Abstract

To compete with electronic processing, optical processors must exploit fully their potential for noninterfering data redistribution from one plane of the processor to another. The performance of partitioned holograms with discrete subholograms is often unsatisfactory for the task of data redistribution and transformation. Some useful coordinate transformations can be performed optically with a single continuous phase holographic optical element, but many desired transformations require the use of two or more holograms to achieve adequate performance. Some new methods for designing such holograms are given. It is shown that the range of achievable transformations is much wider than previously demonstrated. The adequacy of the stationary phase approximation is examined. A theory is then developed to enable prediction of the space-bandwidth product of the transformation and of crosstalk levels. For specific applications, the required holograms were designed, generated as continuous tone holograms using a computer-controlled laser beam writer, and copied onto phase-only material to produce computer-originated holograms of high diffraction efficiency. The performance of these multiple hologram systems was then experimentally investigated and compared to the theoretical predictions.

© 1986 Optical Society of America