Phase retrieval from a set of intensity measurements: theory and experiment

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Abstract
The method for phase retrieval from a set of intensity measurements is described and thoroughly investigated. This method is based on application and further minimization by gradient procedures of the functional of reconstruction error in all the planes of recording. The method is shown to result in the well-known Gerchberg–Saxton algorithm [ Optik (Stuttgart) 35, 237 ( 1972)] if two intensity measurements (in the pupil and the focal planes of a lens) are used. Numerical simulation revealed the following advantages of the method: the convergence of iterative procedures is improved, the range of reconstruction turns out to be wider, and the stability of procedures with respect to the additive noise in intensity measurements is enhanced. Experimental data confirming the conclusions of numerical simulation are presented. A nonlinear optical spatial filter is also described. The possibility of applying this filter to the problem of recovering phase from intensity measurements in the input and the output planes of the filter is shown.

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