A New Method for Phase Retrieval in the Optical System

In this letter, a new recursive algorithm to implement phase retrieval from two intensities in the two-dimensional Fourier transform domain is presented. In terms of the cascading property and additivity of the order of the fractional Fourier transform, a set of convolution equations is exactly derived. Applying recursive algorithm, these equations can be easily solved. This approach simplifies significantly computational manipulations comparing with conventional iterative algorithms and does not need initial phase distribution.