An algorithm for phase retrieval with Bayesian statistics is discussed. It is shown how the statistics of Kol-mogorov turbulence can be used to compute the likelihood for a particular phase screen. This likelihood is then added to that of the observed data to produce a functional that is maximized directly by use of conjugate gradient maximization. It is shown that although this can significantly improve the quality of the phase estimate, the issue is complicated by local maxima introduced by the possibility of phase wrapping. The causes of the local maxima are analyzed, and a method that increases the likelihood of convergence to the global maximum is presented. # 1998 Optical Society of America [S0740-3232(98)01009-6] OCIS codes: 100.170, 010.210.
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