On the uniqueness question in the problem of phase retrieval from intensity measurements

The treatment of the problem of deducing the phase of an optical wavefield from image- and diffraction-plane intensity measurements recently presented by Robinson [ J. Opt. Soc. Am68, 87– 92 ( 1968)] is shown to be valid only in the limit of geometrical optics. A simple proof and example of the nonuniqueness of the phase retrieval problem in this limit is presented. It is argued that although the phase retrieval is not unique in the geometrical optics limit it does appear to possess a unique solution within the framework of the diffraction theory of image formation.