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

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

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

5. 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’

6. 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’

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

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

9. Solving I = |Uf|2 Image sharpening algorithm
Intensity metrics maximizing
Muller et. al theory
Buffington et. al 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’

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

11. 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’

12. 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’

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

14. 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’

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

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

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