Experimental results of tomographic reconstruction on ONERA laboratory WFAO bench. A. Costille*, C. Petit*, J.-M. Conan*, T. Fusco*, C. Kulcs ár**, H.-F. Raynaud** *ONERA, DOTA – Unité HRA, Châtillon ** L2TI, Université Paris 13, Villetaneuse [email protected]. Overview. Context - PowerPoint PPT Presentation
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Experimental results of tomographic reconstruction on ONERA laboratory WFAO
bench
A. Costille*, C. Petit*, J.-M. Conan*, T. Fusco*, C. Kulcsár**, H.-F. Raynaud**
• 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)
Context - HOMER bench – Experimental results - Conclusion
• 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
AO4ELT – 26/06/09 – A. Costille
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)
Context - HOMER bench – Experimental results - Conclusion
nnn
nntur
nn
nnnnoptnnnn
Pu
A
NuDMDMyH
/1
//1
21/11//
ˆ
ˆˆ
ˆˆˆ
6
AO4ELT – 26/06/09 – A. Costille
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)
Context - HOMER bench – Experimental results - Conclusion
nnn
nnv
nn
nnntur
noptnnnn
vPu
vAv
NuDMvNDMyHvv
/1
//1
21/11//
ˆ
ˆˆ
ˆˆˆ
v
7
Interaction matrices
AO4ELT – 26/06/09 – A. Costille8
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 %
Context - HOMER bench – Experimental results - Conclusion
AO4ELT – 26/06/09 – A. Costille9
2. Calibration aspects
Context - HOMER bench – Experimental results - Conclusion
• 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
AO4ELT – 26/06/09 – A. Costille10
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)
Context - HOMER bench – Experimental results - Conclusion
65%
55% 58%
62%
AO4ELT – 26/06/09 – A. Costille11
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
Context - HOMER bench – Experimental results - Conclusion
Position in the FoV (δ)
Pos
ition
in t
he F
oV (
δ)
200
0
-200
200-200 0
55%
LTAO
AO4ELT – 26/06/09 – A. Costille1212
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
Context - HOMER bench – Experimental results - Conclusion
AO4ELT – 26/06/09 – A. Costille1313
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
Context - HOMER bench – Experimental results - Conclusion