reference contains a dynamic part, constantly evolving due to quasi-static aberrations and wavefront chromaticity. The accurate calibration of the WFS, through the reference, is therefore a significant challenge for any AO system, on top of the fact that the static part cannot be accurately measured.

Therefore, a continuous way to measure the ideal reference is required for high accuracy wavefront correction.

Finding this ideal reference is especially critical to ExAO systems, where a slight deviation can introduce slow/static speckles that appear similar to a planet image.

ALGORITHM DESCRIPTION

Because the ideal reference changes continuously, the role of DrWHO is to update frequently, on seconds timescales, the actual reference, and ensure the AO loop converges towards a correction of NCPA. In the context of high contrast imaging, the algorithm does so by wisely selecting the WFS images corresponding to the best lucky imaging of coronagraphic or non-coronagraphic images, in terms of contrast or intensity for the former, and Strehl ratio or other metric for the latter. Hence, the WFS and coronagraphic images first need to be synchronized in time.

The algorithm proceeds as follows: on a defined timescale T DrW HO (of the order of tens of seconds for example), the algorithm first selects the best frames according to a score metric, and a predefined selection fraction P , in percent. Then, out of those P % frames, the corresponding WFS raw frames are extracted from the AO telemetry and averaged; the resulting WFS frame replaces the WFS actual reference, and the algorithm is iterated to continuously optimize the WFS reference. Hence, as DrWHO proceeds, the point of convergence of the AO loop includes NCPA and other aberrations of a timescale longer than T DrW HO , which are thus compensated for. The image quality then improves and presents less speckles features. In fact, the frequency of the aberrations that DrWHO can correct depends on concentric circles, and second a separation in smaller zones (of ≈ 1λ/D). In both cases, there are two approaches that can be explore: (1) the use of FT to link focal plane position to WFS modes, or (2) use the response matrix, which we have, to explicitly identify the WFS response to sine waves on the DM.

Zonal DrWHO with concentric circles

Given the physical relationship between focal plane and pupil plane, the first optimisation for the upgrade of DrWHO is to take advantage of the difference in spatial frequencies in the PSF: the inner part is mainly composed of low orders, while the outer part is mainly higher orders. A possibility is to separate the PSF in different concentric circular zones, each zone being the starting point for an independent DrWHO optimization loop, leading to as many loops as there are zones.

As we optimize each zone separately and then we modify, for each zone, the corresponding spatial frequencies in the WFS reference. There is then a greater dimension of the number of DrWHO sub loops we could have, and we would find a way to take advantage of the high dimensionality of the problem, break things in multiple dimensions, and more specifically, the optimization is parallelized. This allows to understand the relationship between the focal plane and the pupil plane, in terms of modal decomposition. Each image of the WFS can then be decomposed in a sum of several images of low and high frequencies, each corresponding to their respective concentric circle in the focal plane. The Fourier Transform (FT) of the image of the pyramid will then allow to acquire the Fourier modes of low orders and high orders. This can be decomposed in several Fourier transform (for each concentric circular zone), and the inverse Fourier transform then gives several images of the pyramid WFS (one for each concentric circle), that when summed up gives the WFS image. This could be achieved without even going in the modal space, and remaining in the spatial frequency space with the Fourier decomposition.

Zonal DrWHO for individual speckle treatment

The focal plane images can be separated in several different zones, ideally of size ≈ 1λ/D. For each of those zones, we apply the chosen quality criteria (the flux, for example). As the DrWHO loop is running one iteration, for each zone of each image of the focal plane, we take the best 10%.

Similarly to the previous section, the relationship between the focal plane and the WFS images can be established through Fourier transforms. In fact, a sine wave in the pupil plane corresponds to a pair of speckle in the focal plane. When computing the Fourier transform of the WFS images, we can find which frequencies are linked with which zones. Hence, looking at a specific selected zone in the PSF, we can find the corresponding frequencies in the Fourier space of the WFS images. Those frequencies, for each best 10% selected zone for each image, are then summed up, yielding to a new combination of frequencies. An inverse Fourier transform is performed on this combination of frequencies, leading to a new WFS image, that is set as new reference to the WFS, thus changing the point of convergence of the AO loop. This new reference includes the frequencies of the atmospheric turbulence that randomly and luckily corrected quasi static speckles for each zone. We note that the center must be dealt differently. The criteria for that zone won't be the minimization of the flux, but rather the maximization of the Strehl in the case of a non-coronagraphic PSF.

The figure 3 shows a schematic view of the idea. This work is on-going and results will be shown in a future study.

CONCLUSION

Below are some noticeable characteristics of the DrWHO algorithm:

1. DrWHO is robust, for both non-coronagraphic and coronagraphic use: the algorithm slowly but surely converges towards a better compensation of static and slow aberrations. As it is based on lucky imaging, it relies on some realisations of residual atmospheric turbulence to reduce wavefront aberrations. DrWHO contributes to getting closer to an absolute sensor, driving the WFS reference to optimize images in the focal plane.

Figure 1 -

 1 Figure 1 -NASA 2019 Earth Day poster.

8 .

 8 As worded by NASA administrator Bill Nelson on Dec. 2022

Figure 3 .

 3 Figure3.2 illustrates the problem quantitatively in terms of contrasts, with the example of the star ǫ Eridani, as if it were observed with SCExAO. The habitable zone (HZ) is at 0.2", and an Earth-like planet would have a contrast of about " 10 ´9in reflected light.Currently, the best raw contrast with SCExAO at this angular separation is 10 ´4, and after post-processing, the contrast can get down to 10 ´6 with conventional speckle calibration techniques. However, the goal is to reach the photon noise limit, which is the fundamental limit. The current fundamental photon noise limit without using the focal plane is 2.35 ˆ10 ´9 (1-σ), for one hour of exposure time at 30% efficiency. As mentioned above, the goal is to use use the focal plane as WFS to bring down this limit, and if so, the raw contrast would become 10 ´5, and the photon noise limit becomes 7 ˆ10 ´10 (1-σ). There is hence great interest in using the focal plane, with the potential of improving the contrast limit by " 400 times.Hence, by improving AO performances and operate at the photon noise limit, planets in HZ could almost be within reach on the best stars with an 8-meter telescope such as Subaru. Realistically, this is not really achievable, it however illustrates the potential gain of >2 order of magnitude with instrumentation development. Some of it is achieved by improving the raw contrast (from 10 ´4 to 10 ´5) and some of it achieved by calibration of residual speckles which allows us to operate at the photon noise limit. My PhD work is mostly about the first part, but provides encouraging evidence for the second part as well, proving that we are able to accurately derive the speckle field from WFS telemetry.

