domain: spi phys phys.phys.phys-optics

text:
Thierry Fusco

Benoit Neichel

Carlos Correia

Leonardo Blanco

Anne Costille

Kjetil Dohlen

François Rigaut

Edgard Renaud

Anne Bonnefoi

Zibo Ke

Kacem El-Hadi

Jérome Paufique

Sylvain Oberti

Fraser Clarke

Ian Bryson

Niranjan Thatte

A story of errors and bias: The optimization of the LGS WFS for HARMONI

Keywords: Wave-Front Sensing, LTAO, ELT, LGS

) we will propose a global design trade-off for the LGS WFS and Tomographic reconstruction process in the HARMONI context. We will show that, under strong technical constraints (especially concerning the detectors characteristics), a mix of opto-mechanic and numerical optimisations will allow to get rid of WFS bias induce by spot elongation without degrading the ultimate system performance (3) beyond HARMONI baseline, we will briefly present alternative strategies (from components, concepts and algorithms point of view) that could solve the LGS spot elongation issues at lower costs and better robustness.

INTRODUCTION

Most of the current AO system are however constrained by the number of targets available to AO correction (the so-called sky coverage), and the need for statistics that requires observing many objects across the largest possible field. Those constraints called for the development of a new generation of AO, called Wide Field AO [WFAO]. By using multiple Laser Guide Stars [LGS], WFAO significantly increases the field of the AO corrected images, and the fraction of the sky that can benefit from such correction. Very recently, such capability has been brought to its apogee by coupling the ESO-operated Adaptive-Optics Facility (AOF) with the cuttingedge instrumentation of the MUSE integral-field (3D) spectrograph. Similar instrumental capabilities on the ELTs (e.g. HARMONI, MOSAIC) will revolutionize the extra-galactic field, as we will be able to reproduce the observation of the galaxy structure and kinematics out to distances of tens of millions of light-years. This will certainly modify our understanding of the galaxy mass assembly mechanisms and the Hubble sequence build-up. The use of multi-LGS in astronomy is however a young technology, and the extrapolation of the technique to the ELTs sizes leads to technological barriers regarding Wave-Front Sensing and associated detectors. For a LGS system, the artificial reference source is created by shining a laser from the telescope. Light from the beam is absorbed and reemitted by atoms in the upper atmosphere (a Sodium layer in the mesosphere) back into the WFS. However, due to the vertical extension of the Sodium layer (typically 20km), the AO guide star is now an extended object, with a complex shape, and temporally evolving with Sodium layer dynamical variations. When considering SHWFSwhich is the baseline of all current LGS-based AO systems -this Sodium layer extension creates elongated spot in each sub-aperture which can be as large as 20" for an ELT. Dealing with such a spot elongation using a classical SHWFS requires a tremendously large number of pixels. It calls for very sensitive (almost photon noise limited), very fast (larger than 500 Hz, most likely 1kHz) and extremely large (typically 5 million pixels) detectors. Such kind of devices is far beyond existing and first generation of WFAO systems on the ELT (currently in their preliminary design phase) which have to consider lower performance detectors (smaller, slower and noisier). The consequence is a reduced wave front sensing performance, creation of spurious effects and biases (so-called "truncations effects") and a limited performance of the full AO system. For spectroscopic studies of distant galaxies, reduced AO performance translates in sensitivity loss, or equivalently, it limits the observation of the faintest and more distant objects.

In this paper we will investigate several methods (both from the opto mechanical side and the control side) allowing to deal with spot elongation on an ELT using existing or close to exist detector technology. We will first recall the main problematic related to the spot elongation. Then we will identify possible mitigation and we will thoroughly study a couple of solution in the frame of the HARMONI project. An exhaustive analysis will be done on a downscaled version of the ELT (in order to fasten the simulation) and the conclusions will be apply to the full-scale system.

3D SODUIM LASER GUIDE STAR AND ELT

LGS spot elongation

Sodium laser guide stars (LGS) increase the sky coverage of adaptive optics (AO) systems. However, the finite height, the double pass through the atmosphere and the elongated size of the LGS, still limits the extent of the sky coverage. Temporal variations of the sodium layer density profile induce errors on centroids of the elongated LGS spots of Shack-Hartmann wave front sensors (SH-WFSs), especially for extremely large telescopes (ELTs) as the spot elongation increases with the telescope diameter. The main aberrations induced by the sodium layer variations are a tip/tilt (if the laser is launch from the side of the primary mirror) and a focus error. These errors are due to the variation of the mean altitude of the sodium layer and must be negated optically by zoom optics in order to keep each LGS spot focused and centered on its sub-aperture. If the laser is launch from the side, non-Centro-symmetric aberrations arise in addition to spherical aberrations, such as astigmatism, coma and trefoil. Square symmetric aberrations are due to: (i) a square truncation of spots by the pixels' boundaries of each sub-aperture, (ii) the spot sampling by a finite number of square pixels (see Figure 1).

Figure 1 Problematic of spot elongation on ELT

Consequently, all the LGS aberrations beyond the focus are due to instrumental artefacts and must be mitigated. To do so, the LGS WFS should ideally feature:

 A large field of view (FOV) per sub-aperture (wide enough to image a 20km-thick sodium profile),  A large number of pixel to sample adequately the sub-apertures,  A threshold-free or a radial-threshold centroiding algorithm,  A calibration procedure and a look-up table to negate the variable optical aberrations of the

LGS path (including zoom optics) for any sodium layer distance, It is almost impossible for a LGS WFS to meet all these requirements. Indeed, if we consider that the small axis has a size of ~1", and if we want to properly sample non-elongated spots, a pixel size of 1" maximum has to be considered. On the other hand, if we want to avoid truncation effects, and get all the elongated spots, we need a FoV per sub-apertures of 25" at least. This leads to 25x25 pixels per sub-aperture. The current baseline being to work with 80x80 sub-apertures per Shack-Hartmann, it means that we need 2000x2000 pixels on the LGSWFS detectors. Obviously, those detectors must be read at high frame rate (> 500 Hz) and with the minimum amount of Read-out-Noise (< 3 e-). Such detectors are not available as of today, and ESO will most likely provide detectors with ~ 800 x 800 pixels (previously called NGSD, then LVSM and now LISA) [START_REF] Downing | Update on development of WFS cameras at ESO for the ELT[END_REF]. As a consequence, and if we want to keep the pixel sampling lower than 1 arcsec, it means that we will have to deal with strong spot truncation. There are several options that have been proposed to deal with spot truncation. Among others, we can cite the following potential solutions:

 Retrieve the LGS induced aberrations working with a truth sensor. Indeed, truncation will introduce a bias in the measurements, bias that will be different for all the sub-aperture, and that will propagate into the tomography to result in some given low order aberrations in the science path. If one can have access to a measurement of those low order aberrations with a Natural Guide Star, it may be possible to update the reference slopes of the LGSWFS in order to remove them from the tomographic reconstruction. This works as a "truth-sensor" that would always provide the reference measurement.  Reject or penalize the corrupted measurements in the LGSWFS, i.e. those that are strongly affected by truncation. This is done numerically when building the tomographic reconstructor. This would certainly be a killer for single LGS systems, but with the H-LTAO system, we have a huge redundancy in the measurements, with a large pupil overlap at all relevant altitudes.  Work with a LGSWFS for which the Field Stop has been over-dimensioned, i.e. its size is larger than a sub-aperture (for instance, using a field stop of 20"x20", for sub-apertures of 10"x10"). In that case, each elongated spot will cover a larger area on the detector, and "leak" on the neighbored sub-aperture. However, by introducing a known tilt on each sub-apertures (i.e. with an optical modification of each lenslet), one can find a configuration where the spots are not superimposed. This is the SPOOF (Spot Packing Optimisation on Optical Frames) concept, recently proposed by Francois Rigaut [START_REF] Rigaut | Private communication[END_REF] that is briefly described in Figure 2 Figure 2 The SPOOF concept. Each sub-aperture of the WFS is slightly tilted so that the largest elongated spot will not overlap each other.

 Work with bigger pixels (as projected on-sky) on the SH-WFS, in order to increase the total FoV per sub-apertures. For instance, using 2" per pixel and 10x10 pixels per sub-aperture would provide 20" FoV. Doing so, we are introducing non-linarities in the SH measurements, as we will be under-sampled on the non-elongated direction. In that case, one can either try to follow the LGSWFS gains (sub-aperture per sub-aperture) and on an almost real time fashion [START_REF] Neichel | Reconstruction Strategies for GeMS[END_REF], or if the performance holds, simply degrade the LGS spot size as seen on sky, to match the pixel size. This can be done easily by defocusing the LGS, or having the WFS detector out-of the lenslet focus.  Adapt the lenslet pupil sampling with the elongation pattern, and adapt the lenselet size across the pupil. This has been proposed by Gendron et al. [START_REF] Gendron | Optical solutions for accommodating ELT LGS wave-front sensing to small format detectors[END_REF]  Finally, it may always be possible to work with pyramid or quad-cells, even in the LGS case [START_REF] Esposito | Pyramid wavefront sensing using Laser Guide Star for 8m and ELT class telescopes[END_REF] In the following we will focus on the classical SH-WFS approach and detailed the possible solution to deal with the large elongation with a limited number of pixels.

Sodium profiles and spot elongation

Because of its spatial and temporal evolution, the definition of reference profiles for the Sodium density is not an easy task. Using several data set acquired by T. Pfrommer et al [START_REF] Pfrommer | High-resolution lidar observations of mesospheric sodium and implications for adaptive optics[END_REF], ESO has identified 7 profiles that could be considered as the "typical" profiles to be expected, and the frequency of occurrence for each of the different shapes is comparable (see ). In the following we will consider either a uniform distribution (for the sake of simplicity) either these 7 profiles perform a first statistical study of the performance of our spot elongation mitigation strategies.

Figure 3

Sodium profiles considered. Those 7 profiles roughly correspond to the main categories of Na profiles, and each would appear ~15% of the time

SPOT ELONGATION AND TRUNCATION: THE PROBLEMATIC

The simulation tools

The full analysis presented hereafter has been done using our Matlab End-to-end simulation code OOMAO [START_REF] Correia | Object-oriented Matlab adaptive optics toolbox[END_REF].

