Optimal strategies for wave fields sensing by means of multiple planes phase retrieval

Abstract

A method for recovering the complex amplitude of a monochromatic light field from a set of intensity measurements is presented. In contrast to current iterative phase retrieval approaches, the proposed method is based on a further constraint of the phase retrieval problem utilizing a set of deterministic criteria derived from the Helmholtz equation. An example of these criteria is the derivation of a new forward propagation operator. The main advantage of the proposed forward propagation operator is the implementation of three intensity constraints compared with the ordinary forward propagation where only one intensity constraint is applied. This allows one to drastically reduce the number of intensity measurements and improve the convergence speed of the proposed method. Four intensity observations, similar to common temporal phase shifting, are required to recover the complex amplitude of arbitrary wave fields without the need for a priori knowledge. The method is experimentally demonstrated and the results are verified by comparing them to those obtained from phase shifting interferometry.