Experimental results of tomographic reconstruction on ONERA laboratory WFAO bench

Experimental results of tomographic reconstruction on ONERA laboratory WFAO

bench

A. Costille*, C. Petit*, J.-M. Conan*, T. Fusco*, C. Kulcsár**, H.-F. Raynaud**

*ONERA, DOTA – Unité HRA, Châtillon** L2TI, Université Paris 13, Villetaneuse

[email protected]

AO4ELT – 26/06/09 – A. Costille

Overview

I. Context

II. WFAO laboratory test bench at ONERA: HOMER

III. Experimental validation of Wide Field AO (WFAO) concepts in closed-loop

IV. Conclusion and perspectives

AO4ELT – 26/06/09 – A. Costille3

I. Context

• AO is limited by the anisoplanatism effect• Development of new WFAO concepts (LTAO and MCAO) and first

instruments:• Multi-analysis• Tomographic reconstruction• New control laws

• Theoretical studies are mature but need for experimental validations

• Development of a WFAO bench HOMER:• Study and comparison of WFAO concept

• Calibration• Field aberrations (WFS and Imaging path) • Model identification for control laws implementation

• Development of new concepts• Comparison of control laws

• Classic control: least-square + integrator• LQG control:

• Estimation and prediction of the turbulent volume, based on a Kalman filter• Projection of the estimated turbulence

Context - HOMER bench – Experimental results - Conclusion


Light source with reconfigurable positions of laser

Ground layer DM (52 actuators, ALPAO

technology)

Second DM (88 actuators, ALPAO

technology)

Wide Field WFS (1002x1004

pixels)

ANDOR EMCCD

Visible Imaging camera (1024x1024

pixels)

7x7 microlens array

Manufactured at ONERA

F = 30mm - dμl = 1.1mm

RTC PC-linux

Shaktiware

λ = 635 nm

Fs < 25 Hz

1. Experimental setup of HOMER benchContext - HOMER bench – Experimental results - Conclusion

4


2. Specificities and equations of the system• Turbulence

• Generated by the DMs with turbulent voltages v : φtur = Nturv• Where Ntur is the influence matrices of DM52 and DM88, φtur the turbulent phase

• Turbulence model: AR1 type : vn+1 = Avvn + bv

• WF Sensing • Measurement equation in AO : sn = Dφ + w

s: slopes, D: WFS model, φ: measured phase, w: measurement noise

• Measurement equations for several directions : sn = DMαφ + w

• Where Mα is the matrix of the projection of the phase in the pupil in directions α

• On HOMER : one wide field Shack-Hartmann (142x142 pixels / sub-aperture)


• 3 WFS on NGS of 16x16 analysis area• Configuration and number of GS modifiable

• Correction phase φcor = Nu• Where N is the influence matrices for correction DM (DM52 in LTAO, DM52 +

DM88 in MCAO)• u the correction voltages


3. Control laws equations

• Integrator control : least-square reconstructor + integrator

• Control equation : un+1 = un + G yn = un + g Mcom sn

• Where g is the integrator gain, Mcom the control matrix : generalized inverse of interaction matrix Mint = DMαN

• LQG control

• Where is the estimated phase in Zernike basis• Atur is the turbulence transition matrix• Hopt is the Kalman Gain

• P = fct(Mβ, N) the projector of the estimated phase on the DM for correction (β correction directions)


nnn

nntur

nn

nnnnoptnnnn

Pu

A

NuDMDMyH

/1

//1

21/11//

ˆ

ˆˆ

ˆˆˆ

6


3. Control laws equations

• Integrator control : least-square reconstructor + integrator

• Control equation : un+1 = un + G yn = un + g Mcom sn

• Where g is the integrator control, Mcom the control matrix : generalized inverse of interaction matrix Mint = DMαN

• LQG control in the DM space

• Where is the estimated voltages• Av is the turbulence transition matrix• Hopt is the Kalman Gain