The Object Oriented Matlab Adaptive Optics (OOMAO) modelling library is a library of Matlab classes developed for the purpose of facilitating a clear, accessible end-to-end model of AO systems. It is publicly available, open-source code. Objects from the different classes are assembled to perform numerical modelling of an Adaptive Optics system. OOMAO can be seen as an extension of the Matlab language; overloaded Matlab operators are used to propagate the wave-front through the system and to update the status of each object. OOMAO allows the user to generate objects that simulate the following hardware: modal or zonal deformable mirrors, imaging devices with extended exposure capabilities, telescopes with user-defined pupils, and Shack-Hartmann WFSs. Additionally, the library can be used to generate multi-layer atmosphere objects. Asterisms can be defined with any number of guide stars in constellations. OOMAO can implement closed-loop, open-loop and pseudo-open loop systems and has been specifically designed for the modelling of tomographic AO systems. It can also deals with the specific M4 geometry.

Spatial and temporal content of aberrations induced by truncation

The very first thing that has been done using these profiles was to understand the spatial and temporal content of the aberrations induced by the spot truncation. . Without turbulence we compute the impact of the spot elongation and truncation on the estimated phase. To do so we simulate a full propagation through the system down to the WFS reconstruction (assuming a basic centroiding for the SH-WFS data) and then we analyse the spatial frequency content of the reconstructed phase. Without any truncation, the elongation will only produce Tilt and focus. Because of the truncation (we consider here a 10" FoV sub-aperture) higher order modes are building up. In a full tomographic reconstruction process, several LGS (6 in the HARMONI case) are recombined to tomographically reconstruct the phase in the volume and then project it in a given direction. Tiptilt and focus will be filtered out during the process (Tip Tilt and Focus will be measured independently on a natural guide star). Hence, without truncation and for high SNR, there will be no impact of spot elongation. In the case of truncated sub-aperture, each WFS will see the "equivalent" static aberrations induced by the truncation, rotated according to the LLT geometry w.r.t. to the LGS pupil. Those aberrations will then be mixed by the tomographic reconstruction and re-projected on-axis by the H-LTAO reconstruction process. Depending on the considered sodium profile it is shown that significant amount of phase (up to a few hundred of nm rms) can be projected onto the 10 (and up to the 100) first Zernike polynomials (see Figure 4). A first approach to reduce the truncation impact that has been investigated in the frame of the H-LTAO study was to simply reject all the sub-apertures that would be truncated. As a first order approach, we can simply set to 0 a given amount of sub-apertures in the measurements, which could be seen as "pupil cropping", and look at the impact on the performance. For very redundant system, such a simple but yet very crude approach, is quite efficient since the same part of the pupil is sensed by several Wave-Front Sensors. As an optimization of this method, it may be possible to weight the measurements in order to only reject the ones along the long axis of the elongation (truncated), while keeping those along the small axis (not truncated). This has been proposed in [START_REF] Bechet | Optimal reconstruction for closed-loop ground-layer adaptive optics with elongated spots[END_REF] where the idea is simply to provide a different weight on the measurements according to their elongation. For each spot, the small axis would be kept, while the long axis would be rejected if truncated. This solution is the one studied and optimized hereafter

4.2

The weighted solutionoptimization of the reconstruction algorithm

HARMONI control law and MMSE regularization process

The current baseline for the tomographic reconstruction, and the one that has been implemented and used in our simulations, is the POLC + static MMSE [START_REF] Ono | Estimation with recursive Toeplitz reconstructor structure for large-scale systems[END_REF]. It is important to highlight that all the simulations that has been done were with the same tomographic algorithm as the one that will be implemented in the RTC. This allowed us to fine tune it, and produce realistic performance estimates. In this 2 steps configuration control law, the most critical aspect is the MMSE process which rely on -Pseudo-open loop data reconstructed from LGS and DM signal -Tomographic reconstructor which accounts for priors on Cn² profile and noise statistics. In the case of elongated spots, noise statistics become no-stationary and a sub-aperture by sub-aperture variance map has to be considered with x and y values depending on the elongated size. Combining a correct noise statistics with accurate turbulence prior will ensure an optimal regularization (and thus optimal reconstruction) process for non-truncated spots and thus will lead to the best possible performance. Because of the truncation, an additional error (bias in our case) is added. The cropping solution (presented above) which simply removes all the sub-aperture affected by truncation (above a given threshold) is equivalent to simply consider an infinite noise weight (both for x and y) for the cropped sub-apertures slopes. In the following we will deal with the spot truncation by simply adding an overweight to the affected sub-aperture signal rather than simply getting rid of them. Because there is not yet any simple analytical expression to quantify the effect of the truncation we have chosen to simply treat the effect in the noise domain as an "over-elongation". It basically means that when we compute the noise variance weighed map for the MMSE we simply stretch the equivalent elongation by a given factor. If this factor is larger than 1, we simply assume in the noise variance computation that the spot are more elongated than they truly are. In other word we over-weight the noise impact in the elongation direction and thus we will reduce the impact of the slopes affected by the truncated spot in the reconstruction process. The very first implementation proposed in this paper is a linear overweight. We are currently investigating quadratic evolution in order to less affect the non-elongated data.

Definition of a downscale system

For the sake of the physical understanding of the truncation problematic and optimization and in order to speed up the simulation process, we have first decided to test the over-regularization process and to quantify its performance on a downscaled version of HARMONI. To do so, we have considered an 8m telescope case and we have modified the LGS properties in the atmosphere to ensure that we will have the same elongation effects on the telescope sub-aperture (together with the same ratio of elongation between small and large axis). This basically means putting the Sodium layer at 40km altitude rather than 90. All the other AO parameters remain the same: 0.5m sub-aperture pitch, 10x10 pixels per sub-apertures, pixel size 1" (although we also have considered other plate scale in order to study the impact of a larger pixel), LGS spot size (non elongated direction) of 1". The LGS number will vary from 3 to 12 in order to study the impact of the signal redundancy for dealing with the truncation effect.

Concerning the Sodium profile we first start with a very simple « top hat » structure for the sodium density (width varying from 0 to 30 km) and we will at the end consider the 7 typical profiles presented in Figure 3. In the following, for all the simulations a median 35 layers ESO Cn² profilehas been considered with a 0.65 arcsec seeing @ zenith and a 30° zenith angle. Finally Figure 6 is showing the signal of a [START_REF] Downing | Update on development of WFS cameras at ESO for the ELT[END_REF] LGS system for all the conditions listed above. LGS case

Flux considerations

Because we are now considering MMSE processes based on regularization aspects and balance between signal and noise, it is fundamental to work in typical flux regime (and with the correct detector characteristics in terms of RON). Concerning the LGS flux, based on several years of OAF operation [START_REF] Oberti | The AO in AOF[END_REF] at Paranal a statistic of photon return has been computed by ESO (see Figure 7). From this information, adding the HARMONI transmission and design (0.5 WFS pitch, 2ms integration time …) we obtain a mean value of 2000 photons/sub-aperture/frame and a pessimistic one of roughly 1000 photons/subaperture/frame. The latter one will be considered in the following associated with a 3e-RON detector.

Impact of LGS number

Now, using the downsized version of the ELT-HARMONI LTAO system, let us first study the impact of the number of LGS on the truncation effects. This is done for a classical POLC+MMSE reconstructor with the "classical" regularization. A top hat sodium profile is considered with various width is consider in order to mimic several conditions of spot elongation (from 0 to 25 km width). Figure 8 shows the behavior of the system for various numbers of LGS and various thickness of the Sodium layer.

Performance

Average phase Long exp. PSF First it shows that increasing the number of LGS, i.e. the diversity in the WFS signal definitely helps to directly solve the truncation problem. Whereas 3 and4 LGS case show a huge performance dependency with the Sodium thickness, increasing the LGS number to 6 and more strongly mitigate this effect. The average phase (over 5000 close loop iterations) clearly shows the bias induced by the truncation. The average phase signature is strongly correlated to the LGS relative position in the pupil. Note that the structure of the average phase will depend on the Sodium profile (in our case it is a top hat profile). It is interesting to note here that the LGS side launch configuration is both a part of the problem and of the solution. Indeed it increases the elongation by a factor 2 (w.r.t the central launch) but it also brings much more diversity in the measurements. The largest elongated data for one LGS are compensated by non (or very small) elongated data coming from the other ones.

Change the WFS orientation

It is obvious that the truncation effects are caused by the ratio FoV / elongated size. In the case of a limited number of pixels and if we want to avoid to consider very large pixel scales (for obvious problem of non- linearity and SNR issues), a simple geometric solution to directly increase this ratio is to play with the SH-WFS orientation. Indeed, having the elongation direction in the x (resp. y) axis is the worst possible case. In the HARMONI configuration the LGS geometry is fixed with respect to the WFS, therefore a sensible solution would be, for a given LGS asterism (associated to given laser projector in the pupil) to rotate each WFS in order to ensure that largest elongation always sit in the sub-aperture diagonal. In that case a direct √2 gain in FoV is directly achievable. This is illustrated in Figure 9 where the gain in performance for a rotated SH is clearly demonstrated.

Figure 9

Impact of WFS rotation with respect to the LGS elongation. [START_REF] Downing | Update on development of WFS cameras at ESO for the ELT[END_REF] LGS have been considered here.

[Left] SR vs Sodium thickness for a 0° and 45° orientation.

[Right] for a 15km Sodium width, evolutuion of the performance as a function of the WFS orientation.

When the adapted weighted process enter into the game

Let us now study the impact of a modification of the weighted map in the MMSE process in order to account for the bias induced by the truncation. To do so we consider the 4 LGS case without any rotation (in order to have strong truncation effects due to the poor WFS signal redundancy). The over weighted (also called over regularization in the figure since what is matter is the ratio between noise and signal which will automatically weighted the ration between Least Square and prior in the MMSE scheme) is evolving from 0.1 to 20.

Figure 10 Impact of the adapted weighted function to account for bias induced by truncation

Figure 10 clearly shows the benefit of having an over-weighted coefficient for the elongated direction in order to account for additional "noise" (in fact bias) brought by the truncation. The non-elongated cases are barely affected and the cases of strong elongation are clearly mitigated. In the case of 15 to 25 = km width, a factor 20 almost completely mitigate the truncation effects.

Of course this over-weighted process is a kind of ad-hoc solution since it does not rely on physical expression of the bias and it could be certainly improved by adding statistically based information on the bias induces by the truncation. This will be the object of further works.

