Page 425 - Introduction to Information Optics

410 7. Pattern Recognition with Optics

Input S r
Reference
Beam R

(a )

Input Sj

Fig. 7.45. An optical wavelet correlator using a PR crystal, (a) Reflection-type WMFs synthesis,
(b) Correlation with a PR WMF.

Thus, by inverse Fourier transforming this equation, the correlation between
the w, and w r can be obtained from the second term. If the input signal s is
identical to the reference signal s r, an array of autocorrelation peaks can be
observed at the back focal plane of lens L3.
To demonstrate feasibility, a fingerprint, shown in Fig. 7.46a, is used for
synthesis of the WMF. Since the typical fingerprints are circular striated-type
patterns, a Mexican-hat-type analyzing wavelet is used. Inserting the finger-
print transparence at the input plane of the PR -based correlator gives the
output correlation distribution, shown in Fig. 7.46b. We see that a sharp
correlation peak can be detected. For comparison, the output correlation
distribution as obtained by a conventional matched filter is depicted in Fig.
7.46c, in which we see that the WMF performs better.