Analytical techniques for designing spot generating holograms

Summary form only given. Phase holograms can, in principle, route light with zero photon loss. In the future, this property of them is likely to be utilized for applications such as free space interconnects and video projection systems. In some of these applications it is necessary to create an array of spots on the replay field. Currently, spot generating holograms are evaluated using computational demanding algorithms like simulated annealing (SA) and error diffusion. These algorithms are so complex and time consuming that it is impossible to evaluate the required hologram in real time. In this paper we present a completely analytical method for evaluating spot generating holograms. The proposed method is much faster and simpler than the SA algorithm while having the same diffraction efficiency. Holograms created using the analytical method are identical with the ones obtained using SA. In terms of computational demand, the phase profile is evaluated in a fraction of a second and this time does not scale up with increasing number of pixels and phase levels.