Real profiles

Let us now consider more realistic Sodium profiles as defined in Figure 3. Again, in order to put the emphasis on the truncation effect we have considered here a 4LGS case. The SH-WFS have been rotated with a 45° angle in order to have the largest elongation in the sub-aperture diagonal. The 7 profiles have been processed and we have studied the final performance with respect to over-weighted (called in Figure 11 "over-regularization factor") coefficient. Figure 11 gathers all the results. For one single profile (the worst one in term of truncation effect) the case of non-rotated SH-WFS has also been added (dashed line in Figure 11). over-regularisation factor). The specific case of a non-rotated SH is plotted for comparison in the case of the strongest truncated profile.

The Figure shows the strong performance dispersion when a "classical" MMSE law is considered (that is without any over-weighted to account for truncation bias). The performance goes from typically 25% (even less than 5% in the case of non-rotated SH-WFS) in the case of the largest and most structured profile (so called "Top Hat Peak" and "Very wide") to 75% for the narrowest ("Single Peak"). The addition of a over-weighted coefficient (between 10 and 50, the sensitivity to this value is hopefully quite low) allows to dramatically reduce the performance dispersion and all the profiles have now more or less the same performance 72.5 ± 2.5 % whereas without the over-weighted process the mean performance computed on all the profile was only 50% with more the ± 20 % dispersion!

Real HARMONI simulations

Finally, in order to quantify the real impact on HARMONI, let us consider a full ELT size simulation with all the HARMONI features included in it. The main parameters are recalled hereafter. A 39m Telescope with 0.3 central obstruction is considered. The turbulence profile is the median 35 layers ESO profile with a global seeing at zenith of 0.65 arcsec. A 30° zenith angle is considered. [START_REF] Neichel | Reconstruction Strategies for GeMS[END_REF] LGS on a regular 35" diameter asterism are used for the high order mode WFS whereas a bright on axis natural guide star is used for Tip-tit and focus sensing (NGS optimisation is beyond the scope of this study). The LGS spots in the non-elontagated direction are supposed to have 1" FWHM. For LGS wavefront sensing, 6 SH-WFS with 0.5m pitch are considered. Each sub-aperture has 10x10 pixels with a projected size on sky of 1". The associated detector RON is 3eand a flux of 1000 photons per sub-aperture and per frame is considered. The centroiding measurement is performed thanks to a classical threshold CoG process. The AO loop embedded a POLC+MMSE control scheme. It runs at 500Hz with a 2 frame delay. For each simulation the same turbulent seeds have been used (so that each result can be directly compare to the other without worrying about convergence issues) and 1000 loop iterations have been considered to compute SR. Finally the 7 typical Sodium profiles are used and performance is estimated for each of them.

The results have been plotted in Figure 12.

Figure 12

Performance as a function of the over-weighted coefficient for a full scale ELT case ( 6LGS) and the 7 profiles. Without over-weighted the average SR (on the 7 profiles) is 62% ± 5% with a factor 10 it goes up to 68% ± 2% whereas the non-elongated case is 71%

Figure 12 shows that, as already demonstrated on the downsized case, the over-weighted coefficient helps in reaching the ultimate performance of the tomography while reducing the dispersion of the results due to the various Sodium profiles. In the case of non-elongated spot, the ultimate performance will be 71%. For elongated case and a classical POLC+MMSE control law the final performance is, in average, 62% associated to a dispersion from a Sodium profile to another of 5%. If a 10 over-weighted coefficient is considered, the average performance goes up to 68% with a dispersion of less than 2%. Finally, if we increase the number of pixel in the WFS (from 10x10 to 14x14), without any adjustment of the MMSE coefficient, a 70% ± 1 % is reached. The final results for HARMONI are gathered in table 1.

CONCLUSION: TOWARD A BASELINE FOR ELT LGS-ASSISTED INSTRUMENTS

This paper presents an analysis of the spot elongation problem for Laser assisted tomographic system on the ELT. The problem is described as well as several solutions (both from the opto-mechanical and the control point of view) to deal with it. A specific solution, using classical SH-WFS has been thoroughly studied. It is based on existing concepts (both from optics and pixel processing point of view) and does not require any specific development. It is therefore shown that, by just adjusting the WFS orientation and playing with the MMSE weighted noise map, it is possible to dramatically reduce the bias effect induced by the truncation. This will allow us to dramatically reduce the risk associated to this particular effect. It will simplify the requirements on our truth sensor especially in terms of temporal frequency.

From the various study proposed in this paper, a baseline for the HARMONI LGS WFS can be derived  More than 10x10 pixels per sub-aperture. Ideally 14x14 pixels wich corresponds for a 78x78 sub-aperture system to 1100x1100 pixels. This is compatible with the C-MORE camera (see [START_REF] Oberti | LGS tomography and spot truncation: tips and tricks[END_REF])  A Pixel size between 1" -1.25". Considering the current AOF measurements of the LGS spot size, 1.25" seems to be a good compromise  A WFS orientation with sub-aperture diagonal in the LGS maximum elongation The 3 combined items will lead to a "effective" FoV of 24.5" which will be more than sufficient to accommodate any spot elongation produced by the sodium layer structures. It should therefore ensure a bias free and efficient tomographic process. On top of that, as a risk mitigation aspect and for the sake of robustness, an adapted reconstructed algorithm with a slightly over-weighted of the most elongated sub-aperture. This will be completed by a low frequency truth sensor (working on a very faint natural guide star and coupled with our fast Tip-Tilt Focus sensor) which will measure any LGS slowly variable non-common path aberrations (including any residual aberrations induced by the truncation effects). Finally, if there is still an issue with the large format detector and only smaller detector (< 800x800) would have been available, the several solutions proposed in this paper could be implemented and combined to further improve the robustness of the system to spot elongation: -Implement fancy tilted µlenses in order to avoid spot overlap and to maximise the detector fill factor. Spoof concept.

-

Increase the spot size up to 2 arcmin together with the increase of the Laser FWHM. The price to pay is here a loss in SNR for ALL the WFS sub-apertures [START_REF] Gach | C-MORE: the laser guide star wavefront sensor[END_REF] And for future systems (next generation of Laser assisted tomographic system on the ELT) a change of WFS concepts may be an attractive path to follow. In particular Fourier-Filtered WFS (Pyramid like, Ingot concept ...) seems to be a promising path for dealing with the spot elongation with a minimal number of pixel [START_REF] Ragazzoni | Extending the pyramid WFS to LGSs: the INGOT WFS[END_REF].

Figure 4 4 . 1

 441 Figure 4 Simulation of the spot elongation on the LGS WFS and phase reconstruction process through tomography (without turbulence) to show the wavefront bias induced by the truncation itself. 6 LGS have been simulated. A NGS is considered to measure and compensate for Tip-Tilt and focus terms. The Sodium profile number 4 (one of the most problematic from the truncation point of view) is considered here

Figure 5

 5 Figure 5 reduction of the bias induced by truncation thanks to the cropping of the most elongated part of each SH-WFS Thanks to the redundancy of the measurements, and the fact that in a side-launch configuration, the elongated spots of one WFS corresponds to the non-elongated spots of another WFS. It is shown that this solution, for the HARMONI configuration and 10"x10" FoV SH-WFS, allows reducing the bias induced by truncation down to a

Figure 6

 6 Figure 6Example of a the downsized system for a 4LGS case

Figure 8 [

 8 Figure 8 [Left] performance of the LTAO system for various number of LGS (3 to 12) and various Sodium Layer thickness. SR has been computed from the average of 5000 loop iteration. [Middle] average phase over the 5000 loop iterations for 3, 4, 6 and 12 LGS and a 20km Na thickness case. The bias induced by the truncation effect is clearly visible. [Right] longexposure PSF computed for the same conditions than the average phases.

Figure 7

 7 Figure 7 several years of Flux return statistics with AOF.

Figure 11

 11 Figure 11 Performance of a 4 LGS tomographic reconstruction for nominal turbulence condition (as defined by ESO for the ELT) and for 7 sodium profiles (single peak and very narrow are superimposed). SH-WFS have been rotated so that elongated spot are aligned with sub-apertures diagonals. Performance is plotted w.r.t the over-weighted coefficient (a.k.a.over-regularisation factor). The specific case of a non-rotated SH is plotted for comparison in the case of the strongest truncated profile.

Table 1

 1 Summary of HARMONI LTAO performance in presence of elongation for several SH-WFS and MMSE control law configurations

	10x10 pixels	10x10pixels -« opt reg » 14x14 pixels	No elongation
	62 ± 5 %	68 ± 2 %	70 ± 1 %	71%

ACKNOWLEDGMENTS

This work has been done in the frame of the HARMONI project. The authors would like to warmly thank all the member of the HARMONI team for their contributions. This work has also been partially funded by the WOLF ANR project (ANR-18-CE31-0018-01), the H2020 Opticon program (grant number 730890), and the LABEX FOCUS


Denis Machon
email: denis.machon@univ-lyon1.fr

Laurence Bois

Défi Jr

Jubgang Fandio

Quentin Martinet

Alexis Forestier

Sylvie Le Floch

Jérémie Margueritat

Vittoria Pischedda

Denis Morris

Lucien Saviot

Revisiting Pressure-Induced Transitions in Mesoporous Anatase TiO2

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Introduction

Mesoporous materials may be an alternative to nanoparticle-based materials for manufacturing (obtaining ceramics from powders of nanoparticles keeping the interesting related properties) and health implications (nanotoxicology). The high surface-to-volume ratio in both cases enhances the properties related to surface effects such as catalysis, Li insertion, reactivity, batteries and supercapacitors [START_REF] Ye | Functional Mesoporous Materials for Energy Applications: Solar Cells, Fuel Cells, and Batteries[END_REF][START_REF] Wang | The Preparation and Application of Mesoporous Materials for Energy Storage[END_REF] . In addition, as in nanoparticles, interfaces and point defects at the surface of mesoporous materials induce additional contributions to the total energy of the system, leading to a new energy landscape that modifies phase stabilities and promotes emergence of new phases with potentially interesting properties.

Following the same interest of using high pressure on nanoparticles [START_REF] Tolbert | High-Pressure Structural Transformations in Semiconductor Nanocrystals[END_REF][START_REF] Machon | Perspective: High pressure Transformations in Nanomaterials and Opportunities in Material Design[END_REF] , the thermodynamics of mesoporous materials can be explored by means of pressure-induced transformations.

