The output of the Vander Lugt filter is shown in equation 2.37 and the

spectral contents are plotted in Figure 3.5. These spectral components

are shown in two dimensions in Figure 3.8. Here the space-bandwidth

product is 7 times larger than the image in the v direction and 3

times larger than the image in the u direction. To produce a

correlation image without stretching, the samples in the u and v

directions should have the same spacing. Usually for convenience, the

hologram contains the same number of points in both directions, giving

a pattern which is 7B by 7B. The FFT algorithm used on most computers

requires the number of points to be a power of 2. This requires that

the hologram be 8B by 8B. For example, if the original images to be

correlated contain 128 by 128 points, the required continuous-tone CGH

contains 1024 by 1024 points. In a binary hologram, each continuous

tone point or cell may require many binary points to record the entire

dynamic range of the image.

 This illuminates the key problem with CGH-matched filters. The

space-bandwidth product becomes large for even small images. Yet it

is the ability of optical processors to handle large images with many

points that makes them so attractive. Holograms created with

interferometric techniques contain a large amount of information or a

large space-bandwidth product. However, these optically-generated

holograms lack the flexibility offered by CGH. Holographic filters

are produced by either optical or computer prior to their actual use.

The filter imparts its required transfer function to the test image

without any further computation of the hologram pattern. Even if the

task is difficult, production of the filter is a one-time job. The

more information stored on the hologram, the greater the potential