Phase retrieval in the focal plane

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Phase retrieval in the focal plane

• Wolfgang Gaessler, Diethard Peter Clemens Storz
• MPIA, Heidelberg, Germany

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Preface Parallel sub-window read
Long exposure
Fast sub-windows in parallel
twin
tscience
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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

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sCMOS

• info_at_pco.de
• Development on back-illuminated

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Focal plane AO
Methods using one image plane for phase retrieval.

• I Uf2
• No unique solution
• Non linear
• Computation intensive
• Simple setup
• No additional parts
• As close as possible to the science image

Bucci, et al. 1997
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Questions

• Could it increase sensitivity?
• Whats already done?
• Is the computation power the limit?
• How could an implementation look like?

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Increased Sensitivity?

• Number of Photons D2
• Number of Sub-Apertures D2
• No gain for AO with larger diameter
• Doesnt this change in focal plane?
• Yes, but needs proper sampling.
• Pixseeing/Pixdiff D2
• Solution Dynamic binning

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Dynamic binning
SNRbin,soft D SNRbin,hard D2
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Solving I Uf2

• 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

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Image sharpening metrics

• Optimization metrics
• S?In(x,y)dxdy n2,3,4 maximize
• S ?ln(I(x,y))dxdy maximize
• Lukosz-Zernike metric minimize
• ? spot radius
• NA aperture
• ? wavelength
• b Lukosz-Zernike coefficient

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Image sharpening algorithms

• Change shape of DM to minimize
• ADN -gt N1 iterations (Murray et. al.2007)
• AD actuator dynamic gt255, N actuator
  gt1000
• Time consuming for high order correction

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Gerchberg Saxon

• Approximate amplitude constant in pupil
• Inverse Fourier transform
• Compare to PSF
• Fourier transform

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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

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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
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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

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What elsespectroscopy

• 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?

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