Understanding phase stabilities in materials with high surface-to-volume ratio is a key to control the properties associated with the new engineered structures. Thus, the exploration of the energy landscapes during compression can lead to polymorphic transition, transformation to metastable state and polyamorphism [START_REF] Machon | Pressure-Induced Amorphization and Polyamorphism: Inorganic and Biochemical Systems[END_REF] . For instance, mesoporous silicon and germanium undergo pressure-induced amorphization on compression and a poly-amorphic transformation during subsequent decompression [START_REF] Deb | Pressure-Induced Amorphization and an Amorphous-Amorphous Transition in Densified Porous Silicon[END_REF][START_REF] Boucherif | Metastable States in Pressurized Bulk and Mesoporous Germanium[END_REF] . TiO 2 is a major oxide material because its properties are essential for many applications [START_REF] Chen | Titanium Dioxide Nanomaterials: Synthesis, Properties, Modifications, and Applications[END_REF] but it is also a typical example of material in which interfaces dictate the phase stability [START_REF] Machon | Interface Energy Impact on Phase Transitions: The Case of TiO 2 Nanoparticles[END_REF] . The interplay between the morphology (nanoparticles, nanowire, nanoribbons) and the crystallographic structure illustrates the influence of the interface on the phase diagram [START_REF] Wang | The Preparation and Application of Mesoporous Materials for Energy Storage[END_REF][START_REF] Li | Morphology-Tuned Phase Transitions of Anatase TiO 2 Nanowires under High Pressure[END_REF][START_REF] Li | Pressure-Induced Amorphization and Polyamorphism in One-Dimensional Single-Crystal TiO 2 Nanomaterials[END_REF][START_REF] Machon | Pressure-Induced Phase Transitions in TiO 2 Rutile Nanorods[END_REF] .

The stable structure in bulk TiO 2 is the rutile-type one. Under increasing pressure, the thermodynamic sequence corresponds to the following set of structures: rutile -α-PbO 2baddeleyite. The first phase transition was reported at 2.6 GPa 13 , 7 GPa 14 , 10 GPa [START_REF] Arashi | Raman Spectroscopic Study of the Pressure-Induced Phase Transition in TiO 2[END_REF] and the second one at 15 GPa [START_REF] Arashi | Raman Spectroscopic Study of the Pressure-Induced Phase Transition in TiO 2[END_REF] . However, often the intermediate α-PbO 2 phase is bypassed and a direct rutile-to-baddeleyite transformation can be observed at ~12 GPa [START_REF] Sato | Baddeleyite-Type High-Pressure Phase of TiO 2[END_REF][START_REF] Gerward | Post-Rutile High-Pressure Phases in TiO 2[END_REF] . The variability observed on the pressure-induced transformations is connected to kinetics that could be related to crystallographic relationships between the structures [START_REF] Machon | Pressure-Induced Phase Transitions in TiO 2 Rutile Nanorods[END_REF] . During decompression, the baddeleyite structure transforms into α-PbO 2 phase at around 7 GPa. This phase is preserved in a metastable state down to ambient pressure [START_REF] Gerward | Post-Rutile High-Pressure Phases in TiO 2[END_REF] .

At the nanoscale, there is a crossing of phase stability because the surface energy favors the anatase structure usually observed in nanoparticles [START_REF] Navrotsky | Energetics of Nanoparticle Oxides: Interplay between Surface Energy and Polymorphism[END_REF] . High-pressure experiments on such samples have shown that the anatase structure is preserved up to 18 GPa before transforming to the high-pressure baddeleyite structure [START_REF] Machon | Interface Energy Impact on Phase Transitions: The Case of TiO 2 Nanoparticles[END_REF][START_REF] Popescu | Compressibility and Structural Stability of Nanocrystalline TiO 2 Anatase Synthesized from Freeze-Dried Precursors[END_REF] . An interesting phenomenon has been evidenced for nanoparticles smaller than 10 nm. Under pressure, the initial crystalline structure undergoes transformation to an amorphous state, a transition that is absent in the case of bulk TiO 2 . This size-dependent pressure-induced amorphization has been extensively investigated [START_REF] Pischedda | Ultrastability and Enhanced Stiffness of ∼6 nm TiO 2 Nanoanatase and Eventual Pressure-Induced Disorder on the Nanometer Scale[END_REF][START_REF] Swamy | Size-Dependent Pressure-Induced Amorphization in Nanoscale TiO 2[END_REF] together with poly-amorphic transformations [START_REF] Machon | Pressure-Induced Polyamorphism in TiO 2 Nanoparticles[END_REF] . The amorphization has been shown to result from the density of defects at the surface which increases the interface energy [START_REF] Machon | Interface Energy Impact on Phase Transitions: The Case of TiO 2 Nanoparticles[END_REF][START_REF] Machon | Size-Dependent Pressure-Induced Amorphization: a Thermodynamic Panorama[END_REF] .

The synthesis of mesoporous materials is a means of creating interfaces and defects, and the mesoporous materials may be considered as the negative image of a collection of nanoparticles [START_REF] Boucherif | Metastable States in Pressurized Bulk and Mesoporous Germanium[END_REF] . A question that arises is whether the surface energy component of mesoporous materials is equivalent to that of a collection of nanoparticles and leads to similar metastable states. If the surface area can be considered equivalent, the curvature of the interface at the nanoscale is different and may lead to other effects [START_REF] Boucherif | Metastable States in Pressurized Bulk and Mesoporous Germanium[END_REF] .

Mesoporous rutile TiO 2 has been studied under high pressure [START_REF] Li | Stability and Phase Transition of Nanoporous Rutile TiO 2 under High Pressure[END_REF] . A transformation to the baddeleyite phase started at 10.8 GPa and was completed at ~26.1 GPa. The rather low transition pressure has been attributed to microscopic strains that develop into the porous structure. This point has been discussed in ref [START_REF] Boucherif | Metastable States in Pressurized Bulk and Mesoporous Germanium[END_REF] . In the case of nanoparticles, the stress can be distributed continuously and smoothly over the spherical shape. On the contrary, discontinuities in the mesoporous network with hyperbolic geometry will lead to inhomogeneities in the stress distribution. During decompression, the baddeleyite phase transformed into the α-PbO 2 structure below ~6 GPa [START_REF] Li | Stability and Phase Transition of Nanoporous Rutile TiO 2 under High Pressure[END_REF] . Surprisingly, the mesoporous structure remained intact after a complete pressure cycle. According to the authors, this could be due to the invasion by the liquid pressure-transmitting medium (mixture of ethanol and methanol).

Mesoporous TiO 2 with anatase-type structure was been studied by the same group by Raman spectroscopy [START_REF] Li | High Pressure Behaviors of Nanoporous Anatase TiO 2[END_REF] . They reported a phase transition from anatase to baddeleyite in the range 15-18 GPa followed by a reversible pressure-induced amorphization (PIA) above 20.5 GPa. On decompression, the α-PbO 2 phase is obtained. Despite this interesting result, the role of porosity is not yet clearly defined because the nature of the porous material was ill-defined.

Their sample consisted of an agglomeration of 30 nm-diameter particles "constructing a nanoporous structure", according to the authors [START_REF] Li | High Pressure Behaviors of Nanoporous Anatase TiO 2[END_REF] . However, neither pore size distribution nor the porosity were clearly mentioned. This information is mandatory, as the impact of the morphology is still not clear. For instance, in 1D nanostructures, it appears that the initial phase at ambient pressure is the main factor influencing the pressure-induced transitions sequence rather than morphology [START_REF] Machon | Pressure-Induced Phase Transitions in TiO 2 Rutile Nanorods[END_REF] .

In the present work, we want to clarify the possible role played by the mesostructure on the pressure-induced polymorphism. Therefore, the first part of this article is devoted to characterizing the texture of the mesoporous material with highlights on the key information provided by a given set of spectroscopic techniques (Terahertz, Brillouin and Raman). The second part deals with the pressure-induced evolution monitored using Brillouin and Raman spectroscopies. A comparison with the results obtained on 7-nm nanoparticles is done and it is shown that the interface effects are very similar in both cases.

Experimental

Mesoporous titania samples were prepared by a sol-gel process with the evaporation induced self-assembly method proposed by Brinker et al. [START_REF] Brinker | Evaporation-Induced Self-Assembly: Nanostructures Made Easy[END_REF] . The poly(ethylene oxide)poly(propylene oxide)-poly(ethylene oxide) triblock copolymer (P-123, (EO) 20 -(PO) 70 -(EO) 20 )) was used as the template and Ti(OBu n ) 4 as the inorganic precursor [START_REF] Liu | Preparation of Large-Pore Mesoporous Nanocrystalline TiO 2 Thin Films with Tailored Pore Diameters[END_REF][START_REF] Soler-Illia | Synthesis and Characterization of Mesostructured Titania-Based Materials through Evaporation-Induced Self-Assembly[END_REF] .

A solution of P-123 (1 g) in ethanol (12 g) is added to a solution of Ti(OBu n ) 4 (3.4 g) in concentrated HCl (3.2 g). The solution is heated at 50 °C for 2 days, and the obtained solid is calcinated at 350°C for 2 h, with a heating ramp of 1 °C min -1 . The detailed synthesis has been reported elsewhere [START_REF] Bois | Chemical Growth and Photochromism of Silver Nanoparticles into a Mesoporous Titania Template[END_REF][START_REF] Couzon | Electrochemical Observation of the Plasmonic Effect in Photochromic Ag Nanoparticle Filled Mesoporous TiO 2 Films[END_REF] .

Characterization of the texture was realized using nitrogen adsorption/desorption isotherms on a BelsorpMini (Bel Instruments, Japan). Prior analysis, samples were outgassed under vacuum (100°C for 4 h). The pore size distribution (max radius) and the mesoporous volume were calculated from the adsorption branch of the isotherms using the Barrett-Joyner-Halenda (BJH) method. The total porous volume was measured at P/P 0 =0.98. TEM pictures were acquired on a Topcon instrument operating at 200 kV in the "Institut Lumière Matière". Prior to the observations, the sample was ground and deposited directly on a copper grid coated with a holey carbon film.

Raman spectra were obtained using a LabRAM HR Evolution Raman Spectrometer (Horiba Scientific) using an excitation wavelength of 532 nm. This spectrometer is equipped with a commercial ultralow frequency module allowing to reach frequency as low as 7 cm -1 .

The laser excitation power was limited to 5 mW at the entrance of the diamond anvil cell (DAC) to avoid heating. The beam was focused on the sample using a long working distance (21 mm) 50x objective, with beam diameter ~2 μm at the surface of the sample. The scattered light was collected using the same objective (back-scattering geometry).

Micro-Brillouin experiments were carried out with a homemade setup that combines a tandem Fabry-Perot interferometer equipped with a photomultiplier tube with an inverted confocal microscope. The Brillouin spectrometer is coupled to a solid-state laser source emitting at 532 nm. The laser power was limited at 10 mW to avoid damaging the sample.

