Gerchberg-Saxton algorithm applied in the fractional Fourier or the Fresnel domain.

The Gerchberg-Saxton (G-S) algorithm is a well-known procedure used in various optical implementations. One of its most common applications is beam shaping of an input plane. In that application the desired beam shape is obtained in the Fourier plane. We propose an algorithm in which the desired shape is obtained in the fractional Fourier or the Fresnel domain. Computer simulations illustrate that the newly defined algorithm can reduce the error between the theoretically desired shape and the actual output by 30 times over the conventional G-S algorithm.