information terms in the output, a spatial carrier of sufficiently
high frequency is required to separate the heterodyned terms from the
on-axis terms. Assuming as an example that the test image and the
reference image are the same size 2B. The output positions of the
various terms can be shown graphically. To prevent the information
terms from overlapping with the on-axis terms, the carrier frequency,
a, must be chosen to center the heterodyned terms at 5B or more. In
the general case, the reference image f(x,y) and g(x,y) may have
different sizes. Let 2Bf represent the size of the reference image
and 2Bg represent the size of the test image. Then the requirement on
the carrier frequency, a, to prevent aliasing is
a = 3Bf + 2Bg. (3.16)
Sampling and heterodyning cause aliasing when improperly
accomplished. The combination of the two in the CGH requires
specific attention to detail. To create a CGH from a continuous image
f(x,y), it must first be sampled and quantized. According to the
Nyquist criteria, there are two samples for the smallest details in
the image. The sampling rate is at least twice the highest spatial
frequency in the continuous image. If a limited number of sampling
points are available, the image should be low pass filtered to limit
the highest frequency in the continuous image to half the number of
sampling points. This can be accomplished in an electronic sensor by
blurring the optics before the detector. When using a television
camera to digitize a transparency or film, the camera must be blurred
to match the detail in the continuous image to the number of points in
the digitizer. The detail required in the reference and test images