domain: spi phys

text:
Ahmad Ali

Guillaume Vanel

Carole Frindel

David Rousseau

Ali Ahmad

Assessing diffractive imaging for cytometry of cells

Keywords: Lens-less imaging, Fourier, cell classification

teaching and research institutions in France or abroad, or from public or private research centers.

INTRODUCTION

Lens-less imaging is a promising biomedical tool currently investigated for a large range of applications [START_REF] Sinha | Lensless computational imaging through deep learning[END_REF]. A specific use case of lens-less imaging consists in diffractive imaging where the modulus of the Fourier transform is directly captured as it corresponds to the Fraunhofer diffraction pattern. In this work, we propose to compare the sorting of 2D single cell images (healthy and unhealthy) in the spatial domain as recently illustrated in [START_REF]Detecting differences of fluorescent markers distribution in single cell microscopy: textural or pointillist feature space?[END_REF] to the modulus of the Fourier domain using textural feature spaces and a convolutional neural network (CNN).

METHODS

We applied the studied approaches on a set of real microscopy images of healthy and unhealthy (cancerous) cells. These images are 3D stacks of breast cell lines from multiple samples that were acquired using Aurox Clarity structured illumination/spinning disk laser-free confocal system in Imperial College of London and looking at mCherry labelled histone-H2B. 2D images were computed from 3D stacks by applying a sum z-projection transform. Finally, cells were segmented into single cell per image of 256 × 256 pixels. The modulus of the Fourier transform is computed then from the 2D images to simulate the diffractive imaging data set that would be produced with a lens-less imaging system. The total amount of single cell images is about 907 cancerous cell images and and 1007 healthy cell images for each studied imaging mode.

For cells classification in spatial and spectral spaces, we used the local binary pattern (LBP), the Haralick coefficient computed from gray-level co-occurence matrix (GLCM), the deep feature multi-scale method based on scattering transform convolution networks (scatnet) for textural feature extraction coupled with SVM classifier and also we included a CNN. Hyper-parameters of textural methods were selected as in [START_REF]Detecting differences of fluorescent markers distribution in single cell microscopy: textural or pointillist feature space?[END_REF] and a PCA was applied to reduce the number of features of LBP and scatnet to 14 equally to the GLCM. The architecture and hyper-parameters of CNN were optimized for both spatial and spectral images including regularisation by early stopping and random data augmentation with: rotation up to 180 • , zoom in/out up to 20% and and brightness change up to 30% of original. Datasets were split into 80% for training and 20% for validation.

RESULTS

Table 1 shows the accuracy metric computed using 10-folds cross validation to evaluate classification performance. Globally, spectral space produces rather similar performance to spatial space when standard textural methods are used. The best results in spectral domain are obtained with the scattering transform. For CNN slightly higher classification performance for spatial and spectral spaces are observed with however a limited difference of few percent.

DISCUSSION AND CONCLUSION

The results demonstrated via simulation on real cells the possibility to use the Fraunhofer diffraction imaging mode to classify cells in healthy and unhealthy classes instead of using spatial space with rather limited loss of performance. This opens new directions for low-cost and fast cytometry performing cell sorting based on diffraction patterns without the need of close-up microscopic lenses.

Table 1 .

 1 Classification results of used methods in both spatial and spectral domain.

		Methods
	Spaces GLCM	LBP	Scatnet	CNN
	Spatial 73.9 % 67.6 % 73.3 % 79.4%
	Spectral 73.6 % 70.1 % 74.1 % 76.5%


Felicity Bodenstein

This issue of JAMS considers the exponential growth of an export market for cultural objects from the African continent since the middle of the nineteenth century, from the first episodes of commercial and military colonialism (Cormack) through to the dramatic rise from the 1890s onwards (Hüsgen, Tsogang Fossi). It then considers the shift away from the categorization of African cultural objects as ethnographic to the flourishing of a "primitive art" (also often termed as "art nègre") 1 trade in Paris (Saint-Raymond, Vaudry) and finally moves through the issue of post-colonial trade (Girard-Muscagorry); closing with an article on the question of illicit trafficking that has marked the currently termed "tribal art" market for African objects. The director of Abidjan Musée des civilisations, Silvie Memel Kassi also considers how the current situation of African museums is changing and how these institutions are preparing in order to offer a suitable environment for returning objects. The central question is the role of commercial transactions in the establishment of systematic collecting practices of cultural material from sub-Saharan Africa, transactions driven by the growing presence of European powers on the continent and motivated by the corollary establishment of specialized ethnographic collections in Europe.

Nowhere can the intertwined development of international trade, curiosity and ethnographic museums be read more clearly than in the correspondence between the Bavarian-born doctor Philipp Franz Siebold, who had spent seven years as the resident physician of the important Dutch trading post Dejima in Japan, and François-Edme Jomard, founder of the Geography Department at the Royal Library in Paris (1828) and participant in the Egyptian Expedition of Napoléon Bonaparte. When Siebold described his plans for such an ethnographic museum in 1843, he deplored what he saw as the "inconceivable indifference" with which European powers considered their ethnographic collections. His own observations reflected the shift in cultural policy that would lead to the creation of most major European public ethnographic museums. Writing to Jomard of the need for such institutions in order to help open up trade routes and facilitate the understanding of extra-European cultures, he surmised: "you who agree with me that it is now or never time for the capitals of the empires of civilized Europe which have colonies or which propose to found them, to create within them museums of geography and ethnography, the existence of which is a prerequisite for the success of their undertakings." 2 Collections of material culture would easily allow the visitor to consider at the same time the potential of foreign raw materials as well as the techniques used to process them into different types of goods, ranging from the most sophisticated artistic forms to simple everyday objects.