  Figure 3.4 shows three main blocks: the AO loop, the telemetry, and where DrWHO operates. DrWHO only impacts the AO loop by updating the reference after using telemetry data. Data: -WFS frames -fast focal plane frames Result: Update the reference of the WFS Initialization: take the reference of the WFS with the internal light source; while AO loop is running do -acquire WFS and fast science focal plane images; -synchronize data cubes; while DrWHO iteration (30 s) is running do -select the 10% best science data; -select the corresponding WFS images; -average selected WFS images; -the resulting WFS frame replaces the WFS reference; -WFS reference updated. end -restart DrWHO iteration Change of AO point of convergence; end Algorithm 1: DrWHO algorithm

6 .

 6 Cameras in SCExAO are named after Hawaiian birds.

Fig. 1 .

 1 Fig. 1. Schematic view an AO system, presenting the problem of NCPAs, especially in the case of exoplanet imaging with a coronagraphic image.

  coronagraphic mode, however further tests are necessary to quantify this.

Figure 4 . 5 -

 45 Figure 4.5β Pictoris images, observed with NEAR. Top: directly stacked images. Bottom: PCA reduction. The images have been rotated by 30 degrees.

Figure 4 .

 4 Figure 4.10 presents the resulting surface brightness profile of the image in Figure 4.5, with the labels of the clumps.

Figure 4 .

 4 11 presents the relative brightness intensity of the C1 clump for the five data sets (Figure11of the paper).

  , the difference lies in how the mass: it is as if M becomes (2/1) 2 ˆM and (3/2) 2 ˆM respectively. Of course, the stellar mass remains the same.

  A vortex: correlations with the CO map from Matrà et al., 2017 (Figure 14 of the paper) and calculations from Kral et al., 2016 could indicate that the clump is a gas vortex. NB: During the review process of this paper, a recent study led by Han et al., 2022 was published. They looked at the temporal evolution of the clump C1, based on three MIR data sets from 2003, 2010

  and absorption compatible with an iron hydride abundance of log(FeH)=--+

  Several molecular opacities have been tested to model the spectra of the observations; in this publication, we considered five trace gases: H 2 O (Polyansky et al. 2018),CH 4 (Yurchenko & Tennyson 2014),C O(Li et al. 2015),C O 2

Figure 1 .

 1 Figure 1. Results of the white-light curve of WASP-127 b. Top: raw light curve, after normalization. Second: light curve, divided by the best-fit model for the systematics. Third: residuals. Bottom: autocorrelation function of the residuals.

Figure 2 .

 2 Figure 2. Spectral light curves fitted with Iraclis for the transmission spectra where, for clarity, an offset has been applied. Left: the detrended spectral light curves with best-fit model plotted. Right: residuals from the fitting with values for the Chi-squared (c 2 ), the standard deviation of the residuals with respect to the photon noise (s), and the autocorrelation (AC). Similar plots for WASP-79 b and WASP-62 b are shown in Figures 3 and 4. The mean s for each of the three planets is between 1.02 and 1.25 times the photon noise.

  Figure 2. Spectral light curves fitted with Iraclis for the transmission spectra where, for clarity, an offset has been applied. Left: the detrended spectral light curves with best-fit model plotted. Right: residuals from the fitting with values for the Chi-squared (c 2 ), the standard deviation of the residuals with respect to the photon noise (s), and the autocorrelation (AC). Similar plots for WASP-79 b and WASP-62 b are shown in Figures 3 and 4. The mean s for each of the three planets is between 1.02 and 1.25 times the photon noise.

Figure 3 .

 3 Figure 3. Top figure: results of the white-light curve of WASP-79 b. Top: raw light curve, after normalization. Second: light curve, divided by the best-fit model for the systematics. Third: residuals. Bottom: autocorrelation function of the residuals. Bottom figure: spectral light curves fitted withIraclisfor the transmission spectra where, for clarity, an offset has been applied. Left: the detrended spectral light curves with best-fit model plotted. Right: residuals from the fitting with values for the Chi-squared (c 2 ), the standard deviation of the residuals with respect to the photon noise (s), and the autocorrelation (AC).

Figure 4 .

 4 Figure 4. Top figure: results of the white-light curve of WASP-62 b. Top: raw light curve, after normalization. Second: light curve, divided by the best-fit model for the systematics. Third: residuals. Bottom: autocorrelation function of the residuals. Bottom figure: spectral light curves fitted withIraclisfor the transmission spectra where, for clarity, an offset has been applied. Left: the detrended spectral light curves with best-fit model plotted. Right: residuals from the fitting with values for the Chi-squared (c 2 ), the standard deviation of the residuals with respect to the photon noise (s), and the autocorrelation (AC).

Figure 5 .

 5 Figure 5. WFC3 spectral data and best-fit models, with 1σ-3σ uncertainties, for the three planets: from top to bottom, WASP-127 b, WASP-79 b, and WASP-62 b.

Figure 6 .

 6 Figure 6. WFC3 spectral data and the contributions of active trace gases and clouds from the best-fit model for each planet. Top: WASP-127 b. Middle: WASP-79 b. Bottom: WASP-62b. In each case, the black line denotes the best-fitm o d e l .

Figure 7 .

 7 Figure 7. Posterior distributions from our WASP-127 b retrieval. The corresponding posteriors for WASP-79 b and WASP-62 b are in the appendix (Figures 8 and 9).

Figure 8 .

 8 Figure 8. Posterior distributions for WASP-79 b.

Figure 9 .

 9 Figure 9. Posterior distributions for WASP-62 b.

Figure 10 .

 10 Figure 10. Observed minus calculated (O -C) transit midtimes for WASP-127 b (top), WASP-79 b (middle), and WASP-62 b (bottom). Transit midtime measurements from this work are shown in gold (HST) and blue (TESS), while literature T 0 values are in red. The black line denotes the new ephemeris of this work, with the dashed lines showing the associated 1σ uncertainties and the black data point indicating the updated T 0 . For comparison, the previous literature ephemeris and their 1σ uncertainties are given in red. In all cases, our results are compatible with the literature but provide a further refinement of the ephemeris.

