Representations of space-variant optical systems using volume holograms

Abstract

A technique is described for recording representations of space-variant optical systems as volume holograms. The transfer-function holographic representations obtained are then placed in the Fourier plane of a coherent optical processor for playback. Due to the space-variant nature of the systems represented, the input plane of the system to be represented holographically is spatially sampled. As a result, the volume hologram medium actually contains a number of holograms that have been angle multiplexed to avoid interference problems. Limitations associated with the thickness of the recording medium are calculated for imaging systems, and experimental results are presented for one lens and two lens magnifiers.

Fractional correlation

“…One of them used holographic filters that were made by use of reference beams with different angles. 4 Another approach was based on the use of different phaseencoded reference beams. 5 Recently a space-variant Fresnel-transform correlator was suggested.…”

Volume Hologram Representation of Space-Variant Systems

“…The extinction angle, be, is the major factor affecting system resolution (2)(3)9). One can show that even in the worst case where the system point spread functions associated with sampling the input plane of S overlap each other completely, it is possible, by properly spacing the reference array point sources, to obtain noninterfering holograms in the thick recording medium.…”

Space-variant ambiguity function processor

“…The former system has space-bandwidth limitations, whereas the latter is of use only for introducing 1-D distortions onto 1-D functions and has a large light loss. However, refinements in such technologies and use of alternate approaches such as multiple holograms 16 and phase-coded reference beams 17 appear to make our initial Mellin transform Dopplerinvariant signal processor concept' 2 more realizable in the near future. For this reason we now expand upon our earlier work in space-variant signal processing by considering the use of such systems with coded waveforms with emphasis on the resultant ambiguity function.…”