The -admittedly Eurocentric -framing of the question of trade in African cultural objects presented in this issue mirrors this historical moment; it does not intend to signify the absence of circulation and commerce of cultural objects before the middle of the nineteenth century within the African continent or from Africa to Europe prior to this period but rather seeks to reflect on the manner in which modes of acquisition, types and quantities of acquired objects changed significantly due to a process of colonization that was economic before it was political. For centuries, Africa had been involved in many forms of global commerce: to the East with China and other areas of the Indian Ocean from the eighth century onwards, and to the West, first with the Portuguese, then increasingly with the Dutch and the British, along a coastline that Europeans named after the "commodities on offer for exchange" -the 'Gold Coast', 'the Ivory Coast', the Grain Coast (modern Liberia) and the Slave Coast, between modern Benin and south-western Nigeria as "Africa became seen by outsiders in the terms of the extraction and consumption of resources". 3 The contact zones created by this commerce led artists and artisans in different parts of the continent to create specific types of objects that might best be qualified as export goods. The most famous case in point were carved objects in "white gold", a term often used for Afro-Portuguese ivories. Produced by Sapi (Sierra Leone) and Beni (Nigeria) artisans to satisfy the taste of European travelers for intricately carved elements with an exotic flair, these pieces became a highly coveted must-have in European princely cabinets. 4 Prestigious because of the precious nature of the material in which they were carved, the value of these oliphants, salt-cellars, spoons, vases and other small vessels translated particularly well transculturally, so that the vast majority of objects from the African continent that were collected in Europe before the nineteenth century Allingham's account documents how the trade of material culture was initially imbricated in a constellation of "curiosity" where natural history retained a place of prime importance well up until the second half of the nineteenth century when the ethnographic became an independent category of inquiry and a domain of trade of equal importance to natural history specimens. In Germany, the growing volume of collections of African objects in ethnographic museums in the second half of the nineteenth century is a good indicator of the development of a market whose main protagonists were active in the international port city of Hamburg.

As was shown by Glenn Penny, in the case of Germany the museums were the principal and the most influential buyers in this new market. 7 The French situation was notably different. Here the ethnographic market was small in comparison to Britain and Germany, and museums, in particular the ethnographic museum at the Trocadéro (1878), acquired their collections mainly through gifts or scientific expeditions, 8 growing exponentially in numbers from 1885 onwards. 9 This remained largely true until a part of the cultural objects that had previously been classified as ethnographic were rebranded as "art". Indeed, from the 1910s onwards, Paris became the main market for the "arts nègres" as they were called (a term that was used interchangeably with "arts primitifs" So, whilst there was a long tradition of commerce and exchange along the coasts and in major trading cities, in many parts of the continent, especially those vast rural geographies that had remained out of the range of direct contact with Europeans, culturally important objects only rarely had the status of commodities, and even when they did it was only relevant in very specific spheres of exchange in which European trade was not included. It is important to note that outside of ivory objects which dominate the literature on European collecting of African objects until the beginning of the nineteenth century, most of the types of objects that would become focal points of European collections -in particular in the domain of the "arts nègres" from the beginning of the twentieth century onwards in avant-garde artistic circles (such as the famous Punu or Fang masks described by Vlaminck and Derain) 12 -were not familiar and had not appeared in collections, private or public before the 1880s, suggesting that they did not circulate out of the continent before the colonial era. This diversity of object status ranging from the inalienable, often religious or political object to the readily produced and easily commodified artefact is the essential background to understanding the typology of acquisition or collecting practices (forms of purchases, gifts and indeed theft) that developed during colonial expansion, as illustrated in this issue by Cormack, Hüsgen and Tsogang-Fossi. The forced or strongly coerced commodification of certain types of objects that had been produced and preserved for specific social uses might be the most significant change in how cultural objects moved out of Africa from the middle of the nineteenth century onwards and it is certainly also one of the most controversial ones. This change was made possible by the enforcement of treaties of trade and protection and justified by the nascent discipline of ethnography and its mission to "salvage" and to document cultures, in particular those "disappearing" through contact with modernity. 13 It is a change that was for a long time readily overlooked because of its strong relationship to contexts of violence (see Cormack in this issue) whilst Eurocentric questions, such as shifts in object status from the ethnographic to the aesthetic, have received far more attention. 14 Thus, understanding the market for cultural objects moving out of Africa, set into circulation either through direct encounters with foreigners or through the intermediary of so-called middlemen, means paying particular attention to commodification as a process, 15 one which took on specific characteristics in the context of extreme power asymmetry that accompanied the extension of colonialism on the continent. It also implies taking into consideration the nuances of object status in terms of property and mobility, considering in particular indigenous concepts of inalienability, 16 Bondaz, is an excellent example of how to bring together two sides of an equation that is very often considered uniquely from a European perspective. This is in large part due to the very unequal state of documentation of the provenance history of objects coming from the African continent in Western collections. The articles in this issue adopt very different strategies in dealing with the opacity of the "social lives" of these objects before their first or indeed second or third sale in Europe: taking one of two main approaches that consist on the one hand of trying to overcome this challenge or, when that is indeed impossible, of trying to get a better understanding of the conditions that have favorized this loss and subsequent absence of knowledge.

Examining the case of objects from the current region of South Sudan, Zoe Cormack considers specifically the history of violence 19 that is associated with different forms of acquisitions related to some of the approximately 15,000 objects from that area that reached European museums between 1840 and 1885. Focusing on the unusually well-documented work of Italian geographer and explorer Giovanni Maini, she examines the nature of the links between collecting and "predatory commerce" in particular during his missions from 1859 to 1872. She shows how his capacity to access material depended on trade networks and especially on the stations called zariba and how, alongside the extraction of local material culture, the practice of collecting also "changed patterns of production in response to a market". Jan Hüsgen's work considers the different modes of collecting related to the work of German colonial officials in the "Togo-Hinterland Expedition" (1894/95). Though presented as having strictly scientific ambitions, the conditions in which many of the acquisitions were made can clearly be directly associated with "punitive" actions that were preceded by forms of resistance. Also, coercive conditions did not hinder actors on the African side from engaging in "intensive and lengthy negotiations for the acquisition of particularly rare objects". first time) provides us with two very contrasting points of view on the ethics of object circulation and its future; current debates indeed show the need for more work and supporting context from historians in order to get a better sense of the many questions that still constitutes such a large part of the lacunary market stories of African cultural objects.

