Page 384 - Introduction to Information Optics

7.2. Recognition by Correlation Detections 369

Fig. 7.17. (a) Objects input to the JTC, (b) Output correlation profile from the NOJTC, (c) Output
correlation profile from the CJTC.

where F(p, q) and R(p, q) are the Fourier spectra of f(x, y) and r(x, y),
respectively. It is apparent that if one removes the zero-order JTPS, the on-axis
diffraction can be avoided. Since the zero-order correlations are derived from
the power spectra of f(x, y) and r(x, j;), these terms can be eliminated from the
recorded JTPS. For example, if we record the power spectral distributions of
2 2
F(p, q)\ and \R(p, q)\ before the joint-transform operation, then these two
zero-order power spectra can be removed by computer intervention before
being sent to the correlation detection operation. Notice that the nonzero-
order JTPS (NOJTPS) is a bipolar function that requires a write-in phase-
modulated SLM for the correlation operation. Thus, the output complex light
field can be written as

r*(oc -2.x 0 ,0)<8> +r(-a - 2x 0, - (7.8)

in which we see that the zero-order diffractions have been removed.
Let us show a result obtained from the NOJTC, as depicted in Fig. 7.17, in
which the input scene represents a set of targets embedded in a noisy terrain.
The input correlation peak intensities as obtained from the NOJTC are shown
in Fig. 7,17b; a pair of distinctive correlation peaks can be easily observed. For