Measurements were done in the backscattering geometry using a 50X long working distance microscope objective.

The THz-TDS setup was coupled to a Ti:sapphire oscillator which delivers 70 fs laser pulses centered at 790 nm at a 82-MHz repetition rate. The laser beam was split into two distinct parts, an excitation beam used to generate the broadband THz radiation and a probing beam used to detect THz pulses transmitted through the sample. A home-made GaAs photoconductive antenna has been used as the THz source. This antenna has been illuminated with a laser beam power of about 50 mW. Hemispherical silicon lenses, with a 4-mm diameter, were used to collect and refocus the THz radiation. The THz-probe beam was confined in a moisture-free environment (pressure <1 mbar) and a four off-axis parabolic mirrors configuration was used. The THz radiation was focused on the sample surface on a spot diameter of about 2 mm. The transmitted THz pulses were detected using electro-optic sampling in a 0.5-mm-thick ZnTe crystal. The THz-probe beam was chopped at 1350 Hz and the THz signal was measured by means of a lock-in amplifier. All measurements were made at room temperature 31 .

High pressure was generated using a membrane DAC with low-fluorescence diamonds.

Mesoporous TiO 2 samples were placed into a 125 μm chamber drilled in an indented stainless-steel gasket. Paraffin oil was used as the pressure-transmitting medium (PTM). With this PTM hydrostaticity is ensured up to 4-5 GPa 32 . The pressure was probed by the shift of the R1 fluorescence line of a small ruby chip. The N 2 adsorption/desorption isotherms and BJH plots are shown in figure 3. The physisorption isotherms correspond to type IV and the hysteresis to type H2 according to the IUPAC classification 33 . This behavior is characteristic of a mesoporous material. The pore size distribution (BJH) is centered at 5 nm in agreement with the TEM images (Figure 2). The mesoporous volume is estimated at 0.26 cm 3 /g. By using the density of anatase (d = 4.23 g/cm [START_REF] Tolbert | High-Pressure Structural Transformations in Semiconductor Nanocrystals[END_REF] ), this gives a porosity ε ~52%. This corresponds to the open porosity, which is a lower limit of the total porosity of the sample.

Results and discussion

Sample characterization at ambient conditions

Total porosity is estimated using two distinct spectroscopic methods. Brillouin spectroscopy probes the sound velocity in a material through its light scattering spectrum, and terahertz spectroscopy probes dielectric properties of the material using a transmission configuration. The knowledge of the sample thickness and the delay Δt = 11.528 ps between the maxima of these THz traces makes it possible to extract the group refractive index of the mesoporous film. The estimated value, n = 2.73, lies somewhere between the refractive index of air (n air =1) and the one of bulk TiO 2 (N = 5.84) at THz frequencies [START_REF] Siefke | Materials Pushing the Application Limits of Wire Grid Polarizers Further into the Deep Ultraviolet Spectral Range[END_REF] . These spectroscopic data can be analyzed using an effective medium approximation. The Maxwell-Garnett and the Bruggeman models [START_REF] Markel | Introduction to the Maxwell Garnett Approximation: Tutorial[END_REF] are commonly used to treat such systems. In our case, as the estimated porous fraction being comparable to that of the host material, the Bruggeman approximation is well adapted. The effective refractive index n is related to the porosity ε through the following equation 36 :

) 1 ( 3 ) 2 )( 1 ( 1 2 2 2 2 2 N n n N n       , ( 1
)
where N is the refractive index of the bulk material. Using this equation, the porosity is estimated at ε~ 57%.

Brillouin spectroscopy measurements

The Brillouin spectrum of the mesoporous film is presented in figure 5. The observed peak is centered at ν B =18 GHz. The Brillouin frequency is given by

    ) ( ) ( 2 V n B  (2)
Where n(ε) is the effective refractive index and ) ( V is the sound velocity in the material.

The function

) ( V
is unknown for TiO 2 but in the case of porous silicon, it has been shown

that m V V ) 1 ( ) ( 0     with m = 1.

Raman Spectroscopy measurements

Raman spectrum of as-made mesoporous TiO 2 sample is shown in figure 6. Five Raman peaks are measured in the range 60-800 cm -1 and are assigned to the anatase structure [START_REF] Ohsaka | Spectrum of Anatase, TiO 2[END_REF] . In bulk TiO 2 anatase, the vibrational representation of the normal modes at the center of the Brillouin zone is given by

u g u g u g vib E E B B A A 2 3 2 2 1 2 1       
Only the modes A 1g , B 1g and E g are Raman active. The peak positions were measured at 144 cm -1 (E g ), 197 cm -1 (E g ), 400 cm -1 (B 1g ), 507 cm -1 (A 1g ), 519 cm -1 (B 1g ) and 640 cm -1 (E g ).

It is interesting to note that the E g mode at 197 cm -1 is clearly visible. This indicates that there is no optical phonon confinement effect for the optical phonons, contrary to what is observed in the case of nanoparticles (see Supp info 31 ). However, additional low-frequency features are observed similarly to what is observed in TiO 2 nanoparticles [START_REF] Pighini | Low-Frequency Raman Characterization of Size-Controlled Anatase TiO 2 Nanopowders Prepared by Continuous Hydrothermal Syntheses[END_REF] . These peaks are associated with the anatase structure as they are sensitive to phase transitions as shown in the following section dedicated to high-pressure transformations. In the case of TiO 2 nanoparticles, a single low-frequency peak attributed to confined acoustic phonons is generally observed and is assigned to the fundamental quadrupolar mode (spheroidal vibration with angular momentum l = 2 noted 1 2 S ) [START_REF] Pighini | Low-Frequency Raman Characterization of Size-Controlled Anatase TiO 2 Nanopowders Prepared by Continuous Hydrothermal Syntheses[END_REF] .

In our spectrum, two low-frequency peaks are observed at ~12.6 cm -1 and ~22.7 cm -1 . In a simple approach, these peaks would correspond to anatase nanospheres with radius 4.8 and 8.7 nm, respectively. However, our mesoporous samples are not made of stacked nanoparticles but correspond to a nanosponge-like structure according to the TEM images (Figure 2). Therefore, we compared these frequencies with those of quadrupolar-like vibrations calculated [START_REF] Saviot | Vibrations of Single-Crystal Gold Nanorods and Nanowires[END_REF] for other nanostructure shapes that can match the TEM images. The diameters for isotropic anatase TiO 2 spheres, shells, cylinders and tubes having a quadrupolarlike vibration at 12.6 and 22.7 cm -1 are given in Table S1 31 . For simplicity, the inner diameter for the empty spheres and tubes was fixed at 5.3 nm according to the TEM images (Figure 2).

In this approach, we neglect the mechanical coupling between adjacent sub-structures of the porous material. Using this simple picture, the 22.7 cm -1 low-frequency peak can be assigned to vibrations of any of these structures. The calculated diameters match at least approximately the sizes observed in the TEM images. On the contrary, the diameters required to reproduce the 12.6 cm -1 peak are about twice as large and do not match with features observed in the TEM images. Therefore, this low-frequency peak is difficult to assign in this simple approach.

Raman features at frequencies lower than those of quadrupolar-like vibrations appear when a mechanical coupling between neighbor nanostructures exists. This has already been observed for coupled nanospheres [START_REF] Girard | Mechanical Coupling in Gold Nanoparticles Supermolecules Revealed by Plasmon-Enhanced Ultralow Frequency Raman Spectroscopy[END_REF] . Therefore, the 12.6 cm -1 peak may be assigned to such coupled vibrations. However, a precise description of the porous nanostructure is required to reproduce this frequency numerically. This goes beyond the scope of this work. Still, the previous assignment will be used in the following: modifications (or the lack thereof) of the low-frequency spectra will be related to changes (or the lack thereof) of the mesoporous structure.

High-pressure experiments on mesoporous TiO 2

Brillouin spectroscopy measurements

Brillouin spectroscopy is compatible with the high-pressure environment and it is possible to follow the Brillouin peak of mesoporous TiO 2 in situ as a function of pressure (Figure 7a).

Peak position was monitored up to 12 GPa. In this pressure range, the structure remains the anatase-type one according to Raman spectroscopy experiments reported in the next section.

The Brillouin peak position is plotted as a function of the pressure in figure 7b, along with the corresponding porosity obtained from equation 2. The value of the porosity decreases rapidly with the increasing pressure and reaches 20-25% at high-pressure. During decompression, the porosity shows some reversibility. This is in agreement with the results obtained on pressurecycled mesoporous rutile TiO 2 [START_REF] Li | Stability and Phase Transition of Nanoporous Rutile TiO 2 under High Pressure[END_REF] for which TEM analysis before and after the pressure cycle showed that the porosity is preserved even after a treatment at 38.8 GPa. This effect has been attributed to the penetration of the pressure-transmitting medium (PTM) into the mesopores.

The PTM used in ref [START_REF] Li | Stability and Phase Transition of Nanoporous Rutile TiO 2 under High Pressure[END_REF] was an alcohol mixture and in our case, it was a paraffin oil, a more viscous liquid. However, a parameter that determined the penetration of the liquid is the wettability and titania has shown little resistance to complete wetting of paraffin oil [START_REF] Nowak | A Comparison of Contact Angle Measurement Techniques Applied to Highly Porous Catalyst Supports[END_REF] . In addition, moderate pressures (compared to those applied in the present study) increase wettability [START_REF] Nowak | A Comparison of Contact Angle Measurement Techniques Applied to Highly Porous Catalyst Supports[END_REF] . In conclusion, as in ref [START_REF] Li | Stability and Phase Transition of Nanoporous Rutile TiO 2 under High Pressure[END_REF] , it can be assumed that the preservation of the porosity during pressure cycling may be due to the invasion of the mesopores by the liquid pressure transmitting medium.