Richard

  were made of ivory. They have been reinterpreted in the last decades as the first examples of a globalized form of artistic practice.Nevertheless, sub-Saharan Africa was the least well represented part of the world in early European public museum collections at the beginning of the nineteenth century, 5 and the growth of trade and circulation of objects from that part of the world developed in parallel to the growing trade for ethnografica, which became a new specialization for dealers from the middle of the nineteenth century onwards. A detailed account of the history of Steven's auction house, one of London's largest auction houses for natural history and ethnographic objects, aptly entitled A Romance of the Rostrum, 6 documents how, in the 1820s, the acquisition of extra-European curiosities shifted from an informal market mainly driven by actors involved in collecting and directly trading or exchanging with each other to the development of a more specialized and professional market where private collections were dissolved and often absorbed by large museum collections.

  until the end of the 1930s). Yaëlle Biro's book, Fabriquer le Regard. Marchands, réseaux et objets d'art africains à l'aube du XXe siècle, reviewed in this issue (Bodenstein) retraces this change, whilst the contribution provided here by Léa Saint-Raymond and Élodie Vaudry traces some of the essential elements in the development of an important secondary market from the 1920s onwards, identifying different types of markets ranging from junk to financial investment.Conversely, the historical record of internal markets on the African continent before the twentieth century is quite sparse with no equivalent to the wealth of anthropological studies that have continued to explore the issue since the seminal work undertaken by Christopher Steiner in the 1980s and 1990s.10 Though not directly related to the question of the market, historical studies on different contexts of production allow us to underline that in many communities, their cultural objects were most probably created outside of open market circuits, often in exchange for other services or related to specific functions (religious, political, social) providing artists and artisans with other means of living from their work than direct sales. 11 Much as was the case in Early Modern Europe, they often depended on relationships with specific institutions such as guilds in order to produce and circulate objects whose function clearly often defined their future destination.

  Tsogang Fossi's study of a set of correspondence at the ethnological museum of Hamburg takes the case of the sale of a collection from the Cameroon Cross River brought together in the first decade of the twentieth century by Alfred Mansfeld. He examines the commodification and first sale of a set of objects of which the potential buyers do not even have as much as a descriptive list. Interestingly, the sale price and the interest of the buyers seem to repose uniquely on the reputation and legitimacy of the European seller, an Austrian medical doctor who had entered the German colonial service in 1904, as the negotiations with museum actors and collectors in Hamburg, Leipzig and Berlin try to settle the destiny of a completely unspecific ensemble whose main selling point was to represent a geographic area from which very little material had as yet been made available. For a difference case study on the role of violence see: Dan Hicks, The Brutish Museum. The Benin Bronzes, Colonial Violence and Cultural Restitution (London: Pluto Press, 2020).The work presented by Léa Saint-Raymond and Élodie Vaudry on the role of the Drouot auction house in Paris as a space for the creation of a secondary market in the 1920s and 1930s shows how a quantitative approach can usefully help to shift away from a focus on the individual gestures of recognition of the talented dealer's "eye" and the "invention" of African art, in order to consider questions of price and profit as an often-unmentioned driving force. Their study also considers how authorial anonymity in relation to the history of the object was used to the advantage of a system of value creation on the European market that allowed other criteria such as the provenance related to Western collectors and artists to become all the more important for the pedigree and price of an object.Alexandre Girard-Muscagorry's proposal of a near-complete object biography underlines the amplitude of what is usually lost in terms of information through the different processes of decontextualization that have stripped the most valued pieces in African art collections of relevant knowledge, but also literally of parts of their materials. The destiny of a Mumuye mask, whose exact provenance in Zing, Eastern Nigeria can be determined thanks to ethnographic fieldwork carried out by Arnold Rubin from 1965 to 1970, along with information about its trajectory to Europe through Foumban, is a clearly-documented example of the continued flow of objects out of the continent after independence, in particular in contexts of crisis, in this case, possibly the economic aftermath of the Biafra civil war. Indeed, seventy-four percent of cultural objects from Nigeria in French collections were acquired after independence, most but not all on the secondary market.20 The case of the Mumuye masks illustrates the theoretical nature of the impact of such international measures as Unesco's 1970 Convention on the Means of Prohibiting and Preventing the Illicit Import, Export and Transfer of Ownership of Cultural Property which was not ratified by France until 1997.The last article by Silvie Memel Kassi, the current director of the Musée des civilisations in Abidjan, the largest museum of the Côte d'Ivoire, provides some of the insights from her doctoral thesis on the illicit traffic of cultural objects from her country and on the gap between existing legislation and the possibility of enforcing it, but also on the fine line between legal and ethical considerations. She places today's illicit trafficking at the end of a long history of cultural extraction practices going back to pre-colonial trade and examines these as an interplay of exogenous and endogenous factors. Her personal experience with the major theft of objects from the museum in 2010 due to security conditions created by a political crisis, but also her more than twenty-seven-year career in museums, allow her to consider the impact that this loss has had on different communities in Côte d'Ivoire and the damage done by the commodification processes to how they consider the value of their own cultural heritage. However, she also provides key examples of current efforts to reverse this process through activism and communication campaigns that she considers as a necessary corollary to legal measures and to restitution. There can be no doubt that reading her text alongside the Maureen Murphy's 2004 interview with the Parisian art dealer Jean Roudillon in this issue (published here for the 20 Sarr and Savoy, Rapport sur la Restitution du patrimoine culturel africain. Vers une nouvelle éthique relationnelle, 132. Journal for Art Market Studies 1 (2020) Felicity Bodenstein Africa: Trade, Traffic and Collections 8

Z. S. Strother, "Breaking Juju," Breaking Trade: Museums and the Culture of Iconoclasm in Southern Nigeria, in Res: Anthropology and Aesthetics 67-68 (2017): 21-41, https://doi.org/10.1086/692780. Journal for Art Market Studies 1 (2020) Felicity Bodenstein Africa: Trade, Traffic and Collections


Y Kremer

J.-F Léger

R Lapole

N Honnorat

Y Candela

S Dieudonné

Laurent Bourdieu
email: laurent.bourdieu@ens.fr

A spatio-temporally compensated acousto-optic scanner for two-photon microscopy providing large field of view

Keywords:

may come

A spatio-temporally compensated acousto-optic scanner for two-photon microscopy providing large field of view

Introduction

Two-photon scanning microscopy (TPSM) is a powerful tool for imaging deep inside living tissues with sub-cellular resolution. The spatio-temporal resolution of currently available TPSM is strongly limited by the galvanometric mirrors which scan the laser beam. Full images at frame rates of 10 to 100 Hz have been obtained, but events occurring at a ms timescale can only be followed by scanning repeatedly a single line. This approach severely constrains the spatial sampling. Because acousto-optic deflectors (AOD) are non-mechanical devices, they allow access at any angle within a few microseconds. Fast point by point scanning strategy using AOD might for this reason increase both the signal-to-noise ratio and the sampling rate with respect to galvanometric full frame imaging, since more time is spent on each point of interest. However, the use of AOD with femtosecond pulses is not straightforward and an accurate description of pulse width and laser beam spot evolution after such an angular dispersive element was only recently proposed [START_REF] Li | Beam spot size evolution of Gaussian femtosecond pulses after angular dispersion[END_REF][START_REF] Li | A generalized analysis of femtosecond laser pulse broadening after angular dispersion[END_REF][START_REF] Li | Dispersion characteristics of acousto-optic deflector for scanning Gaussian laser beam of femtosecond pulses[END_REF][START_REF] Zeng | Pulse broadening of the femtosecond pulses in a Gaussian beam passing an angular disperser[END_REF]. Many issues have indeed to be overcome in order to implement AOD as standard scanners in TPSM.

