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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 20, Iss. 8 — Aug. 1, 2003
  • pp: 1490–1504

Diversity selection for phase-diverse phase retrieval

Bruce H. Dean and Charles W. Bowers  »View Author Affiliations


JOSA A, Vol. 20, Issue 8, pp. 1490-1504 (2003)
http://dx.doi.org/10.1364/JOSAA.20.001490


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Abstract

Wavefront-sensing performance is assessed for focus-diverse phase retrieval as the aberration spatial frequency and the diversity defocus are varied. The analysis includes analytical predictions for optimal diversity values corresponding to the recovery of a dominant spatial-frequency component in the pupil. The calculation is shown to be consistent with the Cramér–Rao lower bound by considering a sensitivity analysis of the point-spread function to the spatial frequency being estimated. A maximum value of diversity defocus is also calculated, beyond which wavefront-sensing performance decreases as diversity defocus is increased. The results are shown to be consistent with the Talbot imaging phenomena, explaining multiple periodic regions of maximum and minimum contrast as a function of aberration spatial frequency and defocus. Wavefront-sensing performance for an iterative-transform phase-retrieval algorithm is also considered as diversity defocus and aberration spatial frequency are varied.

© 2003 Optical Society of America

OCIS Codes
(100.5070) Image processing : Phase retrieval
(110.6760) Imaging systems : Talbot and self-imaging effects
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

Citation
Bruce H. Dean and Charles W. Bowers, "Diversity selection for phase-diverse phase retrieval," J. Opt. Soc. Am. A 20, 1490-1504 (2003)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-8-1490


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  39. If inaccurate pupil data are applied in the iterative-transform sense (Fig. 1), the pupil amplitude and the phase information become mixed, resulting in artificial aberrations in the phase estimate. For example, a pupil amplitude function consisting of a shifted central obscuration in a two-mirror system can lead to phase-retrieval estimates with artificial coma. But this ambiguity is resolved when utilizing diversity images on both sides of focus since the defocused PSF is asymmetric about focus (for a shifted central obscuration), while true coma produces a symmetric PSF about focus.

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