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This paper discusses an iterative computer method that can be used to solve a number of problems in optics. This method can be applied to two types of problems: (1) synthesis of a Fourier transform pair having desirable properties in both domains, and (2) reconstruction of an object when only partial information is available in any one domain. Illustrating the first type of problem, the method is applied to spectrum shaping for computer-generated holograms to reduce quantization noise. A problem of the second type is the reconstruction of astronomical objects from stellar speckle interferometer data. The solution of the latter problem will allow a great increase in resolution over what is ordinarily obtainable through a large telescope limited by atmospheric turbulence. Experimental results are shown. Other applications are mentioned briefly.
James R. Fienup (1980) studied this question.