First, large spatio-temporal distortions of the femtosecond pulses are introduced by the AOD due to the propagation and the diffraction in the deflectors. These complex distortions need to be measured and compensated to use AOD in two-photon microscopy. Many recent papers have measured and compensated the angular and the temporal dispersions separately. An additional dispersive element placed before the AOD was used to create a spatial dispersion of same magnitude but opposite sign than the one due to the AOD at the center of the field of view (FOV): e.g. a prism [START_REF] Lechleiter | Multi-photon laser scanning microscopy using an acoustic optical deflector[END_REF][START_REF] Roorda | Video-rate nonlinear microscopy of neuronal membrane dynamics with genetically encoded probes[END_REF], a diffraction grating [START_REF] Iyer | Compensation of spatial and temporal dispersion for acousto-optic multiphoton laser-scanning microscopy[END_REF] or an acousto-optic modulator (AOM) [START_REF] Ngoi | Angular dispersion compensation for acousto-optic devices used for ultrashort-pulsed laser micromachining[END_REF][START_REF] Salome | Ultrafast random-access scanning in two-photon microscopy using acousto-optic deflectors[END_REF]. Compensation of temporal dispersion was usually obtained through double pass within a pair of prisms or gratings [START_REF] Fork | Negative dispersion using pairs of prisms[END_REF]. The large group delay dispersion (GDD) introduced by TeO2 which our AOD are made of, requires inter-prism distance of the order of 1m, which induces constraints on the space, the optical alignment and therefore on the possibility to implement research and commercial prototypes.

AOD and setups for temporal and spatial compensation are also introducing large power loss. Two crossed TeO2 AOD in shear mode have typically a transmission of 50%, spatial compensation setups (AOM or prism) 70 to 80%, and temporal compensation setup consisting of a double pass in a pair of prisms about 70%. Taking into account typical transmission of the rest of the microscope including the objective, the remaining available power at the sample might only be 5 to 10 % of the initial power and therefore strongly limits the depth of imaging in vivo. Recent studies have shown that placing the dispersive element (AOM or prism) used for spatial compensation at a distance of the AOD can simultaneously create the appropriate negative dispersion [START_REF] Zeng | Simultaneous compensation for spatial and temporal dispersion of acousto-optical deflectors for two-dimensional scanning with a single prism[END_REF][START_REF] Zeng | Acousto-optic modulator system for femtosecond laser pulses[END_REF][START_REF] Zeng | Analysis of the dispersion compensation of acousto-optic deflectors used for multiphoton imaging[END_REF]. This configuration allows minimization of laser power loss and facilitates optical alignment. However such a single pass in a pair of angular dispersive elements is known to create spatial distortions, as e.g. spatial chirp (SC) [START_REF] Gu | Spatial chirp in ultrafast optics[END_REF]. In absence of geometrical aberrations and in a neither scattering nor absorbing sample, SC is in principle suppressed at the focal point of the objective. The situation is more complex in scattering samples or in presence of e.g. spherical aberrations. As the path of border wavelengths will be different from the one of central wavelengths, scattering and/or aberrations might contribute to an increase of the pulse duration at the focal point, thus reducing fluorescence excitation in an uncontrolled manner. Finally, misalignment of such angular dispersive systems as well as propagation of pulses having spatial chirp through optical windows can also generate pulse front tilt (PFT) [START_REF] Akturk | Pulse-front tilt caused by spatial and temporal chirp[END_REF]. It is therefore important to carefully characterize and minimize the SC and PFT created by the AOM-AOD scanner.

Moreover, the number of points N scanned with an AOD (and therefore the available FOV) is limited by their physical dimension and their maximal scan angle Dq (N=(p/4) Dq D/l). Most systems used in the literature have a scanning range Dq~40mrad and a physical dimension of a few millimeters (typically 4mm) corresponding to ~ 200 points per line. As a consequence, the FOV has to be smaller than about 100µm in order to have a diffraction limited point spread function (PSF) at the center of the field of view (~0.5µm). Larger FOV are only achievable using AOD with larger scanning angle and/or aperture. Finally, the widespread use of AOD as scanners in TPSM requires that they might be used with tunable lasers over a large bandwidth [START_REF] Zeng | Acousto-optic modulator system for femtosecond laser pulses[END_REF]. This implies to design AOD as well as compensation setups that are efficiently tunable over similar bandwidths.

In this letter, we fully characterize a custom made AOD scanner from the company A&A having exceptional physical dimensions and performance: 13mm aperture, 50mrad scanning range, a tuning range of 720-880nm allowing access to about 850 points per line (7.10 5 points in the FOV). Spatial and temporal compensations are obtained using an AOM placed at distance of the AOD. Using a GRENOUILLE, an easy to align Frequency-Resolved Optical Gating (FROG), i.e. a spectrally resolved auto-correlator, we show that temporal broadening and spatial dispersion can be minimized using this setup. Moreover, we have characterized the spatio-temporal distortions including spatial chirp and pulse front tilt which arise from the single pass in the AOM-AOD setup. We demonstrate that the fine tuning of the AOM-AOD setup and the use of large aperture AOD allow minimization of PFT and SC.

