1. AO4ELT, June 2009 1 Wide Field AO simulation for ELT: Fourier and E2E approaches C. Petit*, T. Fusco*, B. Neichel**, J.-F. Sauvage*, J.-M. Conan* * ONERA/PHASE ** Gemini Observatory, Chile

2. AO4ELT, June 2009 2 Optimization of simulation tools for: XAO analysis (VLT, ELT) Phase A studies of tomographic AO systems for E-ELT Context

3. AO4ELT, June 2009 3 Context: Wide field AO for E-ELT Performance Field of analysis SR ~ 50 % In few arcsec² SR ~ 30% in 1x1 to 2x2 arcmin² Uniform reduction of seeing (x2) in 10x10 arcmin² EE > 30% in few arcsec² Multiplexing: ~ 40 objects in 5x5 arcmin² GLAO MAORY MCAO ATLAS LTAO MOAO EAGLE

4. AO4ELT, June 2009 4 Context: simulation tools requirements Systems characteristics are different: XAO: Limited field of analysis/correction, single DM, single NGS-WFS High Number of Degrees of Freedom (HNDF) for VLT or ELT LTAO: Extended field of analysis, single limited field of correction Multiple NGS-LGS WFS, 1 DM MCAO: Extended field of analysis and correction Multiple NGS-LGS WFS, 2 or more DMs MOAO: Huge field of analysis, multiple directions of correction Multiple NGS-LGS WFS, multiple DMs Extended parameter space to explore: Number, position, magnitude of LGS/NGS Characteristics of associated WFSs (pitch, sampling, nb of pixels …) Number, position, pitch of DMs Tomographic reconstruction: Number, position, accuracy of models for estimated layers Types of reconstructors Dependency of results with zenith angle, turbulence conditions …

5. AO4ELT, June 2009 5 Optimization of simulation tools for: XAO analysis (VLT, ELT) Phase A studies of tomographic AO systems for E-ELT  Need for fast, computationnally efficient simulation tool, for fast first-hand estimation of performance → Fourier code  Need also for detailed simulation and refined performance estimation on specific cases → End2end code Context

6. AO4ELT, June 2009 6 End2end approach Classic Monte Carlo simulation Explicit simulation in direct space of each component Multi wavelength systems Turbulence layers (Kolmogorov/von Kaman statistics, Taylor hypothesis) Propagation (geometric or Fresnel…) LGS: cone effect, elongation, TT Defocus indetermination … WaveFront Sensor (shack-hartmann, pyramid … with/without spatial filtering) Control (including mixed NGS/LGS tomographic reconstruction) Deformable Mirror System delays Post focal applications (coronography …) … whatever you want and know how to simulate

7. AO4ELT, June 2009 7 End2end approach PRO Possibility to refine endlessly components models Access to any data, time series … Simulation of any kind of error (model errors, miscalibration …) Highly representative of real experimental systems (Xcheck with NAOS, BOA@ONERA, HOMER@ONERA …) CONS Iterative simulation: time consuming -> not suited for fast dimensioning addressing a large parameter space Computation of many matrices, vectors etc: memory space and CPU consuming For ELT: beyond capacities of « standard » computers if applied basically

8. AO4ELT, June 2009 8 Description of phase in Fourier domain Hypothesis: System is linear, spatially shift invariant (stationnarity) Each layer are independent Consequences: System and physics can be described by sparse linear operators Simple and fast sparse matrix computation Result is residual DSP of phase Infinite pupil until DSP computation, final pupil only for PSF computation Possibility to introduce model errors etc … B. Neichel, T. Fusco & J-M Conan “ Tomographic reconstruction for Wide Field Adaptive Optics systems: Fourier domain analysis and fundamental limitations “, JOSAA, 26-1, 2009 Fourier approach: Principle

9. AO4ELT, June 2009 9 Fourier approach: abilities Can take into account Multi-pitch DMs Generalized fitting Multi-pitch WFSs Generalized aliasing Tomographic reconstruction (Least Square, MMSE …) Temporal error (related to translation of turbulence during integration, servo-lag) Indetermination of low order modes (for TT defocus indetermination using LGS) … Can’t take into account (due to stationnarity hypothesis) Finite pupil:

10. AO4ELT, June 2009 10 E2E : finite pupil Fourier : infinite pupil -> Fourier estimation is optimistic Fourier approach: error related to infinite pupil hypothesis (unseen region)

11. AO4ELT, June 2009 11 Fourier approach: abilities Can take into account Multi-pitch DMs Generalized fitting Multi-pitch WFSs Generalized aliasing Tomographic reconstruction (Least Square, MMSE …) Temporal error (related to translation of turbulence during integration, servo-lag) Indetermination of low order modes (for TT defocus indetermination using LGS) … Can’t take into account (due to stationnarity hypothesis) Finite pupil: Possibility to include ad’hoc corrective term LGS: Elongation: WFS noise increase and structure can be accounted for Cone effect: approximative solutions exist but tricky. Example: can be accounted for through turbulence profil stretching … (see further)

12. AO4ELT, June 2009 12 Fourier approach PRO Fast, not memory/CPU consuming Easily scalable to ELT Representative in first approximation of real performance (compared to end2end) Allows fast and extensive dimensioning of large systems CONS Global error evolution (no explicit access to time series, particular data …) Lack of precision in particular configuration Problem to simulate edge effects, system with small pupils overlap Problem to simulate LGS (cone effect, spot elongation, low order modes indetermination)

13. AO4ELT, June 2009 13 Fourier vs End2End: performance & limitations Consequently: Use Fourier for fast dimensioning But ensure validity wrt end2end, particularly accounting for LGS → issue 1 Bring end2end towards ELTs complexity → issue 2 Issue 1: Ensure that Fourier tool is valid wrt end2end Validity in full plane wave configuration ? Ability to approximate full spherical configuration ? Ability to handle spherical+plane wave configuration ?