Figure 11 .

 11 Figure 11. Correlation between the retrieved temperature and the equilibrium temperature for the planets studied in Tsiaras et al. (2018).W eo b s e r v eag l o b a l trend wherein the retrieved temperature is lower than the calculated equilibrium temperature and derived a best fit for this trend. WASP-127 b, WASP-79 b, and WASP-62 b have been added; we can see that they follow this trend as well.

  Low-and high-resolution spectra of WASP-127 b have been collected with ground-based instruments. Palle et al. (2017) obtained low-resolution spectroscopy with the Andalucia Faint Object Spectrograph and Camera (ALFOSC) spectrograph m o u n t e do nt h eN o r d i cOptical Telescope (NOT),c o v e r i n gt h e spectral range 0.45-0.85 μm. A slope was detected in the optical wavelength spectrum, interpreted as Rayleigh scattering and potentially Na. They also attribute the trend to TiO/VO with low significance. Chen et al. (2018) observed with the OSIRIS spectrograph, mounted on the Gran Telescopio Canarias (GTC) telescope, covering the range 0.4-1.0 μm. They presented detection of alkali metals (Na, K and Li) and hints of clouds and water with a retrieved abundance of log(H 2 O)=-2with the HST STIS and WFC3, combined with Spitzer data from IRAC 1 and 2, also concluded that water was present in the atmosphere. Spake et al. (2020) used a Markov Chain Monte Carlo model to fit the data, resulting in a best-fit solution detecting H 2 O, CO 2 , Na, and K; their water abundance of log(

Figure 13 .

 13 Figure 13. Expected abundances of WASP-127 b generated by Exo-REM, assuming chemical nonequilibrium for C-, N-, and O-bearing species; an eddy diffusion coefficient of 10 8 cm 2 s -1 ; and a metallicity of three times solar (Lodders 2019). We have included TiO and VO to the Exo-REM run but found their predicted abundances to be negligible (<10-14 ).

Figure 14 .

 14 Figure 14. Mean temperature profile of WASP-127 b, assuming radiative transfer equilibrium, generated by Exo-REM. The condensation profiles of various species are represented as dotted lines.

Figure 12 .

 12 Figure 12. Typical contribution function of our retrievals. We can see the effect of the H 2 O lines. The rise in sensitivity at ≈10 4 Pa is due to the opaque cloud.

4. 3 .

 3 WASP-79 b Sotzen et al. (2020) utilized the same WFC3 data set, along with observations from ground-based facilities, TESS, and Spitzer, to study the atmosphere of WASP-79 b. Their retrieval results indicates the presence of H 2 O, Na, and FeH. Our retrieved water abundance is consistent with that from Sotzen et al. (2020): (-2.20<log(H 2 O)<-1.55).

Figure 15 .

 15 Figure 15. Simulated Ariel and JWST observations of the best-fit solutions retrieved in this work. For Ariel, WASP-127 b is for a single observation, while WASP-79 b and WASP-62 b have three stacked transits each. The transit depths have been offset to show the difference in the size of the atmospheric features between the planets. We note that, according to the work of Edwards et al. (2019), WASP-79 b and WASP-62 b may be more suited for study with Ariel via emission spectroscopy. JWST simulations have been performed using ExoWebb (B. Edwards et al. 2020, in preparation) for a single transit with NIRISS GR700XD as well as an observation with NIRSpec G395H.

  Figure inspired by Figure 1 in Guyon et al., 2020. . . . . . . 3.11 Figure 2 in Guyon et al., 2018. A detailed description of the CACAO architecture. The small grey boxes are data streams. There are three primary paths: 1-the zonal reconstruction, going straight from the WFS measurements to the DM through the control matrix; 2-the modal reconstruction, converting WFS measurements into mode coefficients, to then apply to the DM; 3-the open loop, where WFS measurements are converted in mode coefficients, for predictive control to be computed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.12 Schematic view of the script's structure and connectedness. . . . . . . . . . . . .

•

  acquire WFS and fast science focal plane coronagraphic images; • synchronize data cubes; while DrWHO iteration (T DrWHO (seconds)) is running do select the P% best coronagraphic science data; -select the corresponding WFS images; -average selected WFS images; -the resulting WFS frame replaces the WFS reference; -WFS reference updated. end • restart DrWHO iteration Change of AO point of convergence;

Table 2 .

 2

			Spectro type	λ, R	Features	Coronagraph
	CHARIS	2.07"x2.07"	Integral field spectrograph	1154-2387nm R = 20 to 90	Simultaneous Direct images & spectra	Lyot, vAPP, Vortex
					H α
	VAMPIRES 3"x3"	H α Continuum	600-850 nm	Polarimetric differential	Lyot
					imager
	FIRST	139 mas	Single mode fiber spectro	600-800 nm R " 400	High angular resolution H α
	REACH	"40mas	Fiber fed	0.97-1.75um R "100,000	High spectral resolution	Lyot
			Determine by		Ultra fast
	MEC	1.5"x1.5"	pixel sensitivity	Y and J bands	photon
			to photons		counting

2 -SCExAO's science instruments brief characteristics

Table 3 .

 3

	4. DrWHO on SCExAO

1 -Input parameters of the DrWHO algorithm. They are set in the bash script runDrWHO, and are called by other scripts.

Table 1 .

 1 ExAO numerical simulations parameters.

	Numerical simulation configuration
	Telescope	D = 8. m diameter No support spiders Central obstruction = 0.12
	Turbulence layer	von Kármán, ground layer only r 0 = 0.16 at 500 nm L 0 = 20 m (to simulate post-woofer residuals)
		||u|| = 10 m s -1
	PyWFS Subapertures Wavelength Guide star magnitude 7 64 × 64 Monochromatic, 750 nm
	Modulation Photon noise only	Circular, 3 λ D radius, 24 points
	Deformable mirror	48 actuators across the diameter
	Focal Plane Camera Wavelength Photon noise only	Monochromatic, 1.65 µm
	RTC controller Loop rate Method Basis Loop gain Controlled modes Modes filtered	2 kHz Linear modal integrator DM Karhunen-Loève (KL) basis (a) 0.3 1505 300

References.

(a)

Ferreira et al. (2018)

.

Table 1 .

