P. Willett et al., ANALYSIS OF IMAGE DETECTION BASED ON FOURIER PLANE NONLINEAR FILTERING IN A JOINT TRANSFORM CORRELATOR, Applied optics, 37(8), 1998, pp. 1329-1341
Signal and image and detection systems based on nonlinear operations o
f Fourier-transformed data often exhibit greater selectivity than stan
dard matched-filtering techniques. One such system is the joint transf
orm correlator. We analyze the performance of the nonlinear joint tran
sform correlator in terms of the output signal-to-noise ratio; this si
gnal-to-noise ratio is evaluated in terms of both output contrast (pea
k-to-noise floor) and output variability (peak-to-peak standard deviat
ion). The main assumption used is that the signal energy is small rela
tive to that of the additive noise; this assumption is defensible in p
ractice owing to the generally small spatial extent of target images r
elative to scenes. With respect to the first performance measure, this
study is an extension of that in an earlier paper [Appl. Opt. 34, 521
8 (1995)]. The previous analysis was carried out under a restriction t
hat the signal and noise spectra were to be similar (actually multiple
s of one another). In the current study there is no such constraint, a
nd all analysis of the second measure is new. The analysis is supporte
d by simulation. A benefit of analytical rather than simulational stud
y is that conclusions can be drawn with greater confidence. One of the
most interesting of these is that the smooth square-root Fourier plan
e nonlinearity, more usually known as the k-law processor with k = 0.5
, offers extremely robust performance with respect to relative noise b
andwidth. (C) 1998 Optical Society of America.