Fourier-plane filtering by a thick grating: a space–bandwidth analysis

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Abstract
The space–bandwidth requirements of thick gratings in the Fourier plane of a coherent optical image processor are analyzed. Based on Kogelnik’s relationship for the diffraction efficiency, relations for the space–bandwidth products of the input image and the point-spread function are obtained in terms of grating parameters. It is concluded that thick gratings, such as photorefractive crystals, are not well suited for implementing shift-invariant operations through Fourier-plane filtering.