Experimental methods

The setup (Fig. 1) consisted of a Tsunami Ti:sapphire femtosecond laser source (Spectra Physics, Irvine, CA) which provided ~ 90fs pulses having a spectrum dl ~11+/-0.5nm (FWHM). The beam was magnified by a first afocal telescope (magnification ~ 8) to a beam diameter D0 of about 11mm (measured at 1/e 2 ), which slightly under-covered the AOM aperture (13mm, ref AA.MTS/A15@720-920nm, A&A, Orsay, France). The AOD pair (A&A, ref AA.DTS.XY/A15@720-920nm) was placed at a distance D of the AOM. D was about 60cm and was carefully adjusted for optimal temporal compensation. The AOD aperture (13mm) was chosen so that it didn't diaphragm the laser beam, despite its spectral divergence after the AOM. A l/2 achromatic waveplate was placed between the AOM and the AOD to adjust the pulse polarization. The AOD exit aperture was imaged by a telescope of magnification 1/3 onto a spectrally resolved auto-correlator (GRENOUILLE 10-50, Swamp Optics, Atlanta). A second l/2 achromatic waveplate was used for convenience to adjust the light polarization. QuickFrog software (version 3.1, Swamp optics) was used to reconstruct the electric field from the measurement. A glass slide placed after the AOD was used to collect a small fraction of the beam which was focalized onto a digital CDD camera (IMI-141-FT, IMI tech, Seoul, Korea) using a f=75mm lens to measure the spatial dispersion of the pulses and to optimize its compensation. The ultrasonic wave frequency and amplitude were controlled in the AOM using a AA.MOD-nC driver (A&A) with a remote control and in the AOD using a DDS-XY-70-140-D8b-3W driver (A&A) and a program written with Labview using a fast digital I/O board (NI PCI DIO 32HS, National Instruments). This large AOM-AOD device will be referred to as scanner 1 in the following.

For comparison, a second scanning system was used. It consists of an AOM (AA.MTS.141/B20/A5@840nm, A&A) and 2 crossed AOD (AA.DTS.XY.250@840nm, A&A) optimized at a wavelength of 840nm, having a smaller aperture of 4.2mm and driven by AA.MOD-nC (A&A) and AA.DDS.1-250.2V (A&A) drivers respectively. In that case, a beam diameter D0~3mm was used at the AOM entrance pupil. This small AOM-AOD setup will be referred to as scanner 2 in the following. It was used with a Mai-Tai Ti:Saphire laser (Spectra Physics), with a spectrum of dl ~14+/-0.5nm (FWHM).

Background

Spatial dispersion

In acousto-optic devices used in the Bragg mode, light is efficiently deflected into the first diffraction order at an angle q given by:

q = l.F/v (1)
where l is the wavelength of the light, F (~100MHz) the acoustic frequency and v (~650m/s) the velocity of the acoustic wave inside the crystal. AOD are working at a central frequency F0 over a bandwidth +/-DF/2, of the order of 15 to 20 MHz. The maximum scan angle Dq is therefore given by Dq = l.DF/v~40mrad. Femtosecond lasers required for non-linear fluorescence absorption have a broad spectrum dl ~ 10-15nm. The spectral components are therefore spatially dispersed by an AOD over an angle dq given:

dq/q=dl/l (2)
As dq is of the order of 1.5 to 2.5mrad, this effect increases the point spread function (PSF) of the microscope (therefore reducing its spatial resolution) and decreases the nonlinear fluorescence absorption and strongly constrains the size of the FOV [START_REF] Salome | Ultrafast random-access scanning in two-photon microscopy using acousto-optic deflectors[END_REF]. With two crossed AOD, the result of this angular dispersion is an elliptical PSF [START_REF] Salome | Ultrafast random-access scanning in two-photon microscopy using acousto-optic deflectors[END_REF].

Temporal dispersion

AOD are made of a material which broadens the pulse duration, since TeO2 is highly dispersive with large group velocity dispersion GVD. In the AOD, the pulse travels a length le along the extraordinary axis (GVD along the extraordinary axis (GVDe) of 4840 fs 2 /cm at 840nm) and a length lo along the ordinary axis (GVD along the ordinary axis (GVDo) of 4720 fs 2 /cm at 840nm), with le+lo=L, where L is the AOD thickness. As a consequence, a transform-limited laser pulse with a Gaussian envelope and of initial duration tin is broadened, by the AOD to a final duration tout, given by:

(3) Typically, pulses are broadened to at least 500fs using standard AOD [START_REF] Iyer | Compensation of spatial and temporal dispersion for acousto-optic multiphoton laser-scanning microscopy[END_REF][START_REF] Salome | Ultrafast random-access scanning in two-photon microscopy using acousto-optic deflectors[END_REF][START_REF] Zeng | Analysis of the dispersion compensation of acousto-optic deflectors used for multiphoton imaging[END_REF].

( ) 2

Compensation of spatial dispersion

It is possible to place an AOM just before the AOD at an angle of 45° with respect to the AOD axes, in order to compensate the spatial dispersion at the centre of the FOV [START_REF] Salome | Ultrafast random-access scanning in two-photon microscopy using acousto-optic deflectors[END_REF]. The frequency in the AOM is then chosen equal to: [START_REF] Zeng | Pulse broadening of the femtosecond pulses in a Gaussian beam passing an angular disperser[END_REF] where F0 is the frequency at the centre of the FOV in both AOD. The AOM behaves like a prism of adjustable apex, so that FAOM can be finely tuned to optimize the compensation. Moreover, an AOM provides a very high transmission above 80%. The angular dispersion is totally compensated at the centre of FOV and partially at the edge, the maximum remaining dispersion being proportional to DF/2 instead of F0 [START_REF] Salome | Ultrafast random-access scanning in two-photon microscopy using acousto-optic deflectors[END_REF]. For frequencies in the AOD F=(Fx,Fy), the corresponding ellipse has a long axis w l , a small axis w s and an ellipticity e given by [START_REF] Salome | Ultrafast random-access scanning in two-photon microscopy using acousto-optic deflectors[END_REF]:

, ; (5)
where wr is the radial resolution of the microscope in absence of AOD, defined as the FWHM of the squared intensity point spread function (IPSF 2 ), fobj is the objective focal length, T is the magnification of the telescope used to image the AOD onto the objective back aperture and . The ellipse angle f is given by: (6)

Simultaneous compensation of temporal and spatial dispersion

Negative GDD can be obtained from devices providing angular dispersion such as prisms or gratings. Most standard pre-compensation setups consist of a double pass through a pair of prisms [START_REF] Fork | Negative dispersion using pairs of prisms[END_REF] and were used to compensate for the positive GDD introduced by AOD. Nakazawa and al. have shown that pairs of AOD provide also negative GVD proportional to their distance [START_REF] Nakazawa | Optical pulse compression using a TeO2 acousto-optical light deflector[END_REF]. For a pair of AOD (or for an AOM AOD setup) separated by a distance D and characterized by their frequencies F, the sound velocity v and the total material thickness L, the group delay dispersion is equal to:

