1 August 1983 Fundamental Performance Limitations For The Phase Retrieval Problem
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Abstract
Precomputable (Cramer-Rao) lower bounds for the integrated mean-square error are presented for the phase retrieval problem. The results are based upon the assumption that the phase is a sample function of a Gaussian random process and that the intensity measurements include additive white Gaussian noise. The bound, which is obtained from an information kernel which is the solution to a Fredholm integral equation, clearly demonstrates the effect of prior statistics, measurement noise and the nature of the linear transformation introduced prior to detection. Several examples are given; in particular, the role of diffraction is shown to be quite important for successful phase retrieval. Finally, the results are extended to include independent measurements of intensity in several planes.
© (1983) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Stanley R. Robinson, Stanley R. Robinson, } "Fundamental Performance Limitations For The Phase Retrieval Problem", Proc. SPIE 0351, Wavefront Sensing, (1 August 1983); doi: 10.1117/12.933913; https://doi.org/10.1117/12.933913
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