Direct Method for Phase Retrieval from the Intensity of Cylindrical Wavefronts

Abstract

Recently there has been some interest shown in the non-interferometric reconstruction of complex wavefields from intensity measurements [1,2]. At the same time it has been shown that for partially coherent systems this is not, in general, possible because different wavefields can exhibit identical intensity distributions [3]. The more restricted problem of finding the complex wave-field corresponding to the three dimensional intensity in a coherent system may be soluble by iterative phase retrieval techniques, but is not directly soluble. We consider a particular subset of the general problem which is demonstrably soluble by a direct method. The particular subset considered is essentially an optical wavefield propagating in a plane. This reduces the problem from three to two dimensions, resulting in a well-posed inverse problem. Initially we assume the system to be coherent, but we note that there are indications that the partially coherent case is also soluble. The solution presented is not just a theoretical curiosity because systems with the required geometry occur in slab waveguides and slit illumination systems.