Hilbert transform and mirror-image optical correlators.
An optical correlator, believed to be novel, adds an x-y mirror image to the input and filter images to perform convolution involving amplitude and phase. The resulting real Fourier transform filters can be loaded into a liquid-crystal device (LCD). In contrast, a complex filter would require high-resolution film. A Hilbert transform and a point source are applied at the filter plane to reduce filter storage and LCD loading time by a factor of 2. An optional spatial filter removes an offset intensity and squares the result. Filters have only twice the number of pixels of the images. Analysis is verified by computer simulation, and performance is discussed.
McAulay
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