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 twin tscience June 22-26, 2009 AO4ELT: ‘Phase retrieval in the focal plane’ 2

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 June 22-26, 2009 AO4ELT: ‘Phase retrieval in the focal plane’ 3

sCMOS info@pco.de Development on back-illuminated June 22-26, 2009 AO4ELT: ‘Phase retrieval in the focal plane’ 4

Focal plane AO I = |Uf|2 No unique solution Non linear 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 June 22-26, 2009 AO4ELT: ‘Phase retrieval in the focal plane’ 5

Questions Could it increase sensitivity? What’s already done? Is the computation power the limit? How could an implementation look like? June 22-26, 2009 AO4ELT: ‘Phase retrieval in the focal plane’ 6

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 June 22-26, 2009 AO4ELT: ‘Phase retrieval in the focal plane’ 7

Dynamic binning SNRbin,soft ~ D SNRbin,hard ~ D2 June 22-26, 2009 AO4ELT: ‘Phase retrieval in the focal plane’ 8

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 June 22-26, 2009 AO4ELT: ‘Phase retrieval in the focal plane’ 9

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 June 22-26, 2009 AO4ELT: ‘Phase retrieval in the focal plane’ 10

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 DM June 22-26, 2009 AO4ELT: ‘Phase retrieval in the focal plane’ 11

Gerchberg Saxon Approximate amplitude constant in pupil Inverse Fourier transform Compare to PSF Fourier transform June 22-26, 2009 AO4ELT: ‘Phase retrieval in the focal plane’ 12

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 June 22-26, 2009 AO4ELT: ‘Phase retrieval in the focal plane’ 13

Low order sensor Non common path error tracker Low order sensor (TT, focus, etc.) Time varying flexure and distortion Slow offload of non common path Guide Star Guide Star Telescope Telescope DM DM Science Focal Plane WFC WFC WFS WFS June 22-26, 2009 AO4ELT: ‘Phase retrieval in the focal plane’ 14

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 June 22-26, 2009 AO4ELT: ‘Phase retrieval in the focal plane’ 15

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? June 22-26, 2009 AO4ELT: ‘Phase retrieval in the focal plane’ 16

June 22-26, 2009 AO4ELT: ‘Phase retrieval in the focal plane’ 17