Optimized Iterative Method for Phase Retrieval Using a Liquid Crystal Spatial Light Modulator

Recovering the phase information of a diffracted beam has a major interest in several fields such as microscopy, materials research and astronomy. Generally, the solutions fall into two broad categories: interferometric methods and iterative methods based on beam propagation. The latter are known to have easier experimental implementations; they are also less sensitive and are considered as “inverse problem” using an iterative algorithm, alternating between spatial domain and Fourier domain [1]. However, iterative methods have certain limitations; they do not converge in all cases. Furthermore, some technical difficulties have limited their application domains. In order to solve these limitations and improve the robustness of these methods, experimental strategies have been employed [2]. Here the idea is to modulate the wavefront in the object plane with M random phase distributions generated with a Liquid Cristal Spatial Light Modulator (LC-SLM) and record M diffraction spectra before launching the iterative algorithm. The important parameter required for proper functioning and convergence of the method is the precise knowledge of all the random phases used during the acquisition. However LC-SLM are known to have a high cross-talk shown by experimental results [3], consequently the real phase displayed on the SLM is different from the expected phase and the algorithm doesn’t converge properly. In order to reduce the effect of the cross talk, we modelized it as a convolution and the retrieval process loop has been modified. The PSF is considered as an elliptical generalized Gaussian function [4].