Raman spectroscopy measurements

The evolution of the Raman spectra of mesoporous TiO 2 as the pressure increases up to 28.3 GPa are shown in figure 8. Up to ~13 GPa, no change is observed except for the usual blue shift of the Raman peaks. Pressure-induced evolutions of the Raman frequencies are reported in Figure S3 31 along with those obtained for nanoparticles (7 nm diameter) and ab initio simulations [START_REF] Saviot | Optical and Acoustic Vibrations Confined in Anatase TiO 2 Nanoparticles under High-Pressure[END_REF] . At ~17-18 GPa, new peaks appear and develop with increasing pressure. Phase transformation is only complete above ~25 GPa. The Raman bands of the high-pressure phase are weak and broad, indicating the appearance of a significant degree of disorder. However, contrary to previous report on mesoporous anatase TiO 2 [START_REF] Li | High Pressure Behaviors of Nanoporous Anatase TiO 2[END_REF] , a total amorphization of the film is not observed in our experiments, above 20.5 GPa. Comparison of the spectrum obtained at the highest pressure in this run to that obtained on TiO 2 nanoparticles (7 nm diameter) at similar pressure is shown in figure 9. The high-pressure phase in nanoparticles has been identified as the baddeleyite structure by synchrotron X-ray diffraction [START_REF] Machon | Interface Energy Impact on Phase Transitions: The Case of TiO 2 Nanoparticles[END_REF] . In the case of the mesoporous sample, the spectrum is similar but shows a higher degree of disorder, maybe a coexistence of amorphous and crystalline regions. This apparent disordering may be due to internal stresses and inhomogeneous stress field because of the mesoporous morphology, as discussed in ref [START_REF] Boucherif | Metastable States in Pressurized Bulk and Mesoporous Germanium[END_REF] .

The impact of a non-homogeneous stress field on the phase transition and the genesis of complex nanostructure results from a competition between polymorphic transition and amorphization. The balance between the amorphous and crystalline domains depends on the surface and the associated defects [START_REF] Machon | Size-Dependent Pressure-Induced Amorphization: a Thermodynamic Panorama[END_REF] .

The low-frequency Raman spectra of mesoporous TiO 2 under pressure are shown in figure 8.

The low-frequency peak shows very little change (linear variation of ~0.06 cm -1 .GPa -1 ) up to ~25 GPa, which corresponds to the end of the transformation from the anatase to the disordered baddeleyite phase. This low pressure-dependency of the peak position was also observed for confined acoustic waves in TiO 2 nanoparticles in agreement with ab initio calculations [START_REF] Saviot | Optical and Acoustic Vibrations Confined in Anatase TiO 2 Nanoparticles under High-Pressure[END_REF] . The peak initially located at 22.7 cm -1 has a larger variation under pressure (~0.5 cm -1 .GPa -1 ) up to 10 GPa. Above this pressure, the pressure-induced change has a plateau (Figure 10). This behavior seems to be correlated with the behavior of the Brillouin peak under pressure (figure 7), an observation that supports the possibility that this lowfrequency Raman peak is related to the porous nature of the sample. The disappearance of these two peaks across the transition indicates that they are related to the initial anatase structure. Raman spectra were recorded during decompression (Figure 11). The disordered baddeleyite structure is observed down to ~15 GPa. New features are observed at P = 7.6 GPa. It is worth noting that the spectrum at 7.6 GPa differs from the one at 3.7 GPa, indicating the appearance of an intermediate structure. Such an observation is similar to the report of an intermediate phase during decompression of anatase nanoparticles or rutile nanorods after a pressure cycle [START_REF] Machon | Interface Energy Impact on Phase Transitions: The Case of TiO 2 Nanoparticles[END_REF][START_REF] Machon | Pressure-Induced Phase Transitions in TiO 2 Rutile Nanorods[END_REF] . Comparison of spectra of nanoparticles and mesoporous TiO 2 after a pressure cycle is shown in figure 9. The similarity of the Raman spectra indicates that the low-pressure phase corresponds to the α-PbO 2 structure. Interestingly, the peaks of the mesoporous sample are narrower than those of the nanoparticles despite an apparent higher degree of disorder of the high-pressure phase. This reinforces our interpretation that the internal stress distribution is highly inhomogeneous because of the hyperbolic geometry of a mesoporous structure [START_REF] Boucherif | Metastable States in Pressurized Bulk and Mesoporous Germanium[END_REF] . On decompression, these stresses are relaxed and there is no broadening effect as it is the case for nanoparticles. The low-frequency Raman spectra during decompression show a re-emergence of the signal below 20.8 GPa. The signal gains intensity and shifts towards low frequencies. This signature indicates that the porosity is partially preserved during the pressure cycle, even after the phase transformation. This effect has also been discussed in the section dealing with the in-situ Brillouin measurements and is in agreement with the literature as well as the results obtained on porous rutile TiO 2 [START_REF] Li | Stability and Phase Transition of Nanoporous Rutile TiO 2 under High Pressure[END_REF] . Since the peak position depends on the sound velocity, the observed shifts may be due to phase transitions that affect the mechanical properties of the materials, especially those of the α-PbO 2 phase. Phase transitions during compression and decompression are very similar to what happens in nanoparticles. First, as in the case of pressure-induced phase transitions in nanoparticles, the intermediate α-PbO 2 phase is not observed on the compression path, whereas bulk anatase can transform to this phase prior to the baddeleyite structure. Secondly, the shift to a higher pressure of the anatase-to-baddeleyite transition for mesoporous anatase is similar to the case of 7-nm diameter particles, as well as the sequence of phase transitions on the decompression path. In the case of nanoparticles, the interface increases the total energy of the system and the pressurization of the nanoparticles leads to the observation of several metastable states as previously reported [START_REF] Machon | Pressure-Induced Polyamorphism in TiO 2 Nanoparticles[END_REF] . Porosification also creates these interfaces that affect phase transformations. Consequently, our experimental observations can be described using a classical thermodynamics approach that includes additional interface energy [START_REF] Piot | Amorphization in Nanoparticles[END_REF] . In the case of mesoporous samples, by analogy with the nanoparticles, the Gibbs energy is upshifted because of the contribution of this interface energy as was discussed for porous Ge 7 .

Conclusions

Anatase TiO 2 mesoporous material was studied under high-pressure. First, an extensive study of the mesoporous texture, especially, the porosity was carried out using different techniques, TEM, Terahertz, Brillouin and Raman spectroscopies. They indicate that the pores have an average size of 5 nm. The porosity at ambient conditions is about 60%.

Upon compression, Brillouin spectroscopy indicates that porosity changes rapidly with increasing pressure and shows a high degree of reversibility during the pressure cycle, mainly in absence of phase transitions (when pressurized up to 12 GPa and decompressed). A phase transition is observed to a disordered baddeleyite structure. The transition starts at ~15 GPa and is completed at ~25 GPa. The high-pressure evolution of the mesoporous TiO 2 is very similar to the nanoparticles of TiO 2 with size of 7 nm. This similarity indicates that the interface energy controlling the phase stability has the same magnitude in both nanostructures.

Therefore, mesoporous samples are a good alternative to nanoparticles in applications requiring a large area.

Supporting Information.

Schematic view of the TeraHertz-Time Domain Spectroscopy set-up; Comparison of Raman spectra of mesoporous and nanoparticles of anatase TiO 2 ; Calculation of the quadrupolar-like vibration frequency for various shapes; Comparison of the pressure-induced variations of the Raman-active modes for nanoparticles, mesoporous TiO 2 and ab initio simulations.

  X-ray diffraction pattern is shown in figure 1. It can be indexed using the anatase-type structure (space group No 141 -amd I / 4 1 ) with a ~ 3.78 Å and c ~ 9.51 Å. No preferred orientation can be deduced from the intensity analysis.

Figure 1 -

 1 Figure 1 -X-ray diffraction of mesoporous TiO 2 . The data is indexed using the anatase-type structure with a = 3.78 Å and c = 9.51Å.

Figure 2 -Figure 3 -

 23 Figure 2 -Transmission Electron Microscopy images of mesoporous titania films with (a) low and (b) high magnification

Figure 4

 4 Figure 4 compares the waveform of the THz pulses propagating in the vacuum (reference trace, black line) to that of the pulses transmitted through a 2 mm-thick porous TiO 2 sample.

Figure 4 -

 4 Figure 4 -THz pulse for both reference and 2-mm-thick porous TiO 2 sample.

  083 where V 0 is the sound velocity in the bulk material (V 0 = 8367 m.s -1 for anatase TiO 2 )[START_REF] Fan | Brillouin Spectroscopy of Acoustic Modes in Porous Silicon Films[END_REF] . Using this relation and the Bruggeman equation (N = 2.6 at λ = 532 nm) giving n(ε) as in the case of the terahertz spectroscopy, one finds n = 1.58 and a porosity ε ~ 60% in very good agreement with the THz spectroscopy results.

Figure 5 -

 5 Figure 5 -Brillouin spectrum of mesoporous TiO 2 .

Figure 6 -

 6 Figure 6 -Raman spectrum of porous TiO 2 . The inset shows the low-frequency range where confined acoustic phonons give rise to additional features.

Figure 7 -

 7 Figure 7 -(a) Brillouin spectra as a function of pressure during compression (up to 12 GPa)/decompression cycle; (b) peak position along with the corresponding porosity as a function of pressure on compression (full symbols) and decompression (open symbols).

Figure 8 -

 8 Figure 8 -Selection of Raman spectra of mesoporous TiO 2 with increasing pressure for (a) the extended 0-950 cm -1 range (b) the low-frequency range -70;+70 cm -1

Figure 9 -

 9 Figure 9 -Comparison of Raman spectra of a powder of TiO 2 nanoparticles (7-nm diameter) (from Ref 9 ) and mesoporous TiO 2 at (a) high pressure (b) after pressure cycle.

Figure 10 -

 10 Figure 10 -Pressure-induced evolution of a low-frequency Raman mode.

Figure 11 -

 11 Figure 11 -Raman spectra of mesoporous TiO 2 with decreasing pressure for (a) the extended 0-950 cm -1 range (b) the low-frequency range -70;+70 cm -1

Acknowledgment

Authors would like to warmly thank Fernand Chassagneux for the TEM images and for fruitful discussions.


Francois Parcy
email: francois.parcy@cea.fr

Francois Parcy

Francois Parcy

Xuelei Lai

Hicham Chahtane

Raquel Martin-Arevalillo

Chloe Zubieta

François Parcy

Contrasted evolutionary trajectories of plant transcription factors

Keywords: transcription factors, Evolution, green lineage

Because of their prominent roles in plant development, transcription factors (TF) play central roles as drivers of innovation in the evolution of the green lineage (viridiplantae). The advent of massive sequencing combined with comparative genetics/genomics allows a rigorous investigation of how TF families have contributed to plant diversification from charophyte algae to bryophytes to angiosperms. Here, we review recent progress on TF family reconstruction and the identification of distantly related TFs present throughout the evolutionary timeline from algae to angiosperms. These data provide examples of contrasting evolutionary trajectories of TF families and illustrate how conserved TFs adopt diverse roles over the course of evolution.

