Bandlimiting effects in an optical Laplace transform computer

Abstract

Data processing in coherent optical systems has been limited to a large extent by operations involving spectrum manipulations through the Fourier transform. By appropriate modification of the Green function kernel of the Rayleigh-Sommerfeld diffraction integral, it should be possible to obtain transform relationships between the input and output of a coherent processor, other than the Fourier transform. Cutrona has suggested a possible implementation for a Laplace transformer but has apparently not attempted a physical realization [IRE Trans. Inf. Theory IT-6, 386 (1960)]. In this study, a Laplace transform computer is described in which it is found that spatial bandlimiting is a restriction on its usefulness. To compensate for this bandlimiting, a convergence filter is described along with a method to produce this and other spatial filters physically for optical processors.