Novel real-time joint transform, Hilbert transform optical correlators are proposed in which only a half or a quarter of the Fourier plane is written onto an optically addressable spatial light modulator. A point source is used to recover the result for the whole plane. As a result, images with a two- or four-times larger space-bandwidth product can be matched in amplitude and phase. The effect of truncating the transform plane is explained with two- and one-dimensional Hilbert transform analysis. Results of computer simulation are shown.
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