Locations at which the Fourier transform F(u, υ) of an image equals zero have been called real-plane zeros, since they are the intersections of the zero curves of the analytic extension of F(u, υ) with the real–real (u, υ) plane. It has been shown that real-plane zero locations have a significant effect on the Fourier phase in that they are the end points of phase branch cuts, and it has been shown that real-plane zero locations can be estimated from Fourier magnitude data. Thus real-plane zeros can be utilized in phase retrieval algorithms to help constrain the possible Fourier phases. First we show a simplified procedure for estimating real-plane zeros from the Fourier magnitude. Then we present a new phase retrieval algorithm that uses real-plane zero locations to generate a simple parameterization of the Fourier phase and uses knowledge about the image to estimate the Fourier phase parameters. We show by example that this algorithm generates improved phase retrieval results when it is used as an initial guess into existing iterative algorithms. We assume that the image is real valued.
© 1994 Optical Society of America
Christopher C. Wackerman and Andrew E. Yagle, "Phase retrieval and estimation with use of real-plane zeros," J. Opt. Soc. Am. A 11, 2016-2026 (1994)