Abstract

In general, the problem of reconstructing an object from its Fourier modulus has no solution when the Fourier modulus is contaminated by noise. Therefore a quasi solution, which we call the ideal estimate of the object to be reconstructed, is defined here based on the concept of territories of the convergence objects of the error-reduction algorithm, and a method that attempts to find that solution is presented. Keeping in mind that the ideal estimate is one of the output-stagnation objects of the hybrid input–output algorithm, we modify the hybrid input–output algorithm so that the output-stagnation objects can be located even when the value of the feedback parameter is not infinitesimally small, and this modified algorithm is combined with the hybrid input–output algorithm itself. The results of computer simulations carried out to test the performance of the proposed method are shown.

© 1999 Optical Society of America

Reconstruction of an object from its Fourier modulus: development of the combination algorithm composed of the hybrid input-output algorithm and its converging part

Hiroaki Takajo, Tohru Takahashi, Katsuhiko Itoh, and Toshiro Fujisaki
Appl. Opt. 41(29) 6143-6153 (2002)

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)

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 iterative phase-retrieval stagnation problem: territories of convergence objects and holes in their boundaries

Hiroaki Takajo, Tohru Takahashi, Hiroaki Kawanami, and Ryuzo Ueda
J. Opt. Soc. Am. A 14(12) 3175-3187 (1997)

Mitigating the effect of noise in the hybrid input–output method of phase retrieval

Russell Trahan and David Hyland
Appl. Opt. 52(13) 3031-3037 (2013)