Holographic Elements For Coordinate Transformations

A novel design technique for generating holographic elements that perform general types of coordinate transformations is presented. The design, which is based on analytic ray-tracing techniques leads to a holographic grating function that can be formed either as a computer generated or as a computer originated hologram. The design procedure is illustrated for a specific holographic element that performs a logarithmic transformation. Such an element is useful for obtaining scale invariance in optical correlation.