Investigation on specific solutions of Gerchberg-Saxton algorithm

The most popular method used to generate the Computer Generated Holograms (CGH) is the Gerchberg-Saxton (GS) algorithm. GS computes an approximation of the desired beam shape, and consequently, some distortions may arise. Although many algorithms have been proposed, exact methods to overcome the problem completely do not yet exist. Here we show, for the first time to best of our knowledge, that in some specific configurations exact solutions of the GS algorithm can be achieved so as to produce a limited number of light intensity spots in a clean array. The basic concept is described and both numerical as well as experimental implementations are provided.