• P = fct(Mβ, D, N) the projector. In MCAO : P = Id

• Control laws applied with the RTC (Shaktiware)


nnn

nnv

nn

nnntur

noptnnnn

vPu

vAv

NuDMvNDMyHvv

/1

//1

21/11//

ˆ

ˆˆ

ˆˆˆ

v

7

Interaction matrices


1. Experimental Conditions

• Turbulent profile• Turbulent layers conjugated with the DMs• Cn2 = 50% in each layer• D/r0 = 7 (global in the pupil)

• WFS on 3 NGS in HOMER FoV• WFS- Imaging field : 420 x 361 λ/D ( i.e. 81’’x 70,4’’ equivalent 8 m telescope)

• Representation of anisoplanatism effect for a 8 meter telescope• Conservation of the angular separation of the footprint in altitude• For D = 8m, FoV = 2’, h = [0,13800]m

• No correction of the non common path aberrations• Impact of the the non common path aberrations :

• 65% of SR on axis, without turbulence• Variation of the SR in the FoV < +/-5 %



2. Calibration aspects


• Model identification for LQG control in DM space• Models of the DMs, of the WFS, of the projector : calibration of interaction matrices• Model of the turbulence, measurement noise

• Relative positions of the WFS in the FoV• Determination of the theoretical positions of the GSs with astrometry• Presence of distortion on the optical path = Deformation of the GS configuration

• Errors in astrometry• Errors on the directions of the WFS• Distortion in the optical path

• Correction of this distortion by our system not possible• Solution: correction of astrometry to take distortion into account

1 sub-pupil of HOMER

1 WFS (real case)

Position in the FoV (δ)P

osi

tion

in t

he

Fo

V (

δ)

0.34

0

-0.34

0.34-0.34 0

PSFs with astrometry

Position dans le champ (δ)

Po

sitio

n in

th

e F

oV

(δ)

0.34

0

-0.34

0.34-0.34 0

PSFs after correction of astrometry


3. Experimental results in WFAO

• SR open-loop : 7% (average)• SR in classic AO

• On axis : 65% and in the border : 12% (anisoplanatism)

• SR in MCAO• SR closed-loop : 56 % (average in the FoV)

Po

sitio

n in

th

e F

oV

(δ

)

0.34

0

-0.34

Position in the FoV (δ)0.34-0.34 0 0.34-0.34 0 0.34-0.34 0

No correction AO correction MCAO correction

Position in the FoV (δ) Position in the FoV (δ)


65%

55% 58%

62%


3. Experimental results in WFAO

• MCAO results:• Slightly better performance with LQG control

• Mean SR – integrator : 53% - LQG : 56%• Turbulence generated by DMs : very favorable for integrator control law

• Good agreement between numerical and experimental results

• LTAO results:• Test with LQG control• Tomographic reconstruction of the turbulence proven (results close to AO case)• Test of tomographic reconstruction according to

• The number of GSs• The position of the GSs


Position in the FoV (δ)

Pos

ition

in t

he F

oV (

δ)

200

0

-200

200-200 0

55%

LTAO


Conclusion

• HOMER is operational in AO, LTAO and MCAO• First experimental validations

• Of closed-loop LTAO• Of LQG control for WFAO systems (LTAO and MCAO)

• Study of the LQG control in WFAO• Gain in performance proven with LQG control• Preliminary studies of model identifications issues and impact of model

errors

• Problems of relative positions of WFS in the FoV• Distortion effect to take into account (not corrected by the system)• Numerical studies on HOMER and VLT case on going



Perspectives

70 %

70 %

70 %

50 % 60 %

70 %

70 %

70 %

• Integration of a turbulent module (summer 2009)• Calibration of the turbulence• Study of control laws in real conditions and comparison of sub-optimal control

laws (POLC…)• Problems of model identification with LQG control

• Choice of the estimation basis• Turbulent model• Calibration of the models of the system components

• Calibration issues for WFAO systems:• Field aberrations in the imaging path• Problems of the relative position of the WFS in the FoV

• Study of LGS :• WFS and control strategy on both LGS and NGS

• Multi-stage WF sensing (additional WFS after the ground DM52)

• HOMER web site : http://www.onera.fr/dota/homer


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Experimental results of tomographic reconstruction on ONERA laboratory WFAO bench

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