 1 Summary of the data used and the observing modes with different instruments. The last line presents the evolution of the C1 position over the years, considering a stellar distance of 19.63 pc.

		2003-12-30	2004-08-30 2010-12-16	2015-09-01 2019-12-15
	Instrument	T-ReCS	VISIR	T-ReCS	VISIR	NEAR
	Telescope	Gemini	VLT UT3	Gemini	VLT UT3	VLT UT4
	Filter	12.3 µm	11.7 µm	10 µm	11.7 µm	11.25 µm
	AO+Coronagraph No	No	No	No	Yes
	Reference	Telesco et al. (2005) This study	Li et al. (2012) This study	This study
	C1 pos (au)	52.9 +0.5 -0.5	52.7 +0.6 -0.6	55 +0.5 -0.5	55.5 +0.4 -0.4	56.1 +0.3 -0.3

Table 1

 1

	Target Parameters

Table 3 Table of Fitted

 3of Parameters for the Retrievals Performed on Our Targets

	Retrieved Parameters	Bounds	WASP-127 b	WASP-79 b	WASP-62 b
	( log H O ) 2 () log FeH	1e-12-1e-1 1e-12-1e-1	--5.25 1.10 -+ 2.71 1.05 0.78 -+ 0.88	--	-+ 2.43 0.76 0.57 -+ 4.42 1.18 0.91	--	-+ 0.52 2.03 1.27 -+ 3.04 2.27 2.18

Table 4

 4 WFC3 Transit Depths and Errors (in ppm) for WASP-127 b, WASP-79 b, and WASP-62 b

	Wavelength	WASP-127 b	WASP-79 b	WASP-62 b
	1.12625	9800±53	11420±74	12012±56
	1.14775	10030±48	11477±59	11993±51
	1.16860	10026±72	11371±71	11890±61
	1.18880	10070±50	11362±71	11983±65
	1.20835	9967±53	11372±61	11909±61
	1.22750	9936±61	11350±70	11909±58
	1.24645	9990±54	11398±72	12036±64
	1.26550	9938±53	11248±64	11913±64
	1.28475	10050±49	11325±76	12024±65
	1.30380	10068±52	11434±73	11999±56
	1.32260	10123±46	11292±58	11820±54
	1.34145	10318±53	11600±72	12151±61
	1.36050	10500±70	11417±74	11964±52
	1.38005	10513±65	11448±59	12120±53
	1.40000	10417±53	11548±72	12065±62
	1.42015	10415±50	11664±71	12082±54
	1.44060	10485±59	11457±56	12019±49
	1.46150	10408±54	11384±73	12102±71
	1.48310	10305±51	11375±75	11901±62
	1.50530	10246±61	11476±78	11901±59
	1.52800	9989±60	11383±89	11907±61
	1.55155	9990±55	11283±58	11837±68
	1.57625	9816±56	11245±61	11907±65
	1.60210	9781±58	11245±87	11796±63
	1.62945	9665±65	11053±80	11734±58

Table 5

 5 Comparison of the Bayesian Log Evidence for Different Models WASP-127 b (No Molecules Log Evidence: 1.73-Model (1)) H 2 O, CH 4 , CO, CO 2 , NH3, FeH, clouds 192.31 3.80 w.r.t. (3) 891 † Lam et al. (2017) ‡ Brown et al. (2017)

	Setup	Log Evidence	Sigma	Retrieved Temperature [K]	Equilibrium Temperature [K]
	(2) H 2 O, clouds (3) H 2 O, CH 4 , CO, CO 2 , NH3, clouds	161.87 161.27	>7 w.r.t. (1) <1 w.r.t. (2)	1027 1005	1400 †
	(4) H 2 O, FeH, clouds	170.20	4.48 w.r.t. (2)	1305
	(5) H 2 O, CH 4 , CO, CO 2 , NH3, FeH, clouds	169.65	4.49 w.r.t. (3)	1304
		WASP-79 b (No Molecules Log Evidence: 173.33-Model (1))
	Setup	Log Evidence	Sigma	Retrieved Temperature [K]	Equilibrium Temperature [K]
	(2) H 2 O, clouds (3) H 2 O, CH 4 , CO, CO 2 , NH3, clouds	187.77 187.88	5.72 w.r.t. (1) <1 w.r.t. (2)	627 618	1716 ‡
	(4) H 2 O, FeH, clouds	191.16	3.09 w.r.t. (2)	948
	(5) H 2 O, CH 4 , CO, CO 2 , NH3, FeH, clouds	190.73	2.89 w.r.t. (3)	996
		WASP-62 b (No Molecules Log Evidence: 176.35-Model (1))
	Setup	Log Evidence	Sigma	Retrieved Temperature [K]	Equilibrium Temperature [K]
	(2) H 2 O,clouds (3) H 2 O, CH 4 , CO, CO 2 , NH3, clouds	187.22 186.66	5.03 w.r.t. (1) <1 w.r.t. (2)	618 566	1475 ‡
	(4) H 2 O, FeH, clouds	192.59	3.72 w.r.t. (2)	890
	(5)

