Optimal 3-D beam forming

A beam propagating in free space is exposed to the laws of diffraction, which tend to deform the wave front. Hence, 3-D beam forming is a very applicable task. For instance it may be useful in designing a special beam to be used for scanning purposes, beam forming for optical communication modules and 3-D beam forming as a tool to exceed system's resolving power. There are several techniques, which allow obtaining a reduced sensitivity to diffraction in a pre-determined region of propagation. In this paper a novel optimal technique is suggested. Using the calculus of variation method we derive an analytic expression for an optimal filter in the mean square error sense, to obtain a 3-D beam forming, which is as close as possible to the desired 3-D distribution. We applied the proposed method for obtaining a scanning beam with improved performances. The suggested approach was tested in computer simulations as well as in optical experiments and was proven to deliver improved performance. Thus one can obtain an extended working region using the resulting beam with confined lateral spread.