(7a) (7b) (7c)
GDDAOD is the positive GDD introduced by the material which the AOD and the AOM are made of and GVDAOD/AOD is negative and proportional to the distance D. Therefore, as previously described by Zeng et al. [START_REF] Zeng | Simultaneous compensation for spatial and temporal dispersion of acousto-optical deflectors for two-dimensional scanning with a single prism[END_REF][START_REF] Zeng | Acousto-optic modulator system for femtosecond laser pulses[END_REF][START_REF] Zeng | Analysis of the dispersion compensation of acousto-optic deflectors used for multiphoton imaging[END_REF], placing an AOM at a distance D of the AOD allows the compensation of both the temporal and the spatial dispersion at the same time with a single setup and using independent control parameters: temporal compensation is controlled by the distance D whereas spatial compensation is adjusted by the AOM frequency fAOM.

0 . 2 F F AOM = 2 0 2 ) ( ÷ ÷ ø ö ç ç è ae - + = vT f F F w w obj r l dl r s w w = s l w w e = 2 2 2 0 2 0 0 ) ( ) ( y x y x F F F F F F F F F D + D = - + - = - = D x y F F D D = j tan AOD AOD AOD AOD AOD GVD D GDD GDD / . + = - 2 2 2 3 2 l p l d n d L c GDD AOD == 2 2 2 3 / 2 v F c D GVD AOD AOD p l - ==

Spatio-temporal distortions: spatial chirp and pulse front tilt

Since this configuration provides a single path trough the two dispersing AOD, fs pulses might contain spatio-temporal distortion, in particular spatial chirp (SC), in which the average wavelength of the pulse varies spatially across the beam [START_REF] Gu | Spatial chirp in ultrafast optics[END_REF]. In our case, the spatial chirp is described by the beam centre transverse coordinate x of each frequency w [START_REF] Gu | Spatial chirp in ultrafast optics[END_REF]. A pulse passing through an AOM placed at a distance D of the AOD has a dispersion . The scanner is imaged onto the GRENOUILLE (or the objective back aperture) by a telescope (magnification T~Da/D0 to match their aperture Da). The spatial dispersion at their aperture is and the spatial chirp

za =dxa/dw =
. The amount of spatial chirp can be estimated by comparing the characteristic length za.Dw (where Dw=2pcdl/l 2 ) and the beam diameter Da:

R= za.Dw/Da = DFdl/vD0. ( 8
)
Equation 8 shows that the spatial chirp increases with the distance D between the AOM and the AOD and decreases with the beam diameter D0 at the scanner aperture. At the typical distance used for temporal compensation (D ~ 50cm), R~1.3mm/D0 and deflectors having an aperture smaller or of the order of 1.3mm will induce strong SC in the pulse, whereas SC will vanish for scanners much larger than this dimension. Angular dispersion as well as propagation of a pulse having some SC through a material induce also some pulse front tilt (PFT) [START_REF] Akturk | Pulse-front tilt caused by spatial and temporal chirp[END_REF][START_REF] Akturk | Measuring pulse-front tilt in ultrashort pulses using GRENOUILLE[END_REF], which consists in the fact that the time at which the pulses reach a plane of reference depends on the transverse coordinate x. PFT increases the pulse duration at the objective focal point. Since a single path through the AOM-AOD setup potentially creates spatio-temporal distortions as PFT and SC, it is important to measure them carefully. Both SC and PFT are easily measured by a single shot second harmonic generation frequency-resolved optical gating devices. Thus we characterized these distortions using a spectrally resolved auto-correlator, as a GRENOUILLE, which is sensitive to PFT and to a lesser extent to SC.

Experimental results

Spatial compensation

Figure 2(a) shows, for three different wavelengths, typical scans of the field of view on the CCD achieved with the large aperture scanner 1. By adjusting properly the AOM frequency in each case, full spatial compensation was achieved at the centre of the FOV. Elsewhere, the laser was focalized as ellipses, which are all oriented towards the centre and which increase in size towards the edges of the image. Whereas their small axis is constant in the FOV, their long axis increases with the distance to the centre. On Fig. 2(b), we measured at 820nm their ellipticity as a function of the shift in frequency with respect to the centre frequency, which is perfectly modeled by Eq. ( 5). Similarly, their angle was measured on Fig. 2(b) as a function of the frequency ratio DFy/DFx. and modeled with Eq.6.

These results are consistent with previous results obtained with small aperture scanners [START_REF] Iyer | Compensation of spatial and temporal dispersion for acousto-optic multiphoton laser-scanning microscopy[END_REF][START_REF] Salome | Ultrafast random-access scanning in two-photon microscopy using acousto-optic deflectors[END_REF][START_REF] Zeng | Simultaneous compensation for spatial and temporal dispersion of acousto-optical deflectors for two-dimensional scanning with a single prism[END_REF][START_REF] Zeng | Analysis of the dispersion compensation of acousto-optic deflectors used for multiphoton imaging[END_REF]. We show similarly on Fig. 2(b) that compensation of spatial dispersion of scanner 2 is achieved at 840nm and modeled perfectly by Eqs.5 and 6, as published previously [START_REF] Salome | Ultrafast random-access scanning in two-photon microscopy using acousto-optic deflectors[END_REF]. The difference in ellipticity measured for the 2 scanners is due, as shown from Eq. ( 5), from the differences in the focal length of the CCD lens used (in order to match their different scan range) and in beam diameter after the AOD (and therefore in spot diameter at the center of the FOV). For the scanner 2, the optimum frequency in the AOM was equal to 142 MHz, with a central frequency in the AOD of 100MHz, in agreement with Eq. ( 4) and with a bandwidth of 35MHz (45mrad).

