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Phase retrieval in the focal plane

Phase retrieval in the focal plane. Wolfgang Gaessler, Diethard Peter Clemens Storz MPIA, Heidelberg, Germany. Preface: Parallel sub-window read. Long exposure. Fast sub-windows in parallel. t win. t science. What the MPIA-Readout Electronic can do. MPIA-ROE3

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Phase retrieval in the focal plane

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  1. Phase retrieval in the focal plane Wolfgang Gaessler, Diethard Peter Clemens Storz MPIA, Heidelberg, Germany

  2. Preface: Parallel sub-window read Long exposure Fast sub-windows in parallel twin tscience AO4ELT: ‘Phase retrieval in the focal plane’ 2

  3. What the MPIA-Readout Electronic can do • MPIA-ROE3 • 1 (3) Sub-windows at science RON (5e-) • 25x25 Pixel • 135 Hz (50 Hz) • Up to 600Hz for one sub-window with 3 times science RON • Even with the old HAWAII 2 chips • Currently, limited by some undersized Flash RAM AO4ELT: ‘Phase retrieval in the focal plane’ 3

  4. sCMOS • info@pco.de • Development on back-illuminated AO4ELT: ‘Phase retrieval in the focal plane’ 4

  5. Focal plane AO Methods using one image plane for phase retrieval. I = |Uf|2 • No unique solution • Non linear • Computation intensive • Simple setup • No additional parts • As close as possible to the science image Bucci, et al. 1997 AO4ELT: ‘Phase retrieval in the focal plane’ 5

  6. Questions • Could it increase sensitivity? • What’s already done? • Is the computation power the limit? • How could an implementation look like? AO4ELT: ‘Phase retrieval in the focal plane’ 6

  7. Increased Sensitivity? • Number of Photons ~ D2 • Number of Sub-Apertures ~ D2 • No gain for AO with larger diameter • Doesn’t this change in focal plane? • Yes, but needs proper sampling. Pixseeing/Pixdiff ~ D2 Solution: Dynamic binning AO4ELT: ‘Phase retrieval in the focal plane’ 7

  8. Dynamic binning SNRbin,soft ~ D SNRbin,hard ~ D2 AO4ELT: ‘Phase retrieval in the focal plane’ 8

  9. Solving I = |Uf|2 • Image sharpening algorithm • Intensity metrics maximizing • Muller et. al. 1974 theory • Buffington et. al. 1977 implementation in telescope • Recently: Murray et. al. 2007, Both et. al. 2005 • Iterative Fourier Transform • Gerchberg Saxton AO4ELT: ‘Phase retrieval in the focal plane’ 9

  10. Image sharpening metrics • Optimization metrics • S=∫In(x,y)dxdy n=2,3,4 maximize • S =∫ln(I(x,y))dxdy maximize • Lukosz-Zernike metric minimize • ρ = spot radius • NA = aperture • λ = wavelength • b = Lukosz-Zernike coefficient AO4ELT: ‘Phase retrieval in the focal plane’ 10

  11. DM Image sharpening algorithms • Change shape of DM to minimize • ADN -> N+1 iterations (Murray et. al.2007) • AD = actuator dynamic ~ >255, N = # actuator ~ >1000 • Time consuming for high order correction AO4ELT: ‘Phase retrieval in the focal plane’ 11

  12. Gerchberg Saxon • Approximate amplitude constant in pupil • Inverse Fourier transform • Compare to PSF • Fourier transform AO4ELT: ‘Phase retrieval in the focal plane’ 12

  13. Implementation by Bucci et. al. 1997 • Penalty algorithm • Representation in Zernike • Minimizes the Intensity with a gradient operator • Stable and usual trapping problem less relevant • O(Nmode ln(Nmode) x Npix) • Converge after some 100 iterations • For low order sensing feasable AO4ELT: ‘Phase retrieval in the focal plane’ 13

  14. Low order sensorNon common path error tracker Guide Star Guide Star • Low order sensor (TT, focus, etc.) • Time varying flexure and distortion • Slow offload of non common path Telescope Telescope DM DM Science Focal Plane WFC WFC WFS WFS AO4ELT: ‘Phase retrieval in the focal plane’ 14

  15. Conclusion • Phase retrieval in the focal plane is a long known problem worked on with several solutions: • Image sharpening • Iterative Inverse Fourier transformation • All are quite time consuming in computation • Dynamic binning could gain some sensitivity and computation power • Low order sensor • But also high order, shown by O. Guyon AO4ELT: ‘Phase retrieval in the focal plane’ 15

  16. What else…spectroscopy • Slit viewer image (put all light into the slit) • Phase retrieval on the PSF of spectral lines • Does this problem even compare to a diffraction grating sensor? AO4ELT: ‘Phase retrieval in the focal plane’ 16

  17. AO4ELT: ‘Phase retrieval in the focal plane’ 17

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