If the input wavefront is known, the optical step may be omitted
altogether. If the input wavefront can be accurately represented by
discrete samples stored electronically, the holographic pattern can be
computed. That is, the input is coded to create a function which can
be recorded on a transparency. In the case of the matched filter, the
Fourier transform of an image is recorded. The image is sampled and
stored on the computer, and equation 2.35 is used to determine the
holographic pattern. Note that the continuous variables are replaced
by discrete steps. At each sample point the actual value is
represented by a finite number. The value may be complex, but the
accuracy is limited by the sampling system. In any case the
holographic pattern is computed and written to the photographic plate.
The writing device is known as continuous-tone when the transmittance
of each point in the holographic plate can be controlled over a wide
range of transmittance values. That is, the transmittance varies
smoothly from clear to opaque, including gray scale values between.
These continuous-tone holograms most closely resemble the optically
generated holograms when the sampling is dense and many gray scale
values are available.
When continuous-tone holograms are written to the photographic
plate using equation 2.35 as the model, they include a D.C. term, a
square magnitude term, and the heterodyned terms due to the tilted
reference wave. Note that the first two terms are real valued and
that the sum of the last two terms is real valued. On the computer,
the film process is emulated using equation 2.35 or other coding
schemes for specific applications. The D.C. and square magnitude
terms need not be included in the computer-generated hologram as long