On the phase retrieval problem in two dimensions

Abstract

The paper contains a discussion of the phase retrieval problem in two dimensions and proposes criteria to select those resolutions of the discrete ambiguity of the zero trajectories which are compatible with the analyticity in two variables of the scattered field.

Zero Trajectories and the Problem of the Reconstruction of the Phase

“…eqns. (1.11)-(1.12), of exponential type in both variables, it is known (see [137], [58]) that its possible irreducible factors are entire functions of order a t most unity; however, it appears one cannot yet exclude that some of these factors may be of nonexponential (i.e. infinite) type (similar to l/I'(z) in one complex dimension).…”

Blind Image Deconvolution

“…Each component has a compact support (S) 2. The spectrum of each component is zero on a single continuous surface [152] called as the zero sheet and 3. The M zero sheets are distinct -they intersect only at discrete points in the 2S dimensional space.…”

Maximum-likelihood estimation of parameterized wavefronts from multifocal data

“…However, the usual PR problem is ill posed, since both distributions are unrestricted 2D functions [1] and a single irradiance measurement does not ensure that the recovered phase is unique [2,3]. A straightforward solution to avoid the ambiguities is to make multiple irradiance measurements near the focal plane, where the minimum number of planes is two.…”