To compensate for the spatial dispersion at different wavelengths in scanner 1, the AOM frequency was changed accordingly, as shown on Fig. 2c. We found that the optimum AOM were binned (bin for DF: 2MHz, bin for DFx/DFy: 0.5). Lines are the theoretical curves obtained from Eqs.5 and 6 respectively. For comparison, spot ellipticity (○) and spot angle (□) are shown for the small scanner 2 using the same bins. C) AOM frequency (•), AOD minimum ( ), centre ( ) and maximum ( ) frequencies and maximum scan angle (○) as a function of the wavelength for the scanner 1. D) Laser spectrum measured before the AOM (□), between the AOM and the AODs (○) and after the AODs (+) for scanner 1. Data were fitted to Gaussians having the same FWHM=11+/-0.5nm. frequency was shifted by a small constant offset of 9MHz with respect to the frequency predicted by Eq. ( 4). This prevented perfect compensation above 880nm, due to the limited bandwidth of our AOM and the scanner was therefore used from 720nm to 880nm. Figure 2(c) shows also the variation of the AOD minimum, maximum and centre frequencies. The F D resulting scan angle was constant as a function of the wavelength, of the order of 56mrad. Within the FOV, the laser intensity was varied by less than 20%. Finally, the typical transmission of the AOM-AOD scanner was of the order of 20%.Theses results demonstrate that compensation of the spectral dispersion is achieved at the centre of the FOV from 720nm up to 880nm and that the remaining dispersions are well modeled by Eqs. ( 5) and [START_REF] Roorda | Video-rate nonlinear microscopy of neuronal membrane dynamics with genetically encoded probes[END_REF].

v cF D D x w p q w 2 ) ( = » ) )( ( ) 2 ( ) ( 0 D D v F c D x
We checked that the scanner 1 did not diaphragm the laser beam in this configuration. Due to the spectral dispersion in the AOM, the beam diameter increases after the AOM as ~1.7mm for D=60cm. Figure 2(d) shows that the laser spectrum is preserved at all locations throughout the optical path (FWHM=11nm), even for the large distance D used for temporal compensation (see below). Therefore, using a beam width of ~11mm at the AOM entrance pupil prevents any clipping in the AOD. For comparison, the standard scanning system 2 required for this reason a beam width of ~ 2.8mm only. The achievable FOV is proportional to the product of the scanning angle and of the beam aperture at the scanner. Therefore our new system (scan angle ~56mrad, beam aperture ~11mm) offers a very significant increase in the available FOV (by a factor of 5) in the configuration where the AOM is placed at distance of the AOD for simultaneous temporal and spatial compensation, as compared to the standard scanning system 2 (45mrad, 2.8mm). For example, using the 20X, NA 0.95, water immersion Olympus objective widely used in two-photon microscopy, a FOV of about 300µm will be obtained, with diffraction limited focalization at the centre of the FOV. On the edge of the FOV, the PSF will be stretched in one direction to about 3.7µm, as estimated using Eq. ( 5). This effect will reduce the resolution and the fluorescence excitation for objects located on the side of the FOV. While scanning an object larger than the PSF, the loss in fluorescence should be proportional to square of the ellipse elongation [START_REF] Salome | Ultrafast random-access scanning in two-photon microscopy using acousto-optic deflectors[END_REF]. This is still acceptable, in comparison to the gain in scanning speed, as long as resolution isn't a priority. Moreover, more time can be spent on the points located near the edges to obtain a constant fluorescence signal.

Temporal compensation

At the optimum AOM frequency for spatial compensation, we adjusted the distance D separating AOD and AOM to compensate for the temporal dispersion of the laser pulse. This adjustment did not affect the spatial compensation, both being independent. The pulse duration was measured as a function of the distance D and at 820nm using the GRENOUILLE (Fig. 3(a)). As the distance D was increased, pulse duration decreased remarkably down to a value of 93+/-3fs for D ~ 63+/-3cm and increased again for larger distances. This demonstrates that excellent pulse compensation was achieved, since the initial pulse duration was almost restored. Using the same configuration, we were also able to compensate temporally for the dispersion of the scanner 2 at 840nm (Fig. 3(b)). In that case, optimal compensation was obtained at a shorter distance D, of about 45+/-3cm, although longer pulses (145+/10fs) were obtained in this case. This might be due to the fact we used pulses with larger FWHM with this scanner (14nm instead of 11nm). Using Eq. ( 7), the negative dispersion introduced by the AOM-AOD setup is ~ 460fs 2 /cm for the scanner 1 at 820nm and ~ 490fs 2 /cm for the scanner 2 at 840nm. Using these values, the scanner 1 has a total GDD ~ 29000 fs 2 and the scanner 2 ~22000fs 2 . Taking into account known values of the ordinary (GVDo) and extraordinary (GVDe) group velocity dispersion of Te02 [START_REF] Salome | Ultrafast random-access scanning in two-photon microscopy using acousto-optic deflectors[END_REF] and the physical size of the scanners, we estimated their GDD. For the large scanner 1, we obtained a GDD at 820nm of ~ 29500 fs 2 (total thickness for each AOD and for the AOM of the scanner 20mm, 10mm interaction with GVDo~4952fs 2 /cm and 10mm interaction with GVDe~5070fs 2 /cm). For the small scanner 2, we estimated at 840nm the GDD to be 21300fs 2 (total thickness for each element 15mm, 4mm interaction with GVDe=4840fs 2 /cm, 11mm interaction with GVDo=4720fs 2 /cm). Both values are in good agreement with the values deduced from the experiments. v F D .

.dl » Fig. 3. Temporal compensation. Pulse duration (fs) as a function of the AOM-AOD distance (D) measured: A) at 820 nm for the large scanner 1; B) at 840 nm for the small scanner 2. The lines are fit to the data using Eq.3. C) Pulse duration (fs) measured as a function of the wavelength l (nm) for the scanner 1 (D=63cm).

We measured for the large scanner 1 by how much the pulse duration varied when the wavelength was changed. Optimal pulse compensation was obtained at different distances D depending on the wavelength and typically varied by 10cm for a 50nm change in wavelength. Experimentally, it is hardly possible to vary D rapidly during an experiment, since AOD have to be aligned precisely to obtain maximum diffraction efficiency. A more practical configuration was obtained by keeping the distance D fixed while varying the wavelength (Fig. 3(c)). In this case, the pulse duration varied from 93fs to 195fs over the scanner bandwidth (720nm -870nm). Such pulse durations are still very convenient for most two photon microscopy experiments.

