Page 113 - Introduction to Information Optics

98 2. Signal Processing with Optics

2.5,3. IMAGE SUBTRACTION

Another interesting application of optical processing is image subtraction,
Image subtraction may be of value in many applications, such as urban
development, highway planning, earth resources studies, remote sensing, me-
teorology, automatic surveillance, and inspection. Image subtraction can also
apply to communication as a means of bandwidth compression; for example,
when it is necessary to transmit only the differences among images in successive
cycles, rather than the entire image in each cycle.
Let us assume two images, J\(x — a, y), f 2(x + a, y), are generated at the
input spatial domain SLM1 of Fig. 2.17. The corresponding joint transform
spectra can be shown as

where F^p, g) and F 2(p, q) are the Fourier spectra of /j(x, y) and / 2(x, y),
respectively. If a bipolar Fourier domain filter,

H(p) = sin(ap), (2.60)

is generated in SLM2, the output complex light field can be shown as

g(a, /I) - C, [/,(x, y) - f 2(x, y)] + C 2U\(x - 2a,y) + f 2(x + 2a, j;)], (2.61)

in which we see that a subtracted image can be observed around the origin of
the output plane. We note that the preceding image subtraction processing is,
in fact, a combination of the joint transformation and the Fourier domain
filtering. Whether by combining the joint transformation and Fourier domain
filtering it is possible to develop a more efficient optical processor remains to
be seen. Now consider an image subtraction result as obtained by the
preceding processing strategy, as shown in Fig. 2.26. Once again, we see that
the subtracted image is severely corrupted by coherent artifact noise, which is
primarily due to the sensitivity of coherent illumination.

2.5.4. BROADBAND SIGNAL PROCESSING

An important application of optical processing is the analysis of a broad-
band signal. Because of the high space bandwidth product of optics, a
one-dimensional large time-bandwidth signal can be analyzed by a two-
dimensional optical processor.
In order to do so, a broadband signal is first raster-scanned onto the input
SLM, as shown in Fig. 2.27. This raster-scanned process is, in fact, an excellent