Abstract

The concept of multiresolution optical correlators is formally introduced. A mathematical analysis is performed for a generalized multiresolution correlator that emphasizes the roles of both input and filter spatial light modulator resolutions. Conditions are derived for overlapping and nonoverlapping correlation orders. A simulation is performed in which it is shown that the predicted performance of composite binary-phase-only filters designed by the conventional design procedure is different from the actual performance when they are implemented in a real optical correlator. The training of filters on multiresolution approximations of high-resolution discrete Fourier transforms generated by multiresolution wavelet analysis (MWA) techniques is proposed. An analysis is performed that shows that training on MWA approximations results in filters whose performance is the same in a real correlator as that predicted by the design procedure. This analysis is confirmed by simulation. Further simulations show that the performance of reduced-resolution filters designed by MWA techniques is markedly superior to the performance of those designed by conventional means. Finally, an analysis is performed that explains why the ratio of zero- to higher-order correlation peak intensities is much greater for the former than the latter.

© 1996 Optical Society of America

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