The problem of recognizing targets in nonoverlapping clutter using nonlinear N-ary phase filters is addressed. Using mathematical analysis, expressions were derived for an N-ary phase filter and the intensity variance of an optical correlator output. The N-ary phase filter was shown to consist of an infinite sum of harmonic terms whose periodicity was determined by N. For the intensity variance, it was found that under certain conditions the variance was minimized due to a previously undiscovered phase quadrature effect. Comparison showed that optimal real filters produced greater signal-to-noise-ratio values than the continuous phase versions as a consequence of this effect.
© 2007 Optical Society of America
Original Manuscript: December 21, 2006
Revised Manuscript: May 16, 2007
Manuscript Accepted: June 24, 2007
Published: August 30, 2007
Paul C. Miller, "Signal-to-noise-ratio analysis for nonlinear N-ary phase filters," Appl. Opt. 46, 6405-6418 (2007)