Efficient control schemes with limited computation complexity for Tomographic AO systems on VLTs and ELTs

Transcription

1 Efficient control schemes with limited comptation complexity for Tomographic AO systems on VLTs and ELTs C. Petit, T. Fsco, J.-M. Conan : ONERA M. Le Loarn, P.-Y. Madec: ESO

2 Overview Context: Tomographic AO for VLT and ELT Tomographic control soltions Simplifying Control Schemes into Single Matrix Vector Mltiply Simlation Reslts Discssion & Perspectives

3 Tomographic AO for VLT MUSE and its AO system GALACSI Adaptive Optics Facility: Deformable Secondary Mirror (DSM) on 8m nit of VLT MUSE: Mlti Unit Spectroscopic Explorer 2nd generation instrment, panoramic integral-field spectrograph in visible. Uses AOF, with Laser Lanch Facility (4 sodim LGS) GLAO/LTAO correction provided by GALACSI with DSM MUSE Narrow Field Mode (NFM) with GALACSI: 7.5 x7.5 FoV 4 off axis 1 NGS for low order modes RTC: SPARTA platform -> Single MVM

4 Tomographic AO for ELT LTAO: ATLAS MCAO: MAORY

5 Context: Tomographic AO control soltions LTAO for VLT or ELT Relies on tomographic control soltions. L 3 Terminology : S-MVM : single matrix vector mltiply M-MVM : mltiple matrix vector mltiply L 2 DM L 1 WFS Control

6 Tomographic AO control soltions GLAO: generalized inverse of interaction matrix, integrator controller + = R glao y S-MVM bt No tomographic abilities, poor performance Virtal DM control vdm R reconstrction in the 2 layers into the 2 DMs from closed-loop data 2 DM = actal grond DM + additional virtal DM in altitde + projection onto the real DM. + = R vdm y dedced from min. var. reconstrctor with «fdge factor»: W MV tomo T T ( DP C P D + ρc ) T T = Col Pα D α ol α w S-MVM. Sb-optimal. Tning isses L 3 L 2 L 1

7 Tomographic AO control soltions Psedo Open Loop Control (POLC): static minimm variance reconstrctor, applied on psedo open-loop measrement + temporal filter: where: In another form: ˆ ϕ ˆ ˆ + 1 = α ϕ + β ϕ + δe e MV int ˆ = Wtomo ( y + M 2) ϕ α = Pβ = 0e Tomographic reconstrction, M-MVM β δ and ϕ = P ˆ β =0 +1 Linear Qadratic Gassian: optimal soltion according to minimm residal phase variance of the dynamic closed-loop control problem ˆ ϕ ˆ ( ˆ + 1/ = A ϕ / + L y y / ) = P ˆ β =0ϕ +1/ with Optimal tomographic reconstrction and control. M-MVM D( P ˆ ϕ yˆ / = α / N 2 )

8 Context: Tomographic AO control soltions Tomographic AO for VLT or ELT LTAO ATLAS Relies on tomographic control soltions (vdm, POLC, LQG ). Efficient soltions imply Mltiple Matrix Vector Mltiplications (M-MVM) Qestion : Can we find a S-MVM control soltion with good performance? wold fit in crrent RTCs sch as SPARTA cold limit the comptation brden for ELT systems LTAO on ELT (ATLAS) is slopes at 500Hz (1Gb/s inpt)

9 S-MVM control strctre Goal: propose a tomographic control soltion for LTAO based on a S-MVM to redce complexity/comply with RTC architectre of the type: Where y R are measrements, are controls, is a matrix and α, β, δ α β + δry = + 2 scalar gains Example: simplest possible R: inverse of interaction matrix -> GLAO

10 Simplified control scheme Objective: «simplify» M-MVM control soltions (POLC, LQG) into S-MVM soltions Example with LQG: Basic eqations In another way: Obstacle to S-MVM: Possible soltions: permtation reqired ˆ ϕ ˆ ( ˆ + 1/ = A ϕ / + L y y / ) = P ˆ ϕ +1 / PA ˆ ϕ ( ˆ / + PL y y / ) = Permtation is possible: find B sch as BP = PA estimated measrement to be handled B happens to be very close to B αidentity can be approx. by scalar gain. + Approximation : Estimated measrements taen as zero Either with POLC or LQG: a S-MVM soltion can be derived sch that = + β 2 α + δry

11 Simplified control scheme: discssion Qestions : stability & performance of the DLQG and DPOLC in the form α β + δry = + 2 Control soltions derived with this approximations proves to be nstable: α, β Approximations lead to that do not satisfy stability constraints! In the end, these coefficients shold be fixed wrt stability criterion Similarly to POLC approach (Gilles et al.) we set new coefficients so that : α + β < 1 δ = 0. 5 Gain matrix R still derived from the initial control law (POLC or LQG) one can hope it preserves some good properties of original control

12 Simplified control scheme: performance Case of stdy: end to end nmerical simlation on LTAO system (low order to speed-p calclations) 8 m telescope 3 or 10 layer trblence profile, Cn² and wind profiles dedced from VLT profiles Good or poor seeing conditions (0.68 or 0.95 ) 4 Shac Hartmann WFS, 8x8 sb. apert. NGS at 30 off-axis + noise (photon noise regime) DM is 9x9 piezo stac 25% mech. copling 500 Hz frame rate, 2 frame delay 2.2µm

13 Compared performance verss noise level: 3 Layer profile Similar reslt at good and poor seeing Observations: Lowest performance is GLAO Optimal performance always provided by LQG POLC, DPOLC, LQG give same performance at high SNR DLQG, POLC and DPOLC provide intermediate performance between vdm and LQG, small advantage for Degraded LQG

14 Compared performance verss gain: 3 Layer profile Similar reslt at good and poor seeing WFE in nm rms Observations: DLQG is less sensitive to the choice of the gain δ

15 Conclsions S-MVM control algorithm have been derived from POLC or LQG Redces on-line comptation load Provides stable and efficient tomographic control Performance are in between vdm and optimal LQG Despite the drastic approx., DLQG eeps LQG good properties : better performance and smaller sensitivity to noise robstness : not very sensitive to parameter tning Performance evalation in MUSE configration are planned on ESO

16 Trade-off optimality comptation cost Withot being as extreme as S-MVM : Use similar approximation to derive a M-MVM LQG in the voltage space wold allow reconstrction on many layers [Costille et al., this conference] with no increase of real time brden (nice property of POLC in voltage space) Go for Sparse iterative methods and avoid solving Riccati eqation Kalman gain dedced from physical considerations [Correia AO4ELT 2009] Ensemble Kalman Filter [see Morgan Gray (LAM) this conference] Exploit spatial invariance of the problem ltra-fast Kalman gain comptation based on spatial invariance & redction of real-time calclations [Paolo Massioni JOSA A 2011 accepted] Keep an eye on properties of interest performance (temporal + noise + tomography( ) errors), robstness