Pulse front tilt and spatial chirp

GRENOUILLE traces allow us to give an estimation of the spatio-temporal distortions of the pulse. Spatial chirp is evidenced as a non-symmetrical trace with respect to the wavelength axis, whereas pulse front tilt is shown by a shift of the trace along the delay axis [START_REF] Akturk | Pulse-front tilt caused by spatial and temporal chirp[END_REF][START_REF] Akturk | Measuring pulse-front tilt in ultrashort pulses using GRENOUILLE[END_REF][START_REF] Akturk | Measuring spatial chirp in ultrashort pulses using single-shot Frequency-Resolved Optical Gating[END_REF][START_REF] Akturk | The general theory of first-order spatio-temporal distortions of Gaussian pulses and beams[END_REF]. Figure 4 shows the GRENOUILLE traces obtained with the two AOD systems at different distances D. In the case of the large scanner 1, the shape of the GRENOUILLE traces were symmetrical with respect to the vertical axis, whatever the distance D (Fig. 4a). In the case of the smaller scanner 2, a shear was clearly observed for D=75cm (Fig. 4(b),D=75cm). The comparison between the two GRENOUILLE traces demonstrates that spatial chirp was specifically present in the case of the small scanner, as expected from Eq. ( 8). Moreover, this effect was clearly evidenced at larger distances D, as shown from Eq. ( 8), typically above ~ 50cm. In opposition, for the scanner 1, no spatial chirp was evidenced by the GRENOUILLE whatever the distance D. This can be attributed to the fact that the dimension of the beam used with the scanner 1 was very large, and therefore the ratio given by Eq. ( 8) and characterizing the importance of SC remains small at all distances. GRENOUILLE also allows us to estimate the PFT as a function of the distance D. Figure 4c shows that the PFT decreases as function of D from a positive to a negative value and reaches a value close to 0 at the distance where the pulse duration was minimum. At that distance, for both scanners, a residual PFT was often found (of the order of ~ 0 to 10 -4 rad) and was very sensitive to the alignment of the setup. Therefore the GRENOUILLE allows control and minimization of the PFT due to the AOM-AOD scanner.

Discussion

In the recent years, many groups have designed two-photon microscopes incorporating AOD scanners and have tried to compensate for spatial and temporal dispersions by different methods including additional optics as prisms, gratings or AOM. First setups were using separate devices for both compensations, whereas it has been shown recently that a single prism or AOM placed at the correct distance of the AOD could correct both simultaneously. However, these compact and easier to align setups were not characterized in terms of spatiotemporal distortions (SC and PFT) which are inherent to a single pass in two refracting devices and might occur in misaligned systems. Since AOD alignment is delicate in this configuration and since SC and PFT might affect two-photon fluorescence excitation, it is important to characterize them properly. Moreover, a severe limitation of AOD is the FOV which can be achieved since their physical dimension is limited in standard systems (4mm in most publications), for a scanning range of about 40mrad. This aperture is even more limited if the AOM is placed at distance to the AOD for simultaneous compensation of temporal dispersion. This paper shows that very large aperture AOD might be used in two-photon microscopy without introducing spatio-temporal distortions and providing very large FOV.

We have shown that a 13mm aperture AOD offering potentially a FOV of typically 300µm using a 20X objective can be used over a bandwidth of 160nm. Spatial compensation at all wavelengths is achieved using an AOM of identical aperture, whereas temporal dispersion compensation is obtained at an AOM-AOD distance of 63cm. This distance is in agreement with the expected value of the GDD introduced by AOD knowing their physical dimension and the GVD of TeO2. We obtained an excellent temporal compensation which allows using an almost fully compensated pulse in a two-photon microscope.

Finally, these large AOD limit the SC introduced by the single pass configuration. Spatial chirp is due to the spatial separation of the pulse wavelengths after the AOD relative to the beam diameter. Since AOD scanners whatever their size introduce the same angular dispersion and since temporal compensation is obtained at distances of same order of magnitude, the use of larger AOD minimizes SC. This might be a great advantage compared to smaller systems where SC will eventually lead to temporal pulse broadening in scattering or aberrant media. E.g. in non-linear microscopy, high numerical aperture objectives are used to image deep in highly scattering medium. In presence of SC, the different frequencies of the pulse travel different path lengths in the tissue. As a result of scattering, the pulse at the objective focus might contain fewer frequencies as expected, thus increasing the pulse width. Finally, the use of the GRENOUILLE allows also finely minimizing the PFT so that it almost vanishes at the distance which compensates for the temporal dispersion. Our experience shows indeed that PFT is often encountered when the AOM AOD scanner is not properly aligned with a GRENOUILLE.

Fig. 1 .

 1 Fig. 1. The optical setup. Laser: Tsunami Ti:Sa laser. AOM: acousto-optic modulator and AOD: acousto-optic deflectors. Both were mounted on goniometric plates for alignment and placed on a rail to adjust their distance. l/2: achromatic half waveplates. GRENOUILLE: single shot second harmonic generation frequency-resolved optical gating devices. M1, M2, M3: dielectric mirrors. Attenuator: variable intensity attenuator.

Fig. 2 .

 2 Fig. 2. Compensation of spatial dispersion. A) Images at 765nm, 820nm and 875nm of the beam scanned by the scanner 1 and focused on the CCD. Spots are separated by 3.7mrad. B) Spot ellipticity (•) as a function of and spot angle (■) as function of DFx/DFy. Data obtained from images at 820nm containing 14x14 ellipses separated by 3.5 MHz (4.4mrad)

Fig. 4 .

 4 Fig. 4. Spatio-temporal distortions. GRENOUILLE traces measured for 3 AOM-AOD distances: A) for the scanner 1 (D=54cm, D=64cm and D=75cm) B) for the scanner 2 (D=17cm, D=40cm and D=75cm). C) Pulse front tilt as a function of the distance D for the scanner 1 (•) and for the scanner 2 (○). Horizontal bar: 100fs, vertical bar: 1nm.

Acknowledgments

This work has been supported by Convention E. 1762 de la Région Ile de France, a « Human Frontier Science Foundation » research grant n°RPG0060/2003-C102, by the French « Ministère de la Recherche et de l'Enseignement Supérieure » (ANR Blanche 2007 n°06-BLAN-0178-02), the SDV department of CNRS (ATIP jeune chercheur 2005), and the « ministère de la recherche » of Luxembourg. We thank Manuel Joffre for several useful comments, Benjamin Mathieu for his help in software programming and Rick Trebino for his advices on the use of the GRENOUILLE.