1 / 24

Study of centroiding algorithms to optimize Shack-Hartmann WFS in the context of ELTs

Study of centroiding algorithms to optimize Shack-Hartmann WFS in the context of ELTs. Sandrine Thomas Don Gavel, Olivier Lardiere, Rodolphe Conan, Sean Adkins. LAO, UCO/Lick Observatory, (b) University of Victoria, (c) Keck Obsevatory.

charo
Download Presentation

Study of centroiding algorithms to optimize Shack-Hartmann WFS in the context of ELTs

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Study of centroiding algorithms to optimize Shack-Hartmann WFS in the context of ELTs Sandrine Thomas Don Gavel, Olivier Lardiere, Rodolphe Conan, Sean Adkins LAO, UCO/Lick Observatory, (b) University of Victoria, (c) Keck Obsevatory AO4ELTs, 25th of June 2009

  2. Designing WFS optimized for Next Generation AO and ELTs Δh • Use of laser guide stars • Extremely large telescopes (ELT): > 10 • Increase of the elongation of the spot to a few arcsec leading to • lower SNR per pixel • non negligible structure and time variability of the sodium profile AO4ELTs, Paris, 25th of June 2009

  3. Polar Coordinate Detector • Rectangular “pixel islands” in each subaperture • Major axis of each rectangle aligned with axis of elongation in that subaperture • Allows good sampling of a CW LGS image along the elongation axis • Allows tracking of a pulsed LGS image CCD optimized for LGS AO wavefront sensing on an ELT AO4ELTs, Paris, 25th of June 2009

  4. Previous results Etotal = Enoise + ELin + Esodium + Ediff + … • Simulation and theoretical derivations shown in Thomas et al, 2008 for a Gaussian spot. • Test of linearity, i.e. sampling and troncature • Added photon and readout noise • Best sampling and size of the array, 1.8pix/fwhm, 4x16 for the polar CCD Readout noise + Photon noise + (background noise)  Time variability + Structure Under Sampling + Truncation Diffraction spike + Cross talk  AO4ELTs, Paris, 25th of June 2009

  5. Real profiles are needed to understand the effect of the sodium layer variability on the performance of the wavefront sensor • 6 nights from November 2005 until March 2008 (Mainly fall and winter) • 97 images -> ~ 30000 synthetic profiles Launch the laser from the Shane Telescope and let the Nickel one drift • Profile evolution • Time scale of refocusing • Thickness evolution • Projection on the CCD of a SHWFS: • Algorithm comparisons • Comparison with other errors Time resolution: ~ 0.5s AO4ELTs, Paris, 25th of June 2009

  6. The night of the February 9th 2006 Time Time Time Altitude Altitude Altitude AO4ELTs, Paris, 25th of June 2009

  7. Truncation effect of the sodium layer The depth of focus of the TMT at 90 km is about 10 meters October 10th 2006, beginning of the night (left), end of the night (right) October 10th 2006 February 9th 2006 <10 m for a FoV greater than 18km <10 m for a FoV greater than 20km 10 km 10 km AO4ELTs, Paris, 25th of June 2009

  8. Time considerations • The depth of focus of the TMT at 90 km is about 10 meters => Need to refocus at about 1m • The temporal power spectrum of the variations will determine how often this measurement needs to be made. An average over all samples gives a -1.7 power law from 0.01 to 1 Hz Similar results from the LIDAR data presented by Pfrommer et al. Extrapolating this power law to the 1 meter variations gives ~0.2s in average (faster end of the NGS WFS rate for the TMT telescope) AO4ELTs, Paris, 25th of June 2009

  9. Δh Projection on the CCD in the context of the TMT • SHWFS: 60x60 subapertures of 0.5m • Detector: 25ms integration time and 500ms readout time. • Readout noise: 1-5 e- • Motion = 0.8 FWHM • Typical seeing condition: 1.19” • No up-link correction 2.102 - 104 photons at 589nm, arriving on SH AO4ELTs, Paris, 25th of June 2009

  10. Time Altitude Projection on the CCD • One line = 1 synthetic profile • Get the number of pixels from the FOV and the pixel size • => get a 2D image • Convolution with diffraction of the subaperture (50 cm) • Convolution with the atmospheric blur (1.19”)    Profile Diffraction Seeing blur AO4ELTs, Paris, 25th of June 2009

  11. Method • Use of different centroiding algorithms to calculate the position of the spot: thresholded CoG, Correlation (Parabolic fit and CoG), Matched filter. • Choice of the reference - average over 12/40/160 images ie 6, 20 seconds • Wavefront reconstruction using Fourier Transform • Decomposition in Zernike coefficients Wavefront reconstruction using Correlation, SNR=18 AO4ELTs, Paris, 25th of June 2009

  12. Motion of the spot, Oct 10th 06 Position of the sub-aperture = 14m, 60x60 sub-apertures Number of pixels: 16x16 Resolution: 1.8 pixels per FHWM Number of pixels: 128x128 Resolution: 14.4 pixels per FHWM AO4ELTs, Paris, 25th of June 2009

