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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. 7, Iss. 3 — Mar. 1, 1990
  • pp: 412–427

Numerical investigation of the uniqueness of phase retrieval

J. H. Seldin and J. R. Fienup  »View Author Affiliations


JOSA A, Vol. 7, Issue 3, pp. 412-427 (1990)
http://dx.doi.org/10.1364/JOSAA.7.000412


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Abstract

Both a new iterative grid-search technique and the iterative Fourier-transform algorithm are used to illuminate the relationships among the ambiguous images nearest a given object, error metric minima, and stagnation points of phase-retrieval algorithms. Analytic expressions for the subspace of ambiguous solutions to the phase-retrieval problem are derived for 2 × 2 and 3 × 2 objects. Monte Carlo digital experiments using a reduced-gradient search of these subspaces are used to estimate the probability that the worst-case nearest ambiguous image to a given object has a Fourier modulus error of less than a prescribed amount. Probability distributions for nearest ambiguities are estimated for different object-domain constraints.

© 1990 Optical Society of America

History
Original Manuscript: July 29, 1989
Manuscript Accepted: October 24, 1989
Published: March 1, 1990

Citation
J. H. Seldin and J. R. Fienup, "Numerical investigation of the uniqueness of phase retrieval," J. Opt. Soc. Am. A 7, 412-427 (1990)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-7-3-412

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