Table 6

 6 Transit Midtimes Used to Refine the Ephemeris of Planets from This Study

	Planet	Epoch	Midtime [BJD TDB ]	References
	WASP-127 b -103	2457808.60283±0.00031	Palle et al. (2017)
	WASP-127 b	-5	2458218.053097±0.000101	This Work *
	WASP-127 b	74	2458548.11973±0.000469	This Work
	WASP-127 b	75	2458552.297636±0.000428	This Work
	WASP-127 b	77	2458560.65431±0.000435	This Work
	WASP-127 b	78	2458564.83219±0.000431	This Work
	WASP-79 b	-531	2456215.4556±0.0005	Brown et al. (2017)
	WASP-79 b	-94	2457815.92207±0.000117	This Work *
	WASP-79 b	69	2458412.892172±0.000299	This Work
	WASP-79 b	70	2458416.554571±0.000311	This Work
	WASP-79 b	73	2458427.541703±0.000332	This Work
	WASP-79 b	74	2458431.204093±0.000347	This Work
	WASP-79 b	75	2458434.866496±0.000321	This Work
	WASP-79 b	76	2458438.528882±0.00029	This Work
	WASP-79 b	77	2458442.191242±0.000292	This Work
	WASP-79 b	78	2458445.853639±0.000326	This Work
	WASP-79 b	79	2458449.515994±0.000314	This Work
	WASP-79 b	80	2458453.178366±0.000317	This Work
	WASP-79 b	81	2458456.840324±0.000363	This Work
	WASP-79 b	82	2458460.503155±0.000335	This Work
	WASP-62 b	-614	2455767.1533±0.0005	Brown et al. (2017)
	WASP-62 b	-140	2457858.41397±0.000266	This Work *
	WASP-62 b	-34	2458326.078168±0.000293	This Work
	WASP-62 b	-33	2458330.490547±0.000294	This Work
	WASP-62 b	-32	2458334.902385±0.000315	This Work
	WASP-62 b	-30	2458343.725961±0.00025	This Work
	WASP-62 b	-28	2458352.550282±0.000278	This Work
	WASP-62 b	-27	2458356.961811±0.000257	This Work
	WASP-62 b	-26	2458361.374157±0.000268	This Work
	WASP-62 b	-25	2458365.786076±0.000295	This Work
	WASP-62 b	-24	2458370.197678±0.000244	This Work
	WASP-62 b	-23	2458374.610308±0.000284	This Work
	WASP-62 b	-22	2458379.021593±0.00025	This Work
	WASP-62 b	-20	2458387.845506±0.000238	This Work
	WASP-62 b	-19	2458392.257448±0.000258	This Work
	WASP-62 b	-17	2458401.081679±0.000286	This Work
	WASP-62 b	-16	2458405.493547±0.000294	This Work
	WASP-62 b	-14	2458414.317213±0.000241	This Work
	WASP-62 b	-12	2458423.141634±0.000372	This Work
	WASP-62 b	-11	2458427.55355±0.0003	This Work
	WASP-62 b	-10	2458431.96504±0.000233	This Work
	WASP-62 b	-9	2458436.376957±0.000258	This Work
	WASP-62 b	-1	2458471.672875±0.000281	This Work
	WASP-62 b	-0	2458476.084548±0.000273	This Work
	WASP-62 b	1	2458480.496509±0.000269	This Work
	WASP-62 b	2	2458484.90846±0.000263	This Work
	WASP-62 b	3	2458489.320399±0.000275	This Work
	WASP-62 b	4	2458493.732346±0.000274	This Work
	WASP-62 b	5	2458498.144285±0.000271	This Work
	WASP-62 b	6	2458502.556272±0.000263	This Work
	WASP-62 b	7	2458506.968201±0.000308	This Work
	WASP-62 b	8	2458511.380161±0.000259	This Work

* Data from HST

Table 7

 7 Continuation of Table 6

	Planet	Epoch	Midtime [BJD TDB ]	References
	WASP-62 b	9	2458515.793014±0.000308	This Work
	WASP-62 b	10	2458520.203407±0.00031	This Work
	WASP-62 b	11	2458524.616007±0.000263	This Work
	WASP-62 b	14	2458537.851688±0.000269	This Work
	WASP-62 b	16	2458546.675279±0.000324	This Work
	WASP-62 b	17	2458551.087738±0.000337	This Work
	WASP-62 b	19	2458559.91167±0.000278	This Work
	WASP-62 b	20	2458564.323603±0.000285	This Work
	WASP-62 b	22	2458573.147116±0.000311	This Work
	WASP-62 b	23	2458577.559142±0.000317	This Work
	WASP-62 b	25	2458586.382966±0.000333	This Work
	WASP-62 b	26	2458590.795328±0.000345	This Work
	WASP-62 b	27	2458595.206831±0.000331	This Work
	WASP-62 b	29	2458604.031175±0.00029	This Work
	WASP-62 b	30	2458608.443135±0.000301	This Work
	WASP-62 b	31	2458612.855056±0.000311	This Work
	WASP-62 b	32	2458617.266322±0.000359	This Work
	WASP-62 b	33	2458621.67842±0.000344	This Work
	WASP-62 b	34	2458626.090956±0.000358	This Work
	WASP-62 b	35	2458630.502921±0.000265	This Work
	WASP-62 b	36	2458634.914867±0.000257	This Work
	WASP-62 b	38	2458643.738117±0.000318	This Work
	WASP-62 b	39	2458648.150206±0.000305	This Work
	WASP-62 b	40	2458652.561559±0.000312	This Work
	WASP-62 b	41	2458656.974299±0.000292	This Work
	WASP-62 b	42	2458661.385862±0.000292	This Work
	WASP-62 b	43	2458665.798175±0.000285	This Work
	WASP-62 b	44	2458670.210186±0.000304	This Work
	WASP-62 b	45	2458674.621865±0.000315	This Work
	WASP-62 b	46	2458679.034395±0.000284	This Work
	Note. All midtimes reported in this work are from TESS unless otherwise
	stated.

  Graph emphasizing the connection between the different observation methods with direct imaging, and the back and forth with theoretical models to guide towards understanding exoplanets and pave the way to understanding habitability. Image courtesy to Olivier Guyon. . . . . . . . . . . . . . . . . . . . . . . . . . .1.11 Jupiter-sized planets are far less abundant than smaller planets: this is partially due to observational biases. However, we still do not know if there are planets at intermediate semi-major axes. Once published in 2025, GAIA DR4 will be able to shed light on the planets' size distribution. Histogram provided by exoplanet.eu. 1.12 Description of the different stages of planet formation, from the formation of a star, to the different disk steps, to fully formed planetary systems. The images are for better visualization of the processes and are a mix of authentic images, and artist impressions. The bottom arrow is a representation of the timescales. 1.13 Evolution of the planetary mass in a core accretion mechanism described in Pollack et al.