  13. Aberrations due to the sodium variations(From simulations only) • No noise, 60x60 subapertures • Using an average of the 10 profiles as a reference, every 10 profiles. • Expected radially symetric aberrations • Defocus (Z4), spherical (Z11), second order Spherical (Z22) • Z14 and Z26 are quadrature trefoil aberrations • Defocus = 38nm Previous results when using a Gaussian elongated spot: 9nm rms WF for SNR = 100 AO4ELTs, Paris, 25th of June 2009

  14. Check simulation with results from the University of Victoria’s bench • 2 sources (LGS+NGS), 1 10x10 DM, 2 SH-WFSs • “LGS-WFS”: 32x32 elongated spots SH-WFS: • subaperture=15x15px, spot sampling =2x8px • the DM stretches the spots during the WFS exposure to reproduce elongated spots • Max. FOV = 20km-thick Na layer for side spots • “NGS-WFS”: 12x12 unelongated spots SH-WFS (subap=8x8px, spot=2px) AO4ELTs, Paris, 25th of June 2009 See Conan et al. talk later

  15. High SNR, 32x32 subapertures Simulations • SNR ~ 140 : Nph = 900, nr = 5e-, 16x16 pixels • Reference is an average of 40 profiles calculated every 40 profiles, (~ 20s) Same kind of aberrations as the case with no noise All algorithms gives very similar results to less than 1nm rms Noise floor due to photon and readout noise: ~0.5nm rms AO4ELTs, Paris, 25th of June 2009

  16. High SNR, 32x32 subaperturesLab results • SNR ~ 140 , 15x15 pixels • Reference is an average of 40 profiles calculated every 40 profiles, (~ 20s) • Same kind of aberrations except for the Zernike 26 • More differences between algorithms • The correlation using a parabolic fit as the peak finder is better except for the different high powered Zernike • Noise floor at about 0.5nm rms. AO4ELTs, Paris, 25th of June 2009

  17. Low SNR, 32x32 subaperturesSimulations • SNR ~ 18 : Nph = 900, nr = 5e-, 16x16 pixels • Reference is an average of 40 profiles calculated every 40 profiles, (~ 20s) • More asymmetric types of aberrations appear due to the low SNR, more particularly Z6, Z9 and Z20-Z21 • The correlation gives best results by 1nm rms • Noise floor due to photon and readout noise increases to 2-4 nm rms AO4ELTs, Paris, 25th of June 2009

  18. Low SNR, 32x32 subaperturesLab results • SNR ~ 18 , 15x15 pixels • Reference is an average of 40 profiles calculated every 40 profiles, (~ 20s) • Apparition of the same non-symmetric aberrations, Z6, Z9, Z20-Z21 • Noise floor increased to 1nm rms for the correlation and 2 for the other two algorithms • The correlation is giving the best results • Those results are lower than simulations: Maybe due to a mismatch in the SNR AO4ELTs, Paris, 25th of June 2009

  19. Conclusions • Sodium layer analysis: • FoV needed to get centroiding accuracy of the order of TMT depth of focus is 20km • Variations of the mean sodium layer altitude are ~1km on a time scale of a few seconds • LGS induced aberrations: • In the context of the TMT, the error due to the sodium layer is 30nm rms. The time scale used was 20s. • At a SNR of 18, the error higher than focus due to the sodium layer is comparable to the error due to photon and readout noise. • The correlation method give better results for such SNRs AO4ELTs, Paris, 25th of June 2009

  20. Future work • Simulation of more turbulent profiles such as the one from Feb 9th 2006 • Understand non-symmetric aberration like Z6, Z9 Z21 • Understand the disagreements between simulations and lab work • Reference update time scale • Add atmospheric turbulence • Simulate the polar CCD • Study the advantage of pulse tracking AO4ELTs, Paris, 25th of June 2009

  21. Acknowledgments • The authors would like to gratefully acknowledge the Gordon and Betty Moore Foundation for postdoctoral support of Dr. Thomas via the Laboratory for Adaptive Optics at UC Santa Cruz.We also gratefully acknowledge the support of the National Science Foundation Science and Technology Center for Adaptive Optics, managed by the University of California at Santa Cruz. This material is based in part upon work supported by AURA through the National Science Foundation under AURA Cooperative Agreement AST 0132798, Scientific Program Order No. 6 (AST-0336888) as amended. AO4ELTs, Paris, 25th of June 2009

  22. Previous results •  compromise between the sampling and the truncation for different values of SNR Etotal = Enoise + ELin Optimal sampling = 1.5 pix Optimal array = 4x16 pix AO4ELTs, Paris, 25th of June 2009

  23. Previous results from Elongated Gaussian spot •  compromise between the sampling and the truncation for different values of SNR • For low SNR : noise dominates, all array sizes are equivalent if sampling ~ 1.1 pix • For medium SNR : sampling = 1.5 pix and array = 4.7 sigma • For high SNR : sampling = 1.5 pix and array = 4.7 sigma If el=4 than for medium SNR and for 1.8 pix, optimal array is 416 pix If el=4 than for high SNR and for 2 pix, optimal array is 620 pix AO4ELTs, Paris, 25th of June 2009

  24. Sodium Profile • Data from Lick Observatory, Don Gavel on Feb 9th 2005 Intensity Time (s) Relative Altitude (km) AO4ELTs, Paris, 25th of June 2009

More Related