ANALYSIS OF IMAGE DETECTION BASED ON FOURIER PLANE NONLINEAR FILTERING IN A JOINT TRANSFORM CORRELATOR

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.