Holographic Coordinate Transformations And Optical Computing

Harold Szu

doi:10.1117/12.964033

13 February 1986 Holographic Coordinate Transformations And Optical Computing

Harold Szu

Proceedings Volume 0634, Optical and Hybrid Computing; (1986) https://doi.org/10.1117/12.964033
Event: Optical and Hybrid Computing, 1986, Leesburg, United States

Abstract

The alignment problem among an object o (7), the OFT lens and a phase hologram exp(iφ(r)) is investigated for holographic coordinate transformations, both theoretically and numerically, using FFT replacing OFT for two interesting examples in human visual systems. The optimum alignment is found to be at a specific saddle point r = r0 of the phase hologram defined by Δφ(r0)= k = 0 and Δ2φ = 0 where the OFT lens axis k = 0 (D.C.) and the object origin r = 0 must be overlayed. The result of such a D.C.-saddle point alignment can be understood in terms of the minimization of high order (cubic and above) contributions of the Fourier phase integral from a general viewpoint of a stationary phase approximation.

Citation Download Citation

Harold Szu "Holographic Coordinate Transformations And Optical Computing", Proc. SPIE 0634, Optical and Hybrid Computing, (13 February 1986); https://doi.org/10.1117/12.964033

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