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Calibration of AO Systems Application to NAOS-CONICA and future «Planet Finder» systems T. Fusco, A. Blanc, G. Rousset Workshop Pueo Nu, may 2003 Département d Optique Théorique et Appliquée ONERA, Châtillon mail : thierry.fusco@onera.fr

Contents Performance limitations of AO systems AO loop calibrations Non-common path aberration calibration Pre-compensation of «unseen» aberrations (application to NAOS-CONICA) 2

Limitations of AO systems AO loop errors fitting error (actuator number, r0) temporal and measurement errors (WFS and corrector characteristics, GS magnitude, r0 and wind speed) Main limitation for current AO systems AO calibration errors calibration of interaction (and reconstruction) matrices and WFS references calibration of temporal transfer functions No-common path aberrations measurement using a phase diversity approach pre-compensation using the AO loop Critical issue for futur XAO systems 3

AO loop calibration Spatial characterisation WFS calibration detector calibration (dark, flat, bkg, gain) pixel scale determination non-linearity effect quantification WFS references Required for open-loop reconstruction (perf estimation, modal optimisation ) Interaction matrix alignment between the deformable mirror and the wavefront sensor measurement noises on interaction matrix computation of command matrix (choice of a modal basis, mode filtering) Temporal characterisation Quantification of all the loop delays WFS integration time pure delay Error Transfer Function measurements See Dessenne PhD Thesis (1999) for complete analytical studies 4

AO loop calibration Pupil mis-alignment effects Pupil mis-alignment between interaction matrix acquistion and AO loop utilisation Significant effects for shift > 5% of a sub-aperture (1% SR loss) => give specifications for system stability and calibration accuracy => definition of calibration procedures 5

AO loop calibration noise on interaction matrix measurement Simulation results Actuators S-H WFS :14x14 subapertures DM : 185 actuators Dmeas = D + σ B X-slopes T D Dmeas T + T = T Various σ Calibration on internal source => only due to photon and detector noise Y-slopes SNR = SNR = 1.2 8 6

AO loop calibration Temporal characterization Gain=0.4 Error transfer function (ETF) sampling frequency corrector law (gain for an integrator) pure delay System Bandwidth = 27 Hz 8

AO loop calibration Temporal characterization VIS WFS Gain=0.4 Error transfer function (ETF) sampling frequency corrector law (gain for an integrator) pure delay Measurements on NAOS using open and closed loop data Test for various WFS modes Theoretical behaviors well restored Definition of system 0db Bandwidth for both VIS and IR WFS Essential calibration for Command optimisation On-line perfomance estimation and turbulence characterisation System Bandwidth = 27 Hz 9

AO loop calibration Conclusion WFS / DM mis-alignment important impact for shift > 5 % of a subaperture (typically) => constraints on system stability and calibration procedures Noise on interaction matrix measurements estimation of a minimum SNR depending on the global error budget => constraints on calibration procedures (fiber flux, integration time ) ) Temporal transfer function calibration required for temporal optimisation of the AO loop (modal opt., Kalman filtering ) Linearity important issue for open loop reconstruction (control optimisation) less critical for SH WFS than Curvature/ 4 Cells / Pyramid 10

Calibration of non-common path aberrations Imaging path not seen by the AO loop : Necessity to compensate for the static aberrations unseen by the AO system Calibration by Phase Diversity 11

Phase diversity principle Phase Diversity principle Φ Φd If = O PSFf (Φ) + nf Id = O PSFd (Φ + Φd) + nd 12

Joint estimation of object and aberrations Minimization with respect to O and Φ of L(O,Φ) = Ι Ο PSFf (Φ) 2 + Ι Ο PSFd (Φ+Φd) 2 f d (Least square estimation [Gonsalves-82]) known phase Dev t of a new «Marginal» estimation of Φ Gain in term of precision and robustness See Blanc et al, JOSAA, vol.20(6), 2003 13

Limitations of the measurement procedure System limitation Defocus distance Camera pixel scale Pupil shape (pupil centering) Image limitations Signal to noise ratio Residual background features Algorithm limitations Number of estimated Zernike polynomials Spectral bandwidth Image centering Pupil model (pixelization effects) See Blanc et al, A&A, 399, p373-383 (2003) and Hartung et al, A&A, 399, p385-394 (2003) 14

Limitations of the measurement procedure System limitations Defocus distance Camera pixel scale Pupil shape (pupil centering) Image limitations Signal to noise ratio Residual background features Algorithm limitations Number of estimated Zernike polynomials Spectral bandwidth Image centering Pupil model (pixelization effects) See Blanc et al, A&A, 399, p373-383 (2003) and Hartung et al, A&A, 399, p385-394 (2003) 15

Limitations of the measurement procedure System limitations Defocus distance Camera pixel scale Pupil shape (pupil centering) Image limitations Signal to noise ratio Residual background features Algorithm limitations Number of estimated Zernike polynomials Spectral bandwidth Image centering Pupil model (pixelization effects) NAOS-CONICA : estimated measurement error ~ 50 nm rms ( SR ~ 98% in K) See Blanc et al, A&A, 399, p373-383 (2003) and Hartung et al, A&A, 399, p385-394 (2003) 16

Estimation of NAOS-CONICA aberrations NAOS-CONICA : large number of observation configurations Precompensate for the static aberrations for any possible setup assign the aberration contributions to various optical components Dichroics (5) Filters (40) and camera objectives (2/7) Separated calibrations of CONICA stand alone and NAOS-CONICA Two ways of introducing the phase diversity focus shift by object defocus introduced by the deformable mirror 17

Estimation of NAOS-CONICA aberrations Focus shift by object CONICA calibration (I) Exemple of CONICA aberration estimation Focused plane Defocused plane Image estimated PSF Image estimated PSF Hartung et al, A&A, 399, p385-394 (2003) 18

Results in term de Strehl ratio 2 SR estimated using phase diversity results SR pd = exp (- <a i >) X SR estimated on focal plane image SR = PSFf (0)/Airy(0) 19

Estimation of NAOS-CONICA aberrations CONICA calibration (II) Example of results for K band Filters (2.03-2.48 µm) 20

Estimation of NAOS-CONICA aberrations Dichroic calibration Defocus induced by the deformable mirror Separation of the contribution to aberrations of dichroic and CONICA a i dichro = a i dich+conica - a i Tot,filter1 21

Closed loop compensation Compensation of the measured static aberrations using NAOS DM combination of CONICA + dichroic aberrations (following the system configuration) {a i } slopes {s i } modification of WFS reference slopes closed loop pre-compensation Example of closed loop pre-compensation J band (1.25 µm) K band (2.16 µm) 60 % 70 % 89 % 93 % huge gain in term of SR Avoid bump on the first Airy ring 22

Conclusion High SR => pre-compensation of imaging path aberrations precise aberration measurements : phase diversity algorithm good knowledge on AO loop properties Only low frequency (> inter-actuator distance) aberrations can be corrected Current results on NAOS-CONICA : internal SR (without turbulence) : 93.5% (in K) for the best configuration goal for a XAO system > 97 %!!!!!!!!!!! Need to refine every error budget item Global design for AO and imaging camera is mandatory global optimisation of the complet error budget 23

Non-Linearity effects Non-linear effects Dmeas computed with amplitude range = input residual phase Important issue for Curvature / 4 cells / Pyramid WFSs Less critical for classical Shack-Hartmann WFSs (if FoV/aperture is large enough) 24