AO-PSF reconstruction for Shack-Hartmann AO systems

Transcription

1 AO-PSF reconstruction for Shack-Hartmann AO systems Application to Altair Gemini-North AO system 1st Victoria Workshop on AO-PSF reconstruction

2 Veran s method - summary Algorithm... WFS measurements covariances to DM structure function, DM commands variances to r0 & L0 to high frequency structure function, Sum of structure functions to AO Optical Transfer Function, AO OTF times TSC OTF to final OTF. Assumptions Final OTF = product of AO & TSC OTFs Means stationary of corrected phase in pupil - wrong but... Mirror and high frequency SF correlation negligible Curvature Sensing: yes. Shack-Hartmann? Correction temporal bandwidth is large Means high loop gain (bright star or slow wind or weak turbulence)

3 Warning: importance of matrix size Matrix size defined by Telescope PSF sampling - to avoid TSC-OTF aliasing... Focal plane angular pixel scale xf must be < 0.5 lambda/d Seeing-limited OTF sampling - to avoid AO-PSF folded wings Natural PSF wings have infinite extension, so frequency sampling ff must be infinitely small. Practically, ff < 1/(8 fwhm) gives 8 fwhm FoV. So, N (1/ ff)/ xf i.e. N 16 D/r0 (lambda) PUEO/CFHT (H, 1.65 mu): 16 x 3.6/0.63 = 92 px (JP. Veran was using 128 px) OK.

4 Orthogonal structure function model

5 Orthogonal structure function model

6 Outer scale effect on r0 assessment Outer scale decreases low order modes variances Kolmogorov modal variances fit does not work if D ~ L0 Solution: assess both r0 and L0 Need a model for variance attenuation due to L0 Winker (JOSA A 1991) developed Von Karman variances, equations involve Hypergeometric functions. Difficult to handle. Winker gave me a grid of A(n,D/L0) values, I fitted a semi-empiric model, valid any radial order n and D/L0 = [ 0.002, 2 ]

7 Outer scale attenuation of modal variances

8 Outer scale attenuation of modal variances

9 More on Uij functions... j i

10 Slopes variances from noisy measurements, 1 WFS noise affects slope variance calculation. Must be subtracted from diagonal of slopes covariance matrix. Veran: developing a statistical model of CS output signal, that includes all knowledge on noise sources. Unnoisy variances are directly extracted from noisy slopes time series statistics. We need full wfs images all along the exposure - telemetry Works for SH-4QU too. A C B D

11 Slopes variances from noisy measurements, 2 Perfect signal (no noise at all, continuous photon flow) - the 4-quadrant output is: Noisy output: Output components of a quadrant, background subtracted: [ADU]

12 Slopes variances from noisy measurements, 3 Mean and variance of quadrant A output: Variance of perfect measurement M = / If and are not correlated yes < >=0 yes > 0 and fluctuation( ) << yes

13 Slopes variances from noisy measurements, 4 Noisy difference and sum linearly related to perfect difference and sum: So,

14 Slopes variances from noisy measurements, 5 How accurate?

15 Slopes variances from noisy measurements, 6 Things to do: Image size evolves with seeing, so centroid gain does. This statistics has to be included. Calculation for SH with sub-apertures images (e.g. NAOS/VLT) Short exposure case include speckle statistics? Low bandwidth case - dimmer stars...

16 OPERA, an IDL-based code for AO-PSF rec. System Parameters Uij, command matrix,... Mirror Commands seeing.pro L0,r0 TSC-OTF On-line telemetry WFS images buffer Off-line, algorithm cov_4qu.pro Cww opera.pro AO-OTF optica.pro Final OTF Final OTF

17 OPERA for Altair, Gemini-North AO system OPERA toolbox is ready to run and available for the community. Algorithm is system independant! But not the telemetry. Only one run so far, May phase screens turbulator m/s wind 128 corrected modes 1.55 microns

18 OPERA for Altair, Gemini-North AO system Fried parameter and outer scale - seeing.pro Zernike Kolmogorov variances to mirror modes variances Best fitting to mirror modes variances gives D/r0 tipt-tilt and defocus modes excluded r0 = / m L0= 23 m not real (phase screens)

19 OPERA for Altair, Gemini-North AO system WFS slopes covariance matrix - covwfs_sh4qu.pro Noise level

20 OPERA for Altair, Gemini-North AO system From r0 to orthogonal structure function - from semi-analytic model

21 OPERA for Altair, Gemini-North AO system Mirror structure function from WFS covariance matrix and Uij functions

22 OPERA for Altair, Gemini-North AO system AO optical transfer function from structure functions - exp(-1/2 SF)

23 OPERA for Altair, Gemini-North AO system Static OTF (from telescope + unknown sources)

24 OPERA for Altair, Gemini-North AO system Final OTF

25 OPERA for Altair, Gemini-North AO system OTF Profiles

26 OPERA for Altair, Gemini-North AO system PSF profiles STREHL: NIRI 0.15, OPERA 0.13 FWHM: NIRI 83 mas/68 mas OPERA 65 mas

27 Opera on Altair... Not too bad, but... Vibrations seen by NIRI and not by Altair High wind, was the high-bandwidth assumption valid? Turbulator was off-axis, but this shouldn t be a problem Effect of aliasing has not been subtracted for this run Strehl is then under-estimated. Bad data, we cannot conclude We definitely need runs to test OPERA. Other systems available? Palomar...

28 Conclusions Good progress, code available Improvements Aliasing, orthogonal SF on square frequency domain, We have to know accurately NCP aberrations, vibrations, Gemini... What are the effects of the assumptions we did? Stationnarity of structure function Real modes are unknown, because actuators cross-coupling! Need tests of the code OPERA- several runs, several systems Comparison with other approaches - S. Egner talk tomorrow