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
Original Manuscript: July 9, 1991
Revised Manuscript: October 23, 1991
Manuscript Accepted: October 25, 1991
Published: March 1, 1992
B. V. K. Vijaya Kumar, Richard D. Juday, and P. Karivaratha Rajan, "Saturated filters," J. Opt. Soc. Am. A 9, 405-412 (1992)