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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

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Optimization of simulation tools for:• XAO analysis (VLT, ELT)• Phase A studies of tomographic AO systems for

E-ELT

Context

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Context: Wide field AO for E-ELT

Performance

Fie

ld o

f an

alys

is

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

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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 …

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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

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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

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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

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• 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

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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:

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E2E : finite pupil Fourier : infinite pupil -> Fourier estimation is optimistic

Fourier approach: error related to infinite pupil hypothesis (unseen region)

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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)

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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)

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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 ?

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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

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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

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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

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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

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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

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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

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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: 2402 x 802 = 108 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 N3/2,• Computation time N3/2,

• Example: projection of phase on DM (M4 dimensioning typ.), i.e. a worst case

• Even if sparse matrix, generaly full matrix.

TT FFFu 1)(ˆ C

CF

CuF ˆVoltagesPixel basis

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End2end simulation for ELT

• Our approach : • Pre-conditioned Maximum likelihood approach :

• Use of sparse matrix (gain in memory) (R. Flicker-SOI)

vLu TFLvALvLvvJ TTT 2)('

IdALLA T '

A L

uF ˆ

(Cholesky)

2

2

2krr

j

k eF

Thresholding needed

VoltagesPixel basis

Typical case :

100x100 act3pix/subaperture

Pre-conditioning ≈ 10hCriterion minimisation ≈ 10s

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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