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.