	List of Figures
	FC 1.10	Flux Concentration
	FLC		Ferroelectric Liquid Crystal
	FWHM	Full width at half maximum
	GAN	Generative Adversarial Network
	GMT	Giant Magellan Telescope
	GPI		Gemini Planet Imager
	GUI		Graphical Unit Interface
	HARPS	High Accuracy Radial velocity Planet Searcher
	HCI		High Contrast Imaging
	HST		Hubble Space Telescope
	HZ		Habitable Zone
	I/O		Input/Output
	IR		Infrared
	IRAS	Adaptive Optics Infrared Astronomy Satellite
	IWA	AU	Astronomical Unit Inner Working Angle
	ADI JWST	Angular Differential Imaging James Webb Space Telescope
	KL	ADI	Atmospheric Detectability Index Karhunen-Loève
	ARES KPIC	Ariel Retrieval of Exoplanets School Keck Planet Imager and Characterizer
	ARPF LESIA	Autoregressive predictive filter Laboratoire d'études spatiales et d'instrumentation en astrophysique
	CCD LOCI	Charge Coupled Device Locally Optimized Combination of Images
	MIR	CFHT	Canada-France-Hawaii-Telescope Mid-infrared
	MJD	CHARIS	Coronagraphic High Angular Resolution Imaging Spectrograph Modified Julian date
	ML	CIA	Collision Induced Absorption Machine Learning
	CMOS MVM	Complementary Metal-Oxyde Semiconductor (detector) Matrix-Vector Multiplication
	CNN NCPA	Convolutional Neural Network Non-common Path Aberrations
	COMPASS NEAR	COMputing Platform for Adaptive opticS Systems New Earths in the Alpha Cen Region
	NFS	CoRoT	Convection, Rotation and planetary Transits Network File Sharing
	NIR	DrWHO	Direct Reinforcement Wavefront Heuristic Optimization Near-Infrared
	OAP	ESPRESSO	Echelle SPectrograph for Rocky Exoplanets and Stable Spectroscopic Obser-Off-axis parabolic mirror
	OG		vations Optical Gain
	OPD	ExAO	Extreme Adaptive Optics Optical Path Difference
	PCA	Exo-REM	Exoplanet Radiative-convective Equilibrium Model Principal Component Analysis
	PDI	LE	Long exposure Polarimetric Differential Imaging
	LESSONS PIAAC	LBT Exploratory Survey for Super-Earths/Sub-Neptunes Orbiting Nearby Phase-induced Amplitude Apodization Coronagraph
	ppm		Stars Parts-Per-Million
	PSF	FT	Fourier Transform Point Spread Function
	DI PyWFS	Direct Imaging Pyramid Wavefront Sensor
	RDI	DM	Deformable Mirror Reference star Differential Imaging
	EFC REACH	Electric Field Conjugation Rigorous Exoplanetary Atmosphere Characterization with High dispersion
		ELT	Extremely Large Telescope(s) coronography
	RMS	ESO	European Southern Observatory Root-Mean-Square

  Dawson et al., 2018. . . . . 1.15 Schematic description of different types of planet formation and evolution through different possible scenarios, leading to different planetary types, here organized into three classes of planet: dense, transitional, and gas-rich. Figure credits: Diego Turrini and Mirko Riazzoli[START_REF] Turrini | The contribution of the ARIEL space mission to the study of planetary formation[END_REF]. . . . . . . . . . . . . . . 1.16 A simplistic schematic view of how retrievals work. Figure from Barstow et al., 2020. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.17 Contrast curves of several ground and space-based high-contrast imaging instruments. Plot created with https://github.com/nasavbailey/DI-flux-ratio-plot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Simplistic schematic of the light propagation through a telescope, through the pupil plane up to the focal plane. Arrows are light rays, while the lines represent wavefronts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Visualization of the frequency decomposition of a signal, in sines and cosines, via Fourier transforms. The Fourier Transform takes an input function in the spatial domain, here in red, and converts it into a new set of functions in the frequency domain, here in blue. Credit: Lucas V. Barbosa. . . . . . . . . . . . . . . . . . . 2.3 Left: Airy pattern, as is the PSF in the-diffraction limited case. Middle: aberrated seeing-limited PSF, limited by atmospheric turbulence, on a short exposure image. Right: seeing-limited PSF, on a long exposure. Here, D{r 0 = 20, r 0 being the Fried parameter. Source: V. Chambouleyron's thesis. . . . . . . . . . . . . . . . . List of Figures 2.18 VNC screenshot of the SCExAO bench, dealing with the bench parameters, with the PyWFS camera, the DM channels, the fast IR focal plane cameras (C-RED2 and C-RED1), the AO loop control GUI, the coronagraph alignment GUI, and the status of the bench. Image credit: Kyohoon Ahn. . . . . . . . . . . . . . . . 3.1 Schematic simplistic view of the challenges of HCI of exoplanetary systems, and their solutions. Several of the solutions in the green boxes are interconnected to each other, as for example the focal plane WFC is inherently linked to the AO. This figure aims to be a brief and simplistic overview of the field. . . . . . . . . . 3.2 High contrast imaging capabilities and challenges, illustrated for the ǫ Eridani system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Updated diagram fromFigure 2.9 including the WFS reference subtraction. . . . 3.4 Simplistic description of DrWHO, presented in Skaf et al., 2022b. . . . . . . . . . 3.5 Simplistic schematic reinforcement learning description of DrWHO: DrWHO is the intelligent agent ought to take action, here the WFS reference update, to increase the reward in an environment, here the score (the SR, or contrast, etc.), in the focal plane image, allowing the transition of the state, here the NCPA. . . 3.6 Example of the COMPASS GUI during simulation. Here, the SR evolution is shown (bottom left, the red dots are the short exposure SR, the blue ones are the long exposure ones); the PSF short exposure (psfSE, bottom right, in logarithmic scale), the PyWFS (pyrLR); the NCPA phase map (top right); the atmosphere (atm); the DM map (dm). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Example of the COMPASS GUI during a simulation with the DM actuators having an unexpected behavior, diverging the AO loop and reducing the SR values (plot bottom left). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 The rebel actuator zero, on the edge of the DM, impacting the wavefront (wfs_0), the PyWFS (pyrLR_0), and the PSF (psfSE_0). . . . . . . . . . . . . . . . . . 3.9 Figure 4 from Skaf et al., 2022b: we projected the references given by DrWHO on the AO control modes to quantify the correction applied. Top: Projection of the references provided by the 15-iteration DrWHO run over the modal basis, with the projection of the opposite of the NCPAs, to better visualize the correction. Bottom: Projection over the first 100 modes. . . . . . . . . . . . . . . . . . . . . 3.10 Schematic view of the data management with shared memories between the WFS

Table 1 .

