Abstract
We propose an iterative method to optimize the phase profile of the initial field so that its intensity profile is observed periodically along the longitudinal (propagation) axis. The new method is inspired from the Gerchberg-Saxton technique, where the Fresnel transform is used, instead of the Fourier transform, for retrieving the phase profile of several light distributions (for example, 15 planes), instead of a Fourier pair of distributions. The additional challenge, with respect to the conventional Gerchberg-Saxton technique, is that the planes where constraints are applied number more than two. It turned out that when the number of periods increased, the spectrum of the obtained initial field converges toward including Montgomery's rings (self-imaging condition). (C) 2010 Optical Society of America