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2.4. Fourier Transform Processing
A
F(p,q) h(x,y)
Fig. 2.13. Holographic construction of a spatial domain filter.
which is identical to the input signal function. Thus, we see that the spatial
domain filter is, in fact, the signal (target) function. We further note that, in
principle, a spatial domain filter can also be synthesized using the holographic
technique, as illustrated in Fig. 2.13, provided the complex Fourier domain
filter function is given. Similarly, the corresponding spatial domain filter can
be shown as
2
h(x, y) = K{\ + /i(x, y) +2 h(x, y)\ cos[27rx 0x (2.36)
where
2.4.3 PROCESSING WITH FOURIER DOMAIN FILTERS
If the Fourier domain filter is inserted in the Fourier plane of a coherent
optical processor (shown in Fig. 2.9), the output complex light distribution can
be shown as
= K[/(x, y) + /(x, y)*f(x , y)*f*(-x, -y)
+ /(x, y)*f( x + a 0, v) + /(x, >•)*/*(- x + a 0, (2.37)
where the asterisk and the superasterisk represent the convolution operation
and the complex conjugation, respectively. In view of the preceding result, we