 1 ExAO numerical simulations parameters.

	Numerical simulation configuration
		D = 8. m diameter
	Telescope	No support spiders Central Obstruction = 0.12
		von Kármán, ground layer only
		r 0 = 0.16 at 500 nm
	Turbulence layer	L 0 = 20 m
		(to simulate post-woofer residuals)
		|| -→ v || = 10 m.s -1
	PyWFS
	Subapertures	64×64
	Wavelength	Monochromatic, 750 nm
	Guide star magnitude 7
	Modulation	Circular, 3 λ D radius, 24 points
	Photon noise only
	Deformable mirror
		48 actuators across the diameter
	Focal Plane Camera
	Wavelength	Monochromatic, 1.65 µm
	Photon noise only
	RTC controller
	Loop rate	2 kHz
	Method	Linear modal integrator
	Basis	DM Karhunen-Loève (KL) basis
	Loop gain	0.3
	Controlled modes	1505
	Modes filtered	300

Table 2 .

 2 Comparison of the long exposure (LE) Strehl ratio between the following cases of the AO loop: no NCPA, NCPA alone, and post DrWHO with the NCPA. The second line corresponds to the RMS of the wavefront for each of those cases, calculated from the SR of the line above with the Maréchal approximation.

		No NCPA with NCPA with DrWHO
	SR LE (%)	87.9	86.8	87.7
	σ OPD (nm RMS)	94.3	98.8	95.1

Although this statement has been made every decade since the first exoplanet discovery. Things get increasingly more challenging to find such a proof.

Detection and characterisation techniques

The music app Shazam is based on Fourier Transform

Yes, another French, again.

This nomination is inherited from the Shack-Hartmann WFS, but is a misnomer.

Side note: this experiment was then revolutionary in our understanding of light, as both a wave and a particle. This duality contributed to the quantum optics revolution and a better understanding of the probabilistic nature of light.

Open source, available here: https://github.com/milk-org/ImageStreamIO.

Open source, available here: https://github.com/cacao-org/cacao.

On-sky validation of image-based adaptive optics wavefront sensor referencing, 2022Below is a paper published in the journal Astronomy & Astrophysics: "On-sky validation of image-based adaptive optics wavefront sensor referencing". This paper focuses on simulation results, and on-sky results in the visible, with the VAMPIRES instrument, and in noncoronagraphic PSF images.

Proxima meaning "nearby" in Latin.

The β Pictoris system: constraints on the planet and the disk structures at mid-IR wavelengths with NEAR, Skaf et al, 2023Below is a paper submitted to the journal Astronomy & Astrophysics on October 5th, 2022, accepted on March 8th.

Article number, page 2 of 15Skaf et al.: The β Pictoris system: constraints on the planet and the disk structures at mid-IR wavelengths with NEAR

Article number, page 3 of 15Skaf et al.: The β Pictoris system: constraints on the planet and the disk structures at mid-IR wavelengths with NEAR

Article number, page 12 of 15Skaf et al.: The β Pictoris system: constraints on the planet and the disk structures at mid-IR wavelengths with NEAR

Available and documented here: https://github.com/ucl-exoplanets/Iraclis

Available and documented here: https://taurex3-public.readthedocs.io/en/latest/

Available here: https://archive.stsci.edu/missions-and-data/hst

https://github.com/ucl-exoplanets/Iraclis

https://archive.stsci.edu/hst/

The Astronomical Journal, 160:109 (17pp), 2020 September Skaf et al.

https://github.com/ucl-exoplanets/TauREx3_public

The Astronomical Journal, 160:109 (17pp), 2020 September Skaf et al.

https://www.exoclock.space

Further author information: (Send correspondence to N.S) .: E-mail: nour.skaf@obspm.fr

Acknowledgements

Acknowledgements Acknowledgements

Acknowledgements. Based [in part] on data collected at Subaru Telescope, which is operated by the National Astronomical Observatory of Japan. The development of SCExAO was supported by the Japan Society for the Promotion of Science (Grant-in-Aid for Research #23340051, #26220704, #23103002, #19H00703 and #19H00695), the Astrobiology Center of the National Institutes of Natural Sciences, Japan, the Mt Cuba Foundation and the director's contingency fund at Subaru Telescope. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. N.S. acknowledges support from the PSL Iris-OCAV project. N.S. and V.D. acknowledge support from NASA (Grant #80NSSC19K0336). K.A. acknowledges support from the Heising-Simons foundation. We would like to thank the referee for their insightful comments.

Acknowledgements. We want to thank the ESO, the Breakthrough Foundation, and everyone involved in the NEAR project. The observations were carried out under the ESO program id: 60.A-9107(K). We want to thank the referee for the constructive feedback that contributed to improving the quality of this paper. N.S. acknowledges support from the PSL IRIS-OCAV project. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (COBREX; grant agreement 885593). French co-authors also acknowledge financial support from the Programme National de Planétologie (PNP). We thanks J. Chilcote for sharing the GPI spectrum of β Pic b. C.D. acknowledges financial support from the State Agency for Research of the Spanish MCIU through the "Center of Excellence Severo Ochoa" award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709) and the Group project Ref. N.H. was partially funded by Spanish MCIN/AEI/10.13039/501100011033 grant PID2019-107061GB-C61 and No. MDM-2017-0737 Unidad de Excelencia María de Maeztu -Centro de Astrobiología (CSIC-INTA). PID2019-110689RB-I00/AEI/10.13039/501100011033. We want to thank the anonymous reviewer for the insightful and constructive comments which helped improve the quality of the manuscript. This work was realized as part of ARES, the Ariel Retrieval Exoplanet School, in Biarritz in 2019. The school was organized by Jean-Philippe Beaulieu with the financial support of CNES. J.P. B. acknowledges the support of the University of Tasmania through the UTAS Foundation and the endowed Warren Chair in Astronomy, Rodolphe Cledassou, Pascale Danto, and Michel Viso (CNES). B.E., Q.C., M.M., A.T., and I.W. acknowledge funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program grant ExoAI (GA No. 758892) and STFC grants ST/P000282/1, ST/ P002153/1, ST/S002634/1, and ST/T001836/1. N.S. acknowledges the support of the IRIS-OCAV, PSL. M.P. acknowledges support by the European Research Council under Grant Agreement ATMO 757858 and by the CNES. R.B. is a PhD fellow of the Research Foundation-Flanders (FWO). W.P., T.Z., and A.Y.J. have received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No. 679030/WHIPLASH).O.V.thanks the CNRS/INSU Programme National de Planétologie (PNP) and CNES for funding support. G.G. acknowledges the financial support of the 2017 PhD fellowship program of INAF. This paper includes data collected by the TESS mission, which is funded by the NASA Explorer Program. TESS data is publicly available via the Mikulski Archive for Space Telescopes (MAST). Software: Iraclis (Tsiaras et al. 2016b),T a u R E x 3(Al-Refaie et al. 2019), pylightcurve (Tsiaras et al. 2016c), ExoTETHyS (Morello et al. 2020),A r i e l R a d(Mugnai et al. 2020), ExoWebb (B. Edwards et al. 2020, in preparation), Astropy (Astropy Collaboration et al. 2018),h5py(Collette 2013), emcee (Foreman-Mackey et al. 2013), Matplotlib (Hunter 2007), Multinest (Feroz et al. 2009), Pandas (McKinney 2011), Numpy (Oliphant 2006),S c i P y(Virtanen et al. 2020).