Introduction

In plants, as in all other organisms, transcriptional regulation is crucial for most biological processes, from basic metabolism to complex organ development. Trans-and cis-regulatory factors, known as transcription factors (TFs) and cis-regulatory elements (cis-elements), respectively, play pivotal roles in this transcriptional regulation. TFs are DNA-binding proteins that bind to specific cis-elements and directly regulate the transcription of DNA to mRNA.

Because of their importance, the evolution of TFs and their cognate cis-elements is tightly linked to the increase of organismal complexity and morphological innovations that occurred during evolution [START_REF] Gupta | Gene networks and the evolution of plant morphology[END_REF][START_REF] Rebeiz | Enhancer evolution and the origins of morphological novelty[END_REF][START_REF] Schmitz | Mechanisms of transcription factor evolution in Metazoa[END_REF] .

With the unprecedented pace of sequencing of genomes and transcriptomes, the repertoire of TFs from a wide variety of plant species (ranging from green algae or bryophytes to angiosperms) is now better characterized [4**, 5**, 6**, [START_REF] Liang | Mesostigma viride Genome and Transcriptome Provide Insights into the Origin and Evolution of Streptophyta[END_REF][START_REF] Cheng | Genomes of Subaerial Zygnematophyceae Provide Insights into Land Plant Evolution[END_REF]. Overall, plant genomes contain a higher number of TFs, more divergent TF families and more unique DNA binding domains (DBD) as compared with genomes from other eukaryotic organisms [START_REF] De Mendoza | Transcription factor evolution in eukaryotes and the assembly of the regulatory toolkit in multicellular lineages[END_REF]. Newly obtained sequence information is also useful in constructing more reliable phylogenetic trees, providing solid ground to understand plant evolution [6**]. Today, only the phylogeny of bryophytes (moss + liverworts + hornworts) remains uncertain: bryophytes could be monophyletic or alternatively, they could be paraphyletic with the liverworts + moss clade sister to land plants or to tracheophytes [10, 11, 12*].

Based on more robust phylogenies, how plant evolution was driven by TF family expansion, alteration of binding affinity, novel cis-element recognition and diversification of protein partners can be better understood. For example, cross-species comparison of TFs gives clues as to which genetic events (i.e. duplications, gene loss) gave rise to alterations in TF families that could be at the source of developmental novelty during evolution.

Evolution of plant TF families

The wealth of recent sequence data has confirmed previous finding as to the origin of some TF, such as the birth of the TCP family in the charophyte lineage [START_REF] Navaud | TCP Transcription Factors Predate the Emergence of Land Plants[END_REF]. But more importantly, it also sheds new light on the evolution of plant TF genes [6**]. Originally, mainly due to lack of sequence information in charophyte algae, several plant specific TF families (such as LEAFY, NAC, GRAS, MIKC-type MADS and ARF) were thought to have arisen after the water-to-land transition. However, newly available sequences revealed that many of these families were already present in the most recent common ancestor (MRCA) of Streptophyta (Figure 1) [START_REF] Wilhelmsson | Comprehensive Genome-Wide Classification Reveals That Many Plant-Specific Transcription Factors Evolved in Streptophyte Algae[END_REF]. It is likely that very few TF families originated in the MRCA of land plants (such as GeBP) or later after the water-to-land transition (such as VOZ) (Figure 1). Even YABBY TFs, sometimes proposed as land plant specific, are found in most branches of eukaryotic life [START_REF] Liang | Mesostigma viride Genome and Transcriptome Provide Insights into the Origin and Evolution of Streptophyta[END_REF][START_REF] Cheng | Genomes of Subaerial Zygnematophyceae Provide Insights into Land Plant Evolution[END_REF][START_REF] Carmell | A widely employed germ cell marker is an ancient disordered protein with reproductive functions in diverse eukaryotes[END_REF]. Thus, the origin of a new type of TF family per se did not likely play a major role in terrestrialization.

Moreover, once plants were able to grow on land, they have largely innovated by building on the TF families that were already present in the MRCA of land plants. Innovations that occurred all along the streptophyte lineage (including for example stomata, vascular tissues, roots, reproductive cones or flowers) used repeated TF family expansions (through local or genomewide duplications) and diversification [START_REF] Rosin | Old dogs, new tricks: Regulatory evolution in conserved genetic modules leads to novel morphologies in plants[END_REF] (Figure 1). TF duplications offer the opportunity for changes affecting the biochemical properties of the TF protein itself (such as changes in DNA binding specificity and protein interaction partners) or its expression pattern (allowing the interaction with a novel set of accessible cis-elements or available protein partners). Some families experienced strong expansion at different stages of plant evolution. The basic leucine zipper domain (bZIP) expanded in charophytes, while basic helix-loop-helix (bHLH) family members increased in land plants. The MADS TF expanded in spermatophyte and grew from a few members to dozens and sometimes over a hundred members in angiosperms (Figure 1), where they participate in a wide variety of processes including development, immune response, stress response and light and hormonal signaling [START_REF] Dröge-Laser | The Arabidopsis bZIP transcription factor family an update[END_REF][START_REF] Feller | Evolutionary and comparative analysis of MYB and bHLH plant transcription factors: Plant MYB and bHLH factors[END_REF][START_REF] Kaufmann | MIKC-type MADS-domain proteins: structural modularity, protein interactions and network evolution in land plants[END_REF].

The new sequence information not only helps to identify the TF family members but also retraces how TFs have diversified their function by the modular assembly of novel protein domains. This is the case for the Auxin Response Factor (ARF) family implicated in transcriptional responses to the auxin phytohormone. In addition to their B3 DBD, ARFs possess a Phox and Bem1 (PB1) domain that, in land plants, mediates ARF interaction with a similar domain present in the auxin/indole acetic acid (Aux/IAA) repressors [START_REF] Guilfoyle | The PB1 Domain in Auxin Response Factor and Aux/IAA Proteins: A Versatile Protein Interaction Module in the Auxin Response[END_REF]. In the absence of auxin, ARFs form complexes with Aux/IAA proteins and are transcriptionally inactive. Auxin triggers Aux/IAA degradation, releasing ARFs for transcriptional activation. The auxin pathway originated only in land plants but was assembled using several components present before: i) ARF proteins (possessing both the B3 DBD and PB1 domain) already present in charophytes but with no described role nor link to auxin, and ii) Aux/IAA and auxin receptor both generated through modifications of proteins present in charophytes

Conservation of TF function over large evolutionary scales

With the advent of genetic analyses in the moss Physcomitrella patens (P. patens) and the liverwort Marchantia polymorpha (M. polymorpha), it became possible to compare TF function over the large evolutionary distance that separates early diverging land plants from angiosperms, and to infer TF roles in the MRCA of land plant or understand how their function evolved [START_REF] Bowman | Evolution and co-option of developmental regulatory networks in early land plants[END_REF].

For TFs involved in vital processes present in all plants, it can be anticipated that both their patens and the flowering plant Arabidopsis [START_REF] Possart | Characterization of Phytochrome Interacting Factors from the Moss Physcomitrella patens Illustrates Conservation of Phytochrome Signaling Modules in Land Plants[END_REF][START_REF] Pham | Phytochromes and Phytochrome Interacting Factors[END_REF]. This conservation is highlighted by experiments in which the Arabidopsis pif quadruple mutant was rescued by the expression of either one of the four PIF orthologs of P. patens [START_REF] Xu | PHYTOCHROME INTERACTING FACTORs from Physcomitrella patens are active in Arabidopsis and complement the pif quadruple mutant[END_REF]. In M. polymorpha, the unique PIF protein is involved in gemma germination, which corresponds to an asexual mode of propagation, and the light-dependent gametangiophore formation (containing the sexual organs). These developmental responses to light involve a similar PIF-phytochrome module as in Arabidopsis.

Thus, this module is conserved at least since plants conquered the land [START_REF] Inoue | Phytochrome Signaling Is Mediated by PHYTOCHROME INTERACTING FACTOR in the Liverwort Marchantia polymorpha[END_REF][START_REF] Inoue | Reproductive Induction is a Far-Red High Irradiance Response that is Mediated by Phytochrome and PHYTOCHROME INTERACTING FACTOR in Marchantia polymorpha[END_REF]. It is even present in streptophytes, however its functionality remains unclear [28*].

The DUO POLLEN 1 (DUO1) MYB TF provides another example where a protein and its biological role were conserved between bryophytes and angiosperms. DUO1 is involved in male gamete development in both M. polymorpha and Arabidopsis [34*]. Reciprocal complementation reveals a conserved function of DUO1 between bryophyte and angiosperms in sperm differentiation. Interestingly, whereas the DUO1 from the charophyte algae Chara braunii is also functional in M. polymorpha, the protein from a zygnematale species is not functional. This is probably due to several substitutions in its DBD, an event that coincides with the loss of sperm mobility in this group [34*].

