correlator in which no active devices are used. That is,

transmittance values cannot exceed one. All pre-processing is

performed on the hologram, only to preserve the real-time capability

of the optical correlator.

 Figure 7.1 shows a flow chart of a simulation of an ideal

correlation. In this case a hologram is not used to perform the

correlation. Rather, the image transforms are multiplied directly in

their complex form. Although this simulation could be used to

represent the effects associated with an on-axis hologram capable of

simultaneous amplitude and phase modulation, no hologram noise, film

noise, or dynamic range limitations are included. This ideal

correlation serves as a standard for latter comparison with off-axis

hologram-derived correlations. There is an interaction between the

pre-processing and the hologram that will affect the influence of the

pre-emphasis. However, the ideal correlation simulation is useful for

determining correlation properties of the images and pre-processing

techniques independent of the influence of the hologram.

 In Figure 7.1, the digitized reference image is stored in a matrix

fij. Likewise, the digitized test image is stored in a matrix gij.

The correlation image will contain more points than each of the input

images. Specifically,'the correlation image contains a number of

points in each direction equal to the sum of the number of points of

the two images in those direction.) In general, the two images are

equal in size and the correlation is twice the size of the images in

each direction. In order for the FFT routine to perform the

appropriate transformation resulting in a 2N by 2N image, the input

images need to be padded to create two images of size 2N by 2N.