Abstract

Two phase retrieval methods are used for the reconstruction of a 2-D object function from its. Fourier transformed moduli obtained with and without an exponential filter at the object plane. One of the methods is a phase retrieval method using only the Fourier series expansion, and the other is a phase retrieval method using the logarithmic Hilbert transform and the Fourier series expansion. These methods extend the range that successful reconstructions of 2-D objects can be obtained by making use of the properties of entire functions of the exponential type. The usefulness of these methods is shown in computer simulation studies of the reconstructions of 2-D real and phase objects from their Fourier moduli.

© 1989 Optical Society of America

Phase retrieval using the logarithmic Hilbert transform and the Fourier-series expansion

N. Nakajima
J. Opt. Soc. Am. A 5(2) 257-262 (1988)

Phase retrieval from two intensity measurements using the Fourier series expansion

N. Nakajima
J. Opt. Soc. Am. A 4(1) 154-158 (1987)

Noniterative two-dimensional phase-retrieval method from two Fourier intensities by use of an exponential filter

Nobuharu Nakajima
Appl. Opt. 42(14) 2492-2497 (2003)

Reconstruction of phase objects from experimental far field intensities by exponential filtering

Nobuharu Nakajima
Appl. Opt. 29(23) 3369-3374 (1990)

High-resolution scanning phase retrieval with a probe beam of unknown modulus

Nobuharu Nakajima
Appl. Opt. 36(17) 3904-3911 (1997)