Use of Fourier Domain Real Plane-Zeros in Phase Retrieval

Throughout a large number of disciplines, including astronomy, wave-front sensing and x-ray crystallography, there exists a class of problems referred to as the phase retrieval problem; given the modulus |F(u,v)| of the Fourier transform of an object f(x,y) and some constraints about the form of f(x,y), reconstruct f(x,y). Several solutions to this problem have been proposed, but our research has concentrated on the iterative Fourier transform algorithm (IFTA) [1,2] which has the advantages of being robust under noisy conditions and not computationally burdensome. An area of difficulty for the IFTA however is that the algorithm often stagnates at a reconstruction with stripe like noise, especially for real, non-negative objects [3]. This paper will present research that we have done to address this problem by using information about locations in the Fourier plane where F(u,v) is identically zero, what we will call Fourier domain real-plane zeros (RPZ's). Two new algorithms will be presented: one corrects a stripe stagnation problem from only a single reconstruction; the other modifies the IFTA to allow it to use locations of RPZ's as an additional constraint and prevents stripe stagnation from occurring altogether.