14. AO4ELT, June 2009 14 Fourier vs End2End: LTAO in full plane wave Good overlap Limited (or null) overlap good agreement in plane wave, to be extended to 16 m See B. Neichel et al. SPIE 2008

15. AO4ELT, June 2009 15 Fourier vs End2End: going to spherical wave Full spherical can be made equivalent to full plane wave (for cone effect, wrt anisoplanatism = pupils overlap) 0 h Criterion of interest: n=α h/D D, Cn²(h) α Criterion of interest: n’=α h/d>n d(h), Cn²(h) α d<D 0 h

16. AO4ELT, June 2009 16 Fourier vs End2End: performance & limitations 0 h Criterion of interest: n=α h/D D, Cn²(h) α 0 h’ Full spherical can be made equivalent to full plane wave (for cone effect, wrt anisoplanatism = pupils overlap) Criterions of interest: n=α h’/D=n’ D, Cn²(h) modified

17. AO4ELT, June 2009 17 Is turbulent profil stretching in plane wave equivalent to spherical wave ? → verification in end2end ELT downscaling: All dimensions scaled down, except angles Full spherical wave equivalent configuration Full plane wave configuration Scaling for a 4, 8,12, 16 m telescope

18. AO4ELT, June 2009 18 Is turbulent profil stretching in plane wave equivalent to spherical wave ? → verification in end2end 6 GS (plane wave or spherical) diameter: 4,8,12,16 m (ELT downscaled) High SNR, λ = 1.65 µm On axis tomographic reconstruction error (LTAO like) 2 layer profil, 2’ FoV → full spherical conf. equivalent to full plane wave conf. providing good stretching → result independent from telescope diameter and FoV 4 layer profil, 1’ FoV

19. AO4ELT, June 2009 19 Fourier vs End2End: performance & limitations Issue 1: Ensure that Fourier tool is valid wrt end2end Validity in full plane wave configuration → yes Validity of full spherical wave equivalent configuration → yes Ability to handle plane+spherical configuration → currently under study by comparison with end2end code to optimize correction term Issue 2: Bring end2end towards ELTs complexity

20. AO4ELT, June 2009 20 End2end simulation for ELT Global issue : manage matrix multiply and inversion with high number of degrees of freedom Typical dimensions of an AO for ELT: 80x80 actuators 3 pixels / subaperture 240 x 240 pixels / aperture Influence Matrix: 240 2 x 80 2 = 10 8 elements  1Go Interaction matrix: 80^4 = 400Mo And after ? 80 actuators: 1Go 100 actuators: 2.4Go array adressing issue (32 Bits related) 200 actuators: 38Go Matrix inversion: Needed memory  N 3/2, Computation time  N 3/2, Example: projection of phase on DM (M4 dimensioning typ.), i.e. a worst case Even if sparse matrix, generaly full matrix. Voltages Pixel basis

21. AO4ELT, June 2009 21 End2end simulation for ELT Our approach : Pre-conditioned Maximum likelihood approach : Use of sparse matrix (gain in memory) (R. Flicker-SOI) (Cholesky) Thresholding needed Voltages Pixel basis Typical case : 100x100 act 3pix/subaperture Pre-conditioning ≈ 10h Criterion minimisation ≈ 10s

22. AO4ELT, June 2009 22 Conclusion & perspective 2 simulation codes available for system analysis Fourier code Xchecked with end2end in plane wave configuration Full spherical wave configuration can be considered as special full plane wave configuration The mixed spherical+plane wave configuration is under study, but what matters is tomographic reconstruction ! End2end code well advanced: Detailed simulation of components LGS WFSing included Mixed LGS+NGS tomographic reconstruction under study AO simulation for ELT is available, currently being optimized for tomographic ELT simulation

23. AO4ELT, June 2009 23 Overview Context End 2 end approach Principle Pro/cons Fourier approach Principle Pro/cons Fourier vs End 2 end: comparison End 2 end towards LNDF

24. AO4ELT, June 2009 24 End2end optimisation: accounting for LGS Issues: TTDefocus indetermination: filtering at measurement level, not a real issue → implemented Spot elongation: to be accounted for at WFS level → not impliemented so far Cone effect:

25. AO4ELT, June 2009 25 E2E : finite pupil Fourier : infinite pupil -> Fourier estimation is optimistic Fourier approach: error related to small pupil overlap (unseen regions)

26. AO4ELT, June 2009 26 Including unseen area related term in Fourier code GS Footprints Residual phase in altResidual phase in pup PSF Perf (SR, EE…) 6 LGS (cone effect) @ 2 arcmin FoV

27. AO4ELT, June 2009 27 Perspectives Develop a MCAO simulation tool based on sparse matrix Tomographic regularisation : C phi non diagonal. B. Ellerbroek : « Minimum variance WF reconstruction »