result may then be inverse Fourier transformed to recreate the
modified image. The aperture, which may be replaced by a complicated
filter, functions to perform specific filtering operations including
Wiener or matched filter. Unfortunately, there are certain
limitations to the functions which can be physically implemented. A
normal transparency merely attenuates the light passing through it.
Its transmission is real and non-negative. Thus, when a transparency
film is exposed to a waveform to be recorded, the phase information in
the waveform is lost. Two pieces of information, the real and
imaginary parts of the waveform, are recorded as only one value, their
magnitude. This loss of information can be corrected by taking
advantage of the redundancy in the wavefront and the use of additional
film space. Using the heterodyning technique proposed by Vander Lugt,
the complex waveform can be recorded on photographic film.
Vander Lugt proposed the use of holographic film to store the
filter response for a matched filter. A lens is used to Fourier
transform the reference and test images. Derivations of the Fourier
transforming capabilities of lenses can be found in the literature.10
The Fourier transform of the reference image is brought to focus on a
photographic film. Film is a nonlinear, time-integrating medium and
thus only the magnitude of the Fourier transform or power spectral
density is recorded. The power spectral density does not contain all
of the original image information. Only the autocorrelation of the
original image can be obtained upon inverse transformation. Neither
the power spectral density nor the autocorrelation uniquely describe
the original image. If a plane wave is mixed with the Fourier
transform of the reference image at the film plane, the film will