Abstract

We discuss the problem of Fourier phase recovery from measurements of the bispectrum phase and present the algorithm for a two-dimensional object by extending the method introduced by Marron et al. [ J. Opt. Soc. Am. A 7, 14 ( 1990)]. The main objective is to unwrap the measured bispectrum phase so that the signal parts of the unwrapped bispectrum phases are linked to the Fourier phases by a linear system of equations: These linear equations are solved in a least-squares sense to recover the Fourier phases. However, in the unwrapping process we have to solve an extremely large linear system of equations, which creates a serious difficulty. To cope with this difficulty, we construct a recursive method that permits us to solvethese equations efficiently without constructing their coefficient matrix. By computer simulations, we verify that the proposed Fourier-phase-recovery algorithm is effective.

© 1991 Optical Society of America

Least-squares Fourier phase estimation from the modulo 2π bispectrum phase

Christopher A. Haniff
J. Opt. Soc. Am. A 8(1) 134-140 (1991)

Unwrapping algorithm for least-squares phase recovery from the modulo 2π bispectrum phase

J. C. Marron, P. P. Sanchez, and R. C. Sullivan
J. Opt. Soc. Am. A 7(1) 14-20 (1990)

Weighted-least-squares phase reconstruction from the bispectrum

Charles L. Matson
J. Opt. Soc. Am. A 8(12) 1905-1913 (1991)

Weighted-least-squares magnitude-spectrum estimation from the bispectrum

Charles L. Matson
J. Opt. Soc. Am. A 8(12) 1914-1921 (1991)

Shift- and rotation-invariant object reconstruction using the bispectrum

Brian M. Sadler and Georgios B. Giannakis
J. Opt. Soc. Am. A 9(1) 57-69 (1992)