ACKNOWLEDGMENTS

Based [in part] on data collected at Subaru Telescope, which is operated by the National Astronomical Observatory of Japan. The development of SCExAO was supported by the Japan Society for the Promotion of Science (Grant-in-Aid for Research #23340051, #26220704, #23103002, #19H00703 & #19H00695), the Astrobiology Center of the National Institutes of Natural Sciences, Japan, the Mt Cuba Foundation and the director's contingency fund at Subaru Telescope. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. NS acknowledges support from the PSL Iris-OCAV project. NS and VD acknowledge support from NASA (Grant #80NSSC19K0336). KA acknowledges support from the Heising-Simons foundation.

ACKNOWLEDGMENTS

The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. Based [in part] on data collected at Subaru Telescope, which is operated by the National Astronomical Observatory of Japan. The development of SCExAO was supported by the Japan Society for the Promotion of Science (Grant-in-Aid for Research #23340051, #26220704, #23103002, #19H00703 & #19H00695), the Astrobiology Center of the National Institutes of Natural Sciences, Japan, the Mt Cuba Foundation and the director's contingency fund at Subaru Telescope. NS acknowledges support from the PSL Iris-OCAV project. NS and VD acknowledge support from NASA (Grant #80NSSC19K0336). KA acknowledges support from the Heising-Simons foundation.

ARES. II. Characterizing the Hot Jupiters WASP-127 b, WASP-79 b, and WASP-62b with the Hubble Space Telescope *

Appendix

The white light curve_tting for the TESS data are in Figure 16 for WASP-127 b, Figure 17 for WASP-79 b, and Figure 18 for WASP-62 b. All transit mid times used for the fitting are listed in Table 6 andTable 7. [START_REF] Foucault | Memoire sur la construction des telescopes en verre argente[END_REF]. Here, figures 7, 8, and 9 describe the principle of the knife-edge test represented by the vertical line: Figure 7 shows a perfect mirror, having a single focal point; Figure 8 shows a mirror with disharmonious outer edges; Figure 9 shows a mirror with several aberrations. . . Analysis of several groups of galaxies from GAMA to determine their varialization state.

Student Researcher, Astrophysics -GEPI -Observatoire de Paris (France) Summer 2014 Visible galaxies spectroscopy ; galaxies' composition, classification.

Private Tutoring in Maths and Physics 2013 to 2017

From middle school to undergraduate level.

Facilitator, Astronomy for general public -professional Summers 2012-2013

Saint-Michel-l'Observatoire Astronomy Center, partnership with the Haute-Provence Observatory CNRS. Wide astronomy outreach activities with children and wide public, with day trainings and night observations.

FORMATION

SCIENTIFIC CONFERENCES

Conference talks

• SPIE Astronomical Telescope + Instrumentation -Montreal -July 2022 "Imaged-based adaptive optics wavefront sensor referencing for high contrast imaging."

• Lyot Conference -Leiden -July 2022 "High contrast imaging wavefront sensor referencing from coronagraphic images."

• Wavefront sensing in the VLT/ELT era VII -Dec 2021 "High contrast imaging wavefront sensor referencing from coronagraphic images."

• SPIE Optics and Photonics -Techniques and Instrumentation for Detection of Exoplanets X -Aug 2021 "High contrast imaging wavefront sensor referencing from coronagraphic images."

• Direct Imaging Tech Talk Feb. 2021 : "Image-base adaptive optics wavefront sensor referencing : a method to compensate NCPA"

• ARES Day -Nov 2020 : "Diaries from TauREx."

• Ariel Consortium Meeting Oct. 2020 : "Unveiling the atmospheric compositions of the hot Jupiters WASP-127b, WASP-79b, WASP-62b."

• WFS 2020-Oct. 2020 : "Dr WHO : a self-automatisation algorithm for high contrast imaging."

• EPSC Sept. 2020 : "ARES. II. Characterizing the Hot Jupiters WASP-127 b, WASP-79 b, and WASP-62b with the Hubble Space Telescope"

Posters

• Exoplanet IV 2022 : "The β Pictoris system : constraints on the planet and the disk structures at mid-IR wavelengths with NEAR." (absent for medical reasons)

• Exoplanet III 2020 : "Characterizing the Hot Jupiters WASP-127 b, WASP-79 b, and WASP-62b."

• Ariel Consortium Meeting Jan. 2020 : "Characterizing the Hot Jupiters WASP-127 b, WASP-79 b, and WASP-62b."

• Ariel Consortium Meeting Oct. 2020 : "Unveiling the atmospheric compositions of the hot Jupiters WASP-127b, WASP-79b, WASP-62b."

nourskaf.com

Journal Club

• LESIA's Astro-café : "Introduction to Machine Learning and Pushing the limits of exoplanets discovery via Direct Imaging."

Initiator & organiser of the 1st international workshop on AI for AO -3 days May 2020 : 40 participants, 9 universities.

ASSOCIATIONS, HOBBIES, LANGUGES

Associations : French Association of Women and Sciences ; French Society of Astronomy ; Space Bus France. Honorary member of the association "Guyane Astronomie".

Travels : Europe, Asia, Africa, North America, Oceania. 35 countries Sports : outdoor sports, scuba diving (PADI open water), free diving, yoga, surf.

Photography : landscapes and night sky pictures.

Languages : French (mother tongue). Anglais (bilingual). Spanish, Italian, Arabic (classical and Lebanese dialect) (beginner to intermediate).

nourskaf.com

Appendix C

Publication List