Optimal synthesis of three-dimensional complex amplitude distributions

The synthesis of three-dimensional (3-D) light distributions is important f or many applications. For example, in scanning applications it is preferabl e that the scanning beam preserve its characteristics over a large distance to yield elongated scanning range. It is evident that any 3-D light distri bution must satisfy the wave equation or, in second-order approximation, th e Fresnel diffraction formula. Thus many desirable 3-D light distributions may not be realizable. We propose a single optical element (OE) that synthe sizes a physical beam within a certain 3-D region. The OE provides the opti mal physical beam in comparison with a desired one in the sense of minimal mean-square error. (C) 2000 Optical Society of America OCIS code: 140.3300.