Phase front retrieval by means of an iterative shadowgraphic method

Abstract

In this paper, we propose an iterative shadowgraphic method (ISM) as an interesting alternative to existing methods for self-referencing optical phase retrieval. Two defocused images of the intensity distribution of the light scattered by a weakly absorbing phase object were sufficient to retrieve the transverse phase distribution of the distorted illuminating beam. An algorithm was developed to correct for diffraction effects in phase maps retrieved with a simple shadowgraphic method. We provide a mathematical proof of the convergence of the algorithm to the true profile of the sought phase object. Several numerical tests were performed of the algorithm showing its capability of recovering the full details of the original phase distribution with increased resolution as compared with the simple shadowgraphic method. The convergence of the ISM was also compared numerically with that of a nonoptimized Gerchberg-Saxton-type algorithm and found to be faster and not affected by stagnation problems.