Abstract

Most previous research into the design of correlation filters considered only input noise and filter spatial light modulators (SLM’s) of an implicitly assumed infinite contrast ratio. We introduce a signal-to-noise ratio that also includes correlation-detector noise and finite contrast SLM’s. Filters maximizing this signal-to-noise ratio exhibit saturation at some frequencies and are called saturated filters. We accommodate SLM’s whose amplitude has a finite maximum and a nonzero minimum. We give algorithms for optimum saturated complex-and real-valued filters. Previous results are reproduced as various limiting cases. The phase-only filter and the binary phase-only filter are limiting cases for large detector noise with, respectively, complex and real modulators.

© 1992 Optical Society of America

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