Abstract

This study sheds new light on the stagnation problem troubling the iterative Fourier transform algorithm used for phase retrieval. This is implemented by the introduction of two concepts, the territory and the hole, which exist in a relationship in the sense that the creation and the annihilation of a hole results in the annihilation and the creation of a corresponding territory. These concepts are brought about in the parameter space formed by the set of objects satisfying the object-domain constraints by means of topographical investigations of the minimization process by use of the error-reduction algorithm, paying particular attention to the cases of $2\times 2$ and $3\times 2$ objects with L-shaped supports. The effect of noise contained in the Fourier modulus on the stagnation phenomena is also clarified by use of these concepts.

© 1997 Optical Society of America

Study on the convergence property of the hybrid input–output algorithm used for phase retrieval

Hiroaki Takajo, Tohru Takahashi, Ryuzo Ueda, and Makoto Taninaka
J. Opt. Soc. Am. A 15(11) 2849-2861 (1998)

Phase-retrieval stagnation problems and solutions

J. R. Fienup and C. C. Wackerman
J. Opt. Soc. Am. A 3(11) 1897-1907 (1986)

Further study on the convergence property of the hybrid input–output algorithm used for phase retrieval

Hiroaki Takajo, Tohru Takahashi, and Takao Shizuma
J. Opt. Soc. Am. A 16(9) 2163-2168 (1999)

Numerical investigation of the uniqueness of phase retrieval

J. H. Seldin and J. R. Fienup
J. Opt. Soc. Am. A 7(3) 412-427 (1990)

Reconstruction of an object from its noisy Fourier modulus: ideal estimate of the object to be reconstructed and a method that attempts to find that estimate

Hiroaki Takajo, Takao Shizuma, Tohru Takahashi, and Seiji Takahata
Appl. Opt. 38(26) 5568-5576 (1999)