The functional conservation of TFs in seemingly divergent developmental processes has also been demonstrated in several cases, where the parallel between bryophytes and angiosperms is less obvious. The TCP family of TF, for instance, controls sporophyte branching in angiosperms and in moss P. patens [START_REF] Ortiz-Ramírez | A Transcriptome Atlas of Physcomitrella patens Provides Insights into the Evolution and Development of Land Plants[END_REF] although their branching structures (axillary meristems or branch initials) are very different. Conservation can also occur between the moss gametophyte (haploid tissue) and the angiosperm sporophyte (diploid). For example, the bHLH TFs ROOT HAIR DEFECTIVE 6-LIKE and LOTUS JAPONICUS ROOTHAIRLESS1-LIKE control root hair development in Arabidopsis and an analogous structure (rhizoids) involved in water and nutrient uptake in the gametophyte of P. patens [START_REF] Tam | Conserved regulatory mechanism controls the development of cells with rooting functions in land plants[END_REF] or M. polymorpha [START_REF] Proust | RSL Class I Genes Controlled the Development of Epidermal Structures in the Common Ancestor of Land Plants[END_REF]. The molecular mechanisms of reproductive development, involving the bHLH TF BONOBO during the germ cell differentiation process, also appear to be partly conserved among land plants [START_REF] Yamaoka | Generative Cell Specification Requires Transcription Factors Evolutionarily Conserved in Land Plants[END_REF]. Finally, the B3 TF ABSCISIC ACID INSENSITIVE 3 (ABI3) involved in abscisic acid (ABA) dependent acquisition of desiccation tolerance and dormancy in seeds of angiosperms such as Arabidopsis and maize is also necessary for ABA induced desiccation tolerance in the gametophyte of P. patens [START_REF] Khandelwal | Role of ABA and ABI3 in Desiccation Tolerance[END_REF] and in gemmae dormancy in Marchantia [START_REF] Eklund | An Evolutionarily Conserved Abscisic Acid Signaling Pathway Regulates Dormancy in the Liverwort Marchantia polymorpha[END_REF]. This provides another example of a presumptive gene network conserved over large evolutionary distance but at work in a different phase of the life cycle. [START_REF] Kaufmann | MIKC-type MADS-domain proteins: structural modularity, protein interactions and network evolution in land plants[END_REF][START_REF] Tanabe | Characterization of MADS-box genes in charophycean green algae and its implication for the evolution of MADS-box genes[END_REF]. The acquisition of novel functions by MIKC-type MADS TFs in land plants, in angiosperms in particular, involved several amplifications of the MIKC-type MADS subfamily followed by changes of their biochemical properties-namely changes in their oligomerization state and protein-protein interaction specificity. These changes progressively allowed the formation of the heterotetramers made of four different proteins that are required, for example, in petal and stamen development in angiosperms [START_REF] Theißen | MADS-domain transcription factors and the floral quartet model of flower development: linking plant development and evolution[END_REF]. Early on, MADS TFs from chlorophytes (devoid of the K domain necessary for tetramer formation) (Figure 2) or the unique MIKC copy from M. polymorpha could only form homodimers [START_REF] Zobell | MIKC* MADS-Box Proteins: Conserved Regulators of the Gametophytic Generation of Land Plants[END_REF]. MIKC-type MADS from the gymnosperm Gnetum gnemon were reported to form heterotetramers [START_REF] Wang | Molecular interactions of orthologues of floral homeotic proteins from the gymnosperm Gnetum gnemon provide a clue to the evolutionary origin of 'floral quartets': Quartet formation of gymnosperm MADS proteins[END_REF], indicating that MADS tetramerization capacity was born sometime between chlorophytes and gymnosperms (Figure 2). This tetramerization capacity became highly promiscuous in the angiosperm-specific SEPALATTA (SEP) MADS clade proteins (also referred to as 'glue' in multiple hetero-tetrameric complexes formation [START_REF] Immink | SEPALLATA3: the "glue" for MADS box transcription factor complex formation[END_REF]) which are able to recruit up to three different protein partners as opposed to the one or two protein types recruited by type II MADS in gymnosperms (Figure 2). Even later, the gamma genome triplication event that occurred in angiosperms increased the number of so-called "hubs" (such as SEPs), members that are highly connected in TF protein-protein interaction networks [START_REF] Zhang | Resurrected Protein Interaction Networks Reveal the Innovation Potential of Ancient Whole Genome Duplication[END_REF]. MIKC-type MADS TF also likely diversified their DNA binding properties. For years, it was thought all MADS TFs have the same DNA binding specificity, recognizing a cis-element called the CArG box. However, ChIP-seq analyses in Arabidopsis revealed that MADS TFs do not bind the same regulatory regions even if large overlaps sometimes exist. This specificity might be explained by slight differences between the CArG box sequences recognized by each tetramer [START_REF] Smaczniak | Differences in DNA-binding specificity of floral homeotic protein complexes predict organ-specific target genes[END_REF] resulting in the initiation of different developmental programs for each floral organ type. Taken together, the MADS TFs fully employed classical patterns of family expansion and neofunctionalization via gene duplication events. This mechanism is in direct contrast to LFY, an ancient TF that is encoded by a single copy gene in most streptophytes. However, it clearly seems that the floral function of LFY in angiosperm was co-opted from an ancestral vegetative role. LFY likely started acquiring a function in reproductive structures of gymnosperms where there is evidence that it controls expression of some MIKC-MADS TF [START_REF] Moyroud | LEAFY blossoms[END_REF][START_REF] Moyroud | A link between LEAFY and B-gene homologues in Welwitschia mirabilis sheds light on ancestral mechanisms prefiguring floral development[END_REF] and this role further expanded in angiosperms. The ancestral meristematic function of LFY became less essential in angiosperms but is still obvious in rice (for tiller growth), legumes (in compound leaves) and even Arabidopsis early flower development [START_REF] Moyroud | LEAFY blossoms[END_REF][START_REF] Chahtane | A variant of LEAFY reveals its capacity to stimulate meristem development by inducing RAX1[END_REF][START_REF] Yamaguchi | A Molecular Framework for Auxin-Mediated Initiation of Flower Primordia[END_REF]. LFY is an outlier to the general theme of TF families diversifying via the addition of protein-protein interaction domains to a core DBD. Even in algae, mosses and ferns, LFY possesses a Sterile Alpha Motif domain, a highly conserved eukaryotic oligomerization domain [START_REF] Sayou | A SAM oligomerization domain shapes the genomic binding landscape of the LEAFY transcription factor[END_REF]. The LFY family did not follow a classical expansion scheme and duplications were rarely retained except at the base of liverworts/moss and in gymnosperms, but the reasons for this remain elusive [55].

Long range evolution of floral TFs

Interestingly, despite a highly conserved DBD sequence, LFY DNA binding specificity changed several times in evolution [START_REF] Sayou | A promiscuous intermediate underlies the evolution of LEAFY DNA binding specificity[END_REF]. High-throughput methods allowing the determination of TF DNA binding specificity (such as DNA affinity purification sequencing (DAP-seq) [START_REF] Bartlett | Mapping genomewide transcription-factor binding sites using DAP-seq[END_REF][START_REF] O'malley | Cistrome and Epicistrome Features Shape the Regulatory DNA Landscape[END_REF] or systematic evolution of ligands by exponential enrichment followed by sequencing (SELEX-seq) [START_REF] Jolma | Multiplexed massively parallel SELEX for characterization of human transcription factor binding specificities[END_REF]) should thus be useful to thoroughly characterize the DNA binding properties of TF families even in cases where sequence conservation suggest they recognize the same cis-elements.

Conclusion

Analyzing how TF evolution has contributed to plant innovation is entering a golden age. The advent of massive genomic data from a wide range of species (1kp/10kp projects [START_REF] Cheng | 10KP: A phylodiverse genome sequencing plan[END_REF][START_REF] Matasci | Data access for the 1,000 Plants (1KP) project[END_REF]) allows the resolution of both phylogenies and genome content. The new tools for gene inactivation or gene modification are hitting more and more species although the capacity to easily transform charophytes algae, hornworts, ferns and gymnosperms remains a limitation. Finally, the combination of new sequence datasets, high-throughput in vitro genomics such as SELEX-seq or DAP-seq, and computational methods will help speed up the process of determining TF binding sites and potentially target genes [START_REF] Lai | Building Transcription Factor Binding Site Models to Understand Gene Regulation in Plants[END_REF]. These data will decipher how TF properties (e.g. DNA binding) have evolved and how this evolution has contributed to innovations all along the green lineage.

This genomic paper provides an overview of regulators present in Chara braunii genome and summarizes the evolutionary novelty enabling terrestrialization. A massive sequence data of streptophytic plants from different lineage refine the green lineage phylogeny, refresh the origins of some gene families and discuss the occurrence of wholegenome duplications in plants.

This paper reconstructed the evolutionary scenario of DUO1 based on biochemistry and multidirectional complementation experiments. This allow the authors to understand some gain and loss of functions related to gametogenesis and shed light on sperm cell mobility trait.

Figures and legends

  [5**,21-23]. Similar to several other hormonal pathways at work in land plants, the ARF TF family later expanded to diversify their roles in numerous developmental or signaling cascades. [5**,24-26].

  biological roles and molecular function (e.g. cis-element recognition) could be conserved. It is indeed the case, for example, for PHYTOCHROME INTERACTING FACTOR (PIFs) that are bHLH TFs involved in light signaling. They are found in most plants from charophytes to angiosperms [28*]. Several PIF target genes and even the modulation of PIF protein stability by light via protein-protein interactions with phytochromes are properties conserved between P.

  TFs important for angiosperm flower development provide interesting examples of how members of an ancestral TF family were able to fulfill new developmental roles over the course of evolution. We describe here two contrasting examples, the MIKC-type MADS TF subfamily and LEAFY (LFY). With multiple roles linked to angiosperm reproduction (e.g. control of flowering time, flower meristem identity, floral organ identity, ovule and fruit development), the MIKC-type MADS, or type II MADS, illustrates well how the expansion of a TF family has provided members involved in multiple angiosperm specific innovations [19,41]. While an ancient MADS is present in the MRCA of streptophytes and chlorophytes, this TF possesses only the MADS DBD (M domain) and C-terminal domain and is designated a type I MADS TF. The type II or MIKC-type MADS emerged prior to the split between charophytes and land plants and is characterized by the addition of an Intervening (I) and Keratin-like domain (K) (involved in dimer and tetramer formation) to a MADS type I TF present in chlorophytes

  LFY plays a key role during flower meristem emergence and fate in flowering plants and is also present in the MRCA of Streptophyta. LFY is a unique case where genetic studies have been performed in a moss, a fern and numerous angiosperms. Studies in P. patens and Ceratopteris richardii revealed LFY's role in cell division of the moss sporophyte and in the apical growth of gametophyte and sporophyte axes in fern [48,49**]. Studies are lacking to elucidate to what extend LFY control cell division/apical growth in early land plants or even in charophytes.

  5**. Bowman JL, Kohchi T, Yamato KT, Jenkins J, Shu S, Ishizaki K, Yamaoka S, Nishihama R, Nakamura Y, Berger F, et al.: Insights into Land Plant Evolution Garnered from the Marchantia polymorpha Genome. Cell 2017, 171:287-304.e15. This paper analyzed the genome of the liverwort M. polymorpha, a member of a basal land plant lineage. The data sheds light on the evolution of land plants and presents an overview of the putative hormonal signaling toolkit evolution. 6**. One Thousand Plant Transcriptomes Initiative: One thousand plant transcriptomes and the phylogenomics of green plants. Nature 2019, 574:679-685.

Figure 1 :

 1 Figure 1: Expansion of several TF families in the green lineage.

Figure 2 :

 2 Figure 2: Evolution of TF proteins involved in floral development

Acknowledgments

Our work is supported by the French National Agency for Research (FloPiNet ANR-16-CE92-0023-01; UbiFlor ANR-17-CE20-0014; ChromAuxi ANR-18-CE12-0014; GRAL, ANR-10-LABX-49-01 and ANR-17-EURE-0003). We thank R. Dumas for proofreading, L. Verhage for her input and we apologize to our colleagues whose work could not be cited due to space limitations.