Page 96 - Introduction to Information Optics
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2.4. Fourier Transform Processing
\m[H( P,
Fig. 2.11. Complex amplitude transmittance.
and the phase delay varies with the thickness of the spatial filter. Thus, a
complex spatial filter in principle can be constructed by combining an
amplitude filter and a phase-delay filter. However, in most cases, this would be
very difficult to realize in practice.
Let us now discuss the technique developed by Vander Lugt for construct-
ing a complex spatial filter using a holographic technique, as shown in Fig.
2.12. The complex light field over the spatial-frequency plane is
E(p, q) - F(p, q) + exp(-/a 0p),
where oc 0 = / sin 6, f, the focal length of the transform lens, and
F(p, q) = \F(p, q)\ exp[z0(p, <?)].
/(*, y) F(p,
Fig. 2.12. Holographic construction of a Fourier domain matched filter, /(x, y), input object
transparency; R, reference plane wave; PH, photographic recording medium.
