Abstract

A method for reconstructing a real object function from the intensity of its Hartley transform is proposed. This method is established as a closed-form expression by making use of the mathematical properties of entire functions of the exponential type. The usefulness of the method is shown in computer-simulation studies of the reconstruction of the one-dimensional real object from its Hartley intensity. In addition it is shown that the theory developed in one dimension is straightforwardly extended to two dimensions.

© 1988 Optical Society of America

Algorithm for the recovery of a real signal from its Hartley-transform modulus only

Bizhen Dong, Benyuan Gu, and Guozhen Yang
J. Opt. Soc. Am. A 8(7) 1048-1054 (1991)

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)

In-line hologram reconstruction using Hartley transform

Meriç Özcan
Appl. Opt. 50(34) H159-H164 (2011)

Two-dimensional phase retrieval by exponential filtering

Nobuharu Nakajima
Appl. Opt. 28(8) 1489-1493 (1989)