In this paper, we present theoretical details and the underlying architecture of a hybrid optoelectronic correlator (HOC) that correlates images using spatial light modulators (SLMs), detector arrays, and field programmable gate array (FPGA). The proposed architecture bypasses the need for nonlinear materials such as photorefractive polymer films by using detectors instead, and the phase information is yet conserved by the interference of plane waves with the images. However, the output of such an HOC has four terms: two convolution signals and two cross-correlation signals. By implementing a phase stabilization and scanning circuit, the convolution terms can be eliminated, so that the behavior of an HOC becomes essentially identical to that of a conventional holographic correlator (CHC). To achieve the ultimate speed of such a correlator, we also propose an integrated graphic processing unit, which would perform all the electrical processes in a parallel manner. The HOC architecture along with the phase stabilization technique would thus be as good as a CHC, capable of high-speed image recognition in a translation-invariant manner.
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