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
Original Manuscript: July 29, 1989
Manuscript Accepted: October 24, 1989
Published: March 1, 1990
J. H. Seldin and J. R. Fienup, "Numerical investigation of the uniqueness of phase retrieval," J. Opt. Soc. Am. A 7, 412-427 (1990)