Abstract

In simple binary detection, cross correlation gives the best possible output signal-to-noise ratio only if the background noise is white. But, because of the ease of implementation, optical cross correlators are often used even in nonwhite-noise situations. General expressions and tight bounds are derived to quantify the loss in signal-to-noise ratio when a cross correlator is used instead of the truly optimal filter. Such a quantification should enable the designer of any optical detection scheme to determine whether the extra effort involved in using the truly optimal filters is worth the signal-to-noise ratio improvements.

© 1984 Optical Society of America

Optimal correlation filters for images with signal-dependent noise

John D. Downie and John F. Walkup
J. Opt. Soc. Am. A 11(5) 1599-1609 (1994)

Localization of signals in images

Terry Caelli and Mark Nawrot
J. Opt. Soc. Am. A 4(12) 2274-2280 (1987)

Lower bound for the suboptimality of cross correlators

B. V. K. Vijaya Kumar
Appl. Opt. 23(13) 2048-2049 (1984)

Fourier cross correlation and invariance transformations for an optimal recognition of functions deformed by affine groups

Joseph Segman
J. Opt. Soc. Am. A 9(6) 895-902 (1992)

Generality of matched filtering and minimum Euclidean distance projection for optical pattern recognition

Richard D. Juday
J. Opt. Soc. Am. A 18(8) 1882-1896 (2001)