The expression in equation 6.12 is general for any t-E curve which
is described by a cubic polynomial. It is useful to explore
analytically the effect of varying reference and signal exposures and
to predict the signal and noise in the recorded pattern. However,
such analytical methods prove unwieldy when complicated signals are
involved. To analyze the more complicated patterns, the pattern and
film must be modeled on a computer. The computer provides the brute
force to expand the input pattern into the non-linear terms expected
from the film. By modeling the film on the computer, it is possible
to plot the experimental film response along with the predicted
response. This permits the comparison between the experimental data
and various order polynomial fits.
It has been recognized in experiments by this author, that cubic
polynomials have difficulty representing accurately the entire range
of the film response. In order to use the cubic polynomial to predict
the inflection point, only the experimental data points near that
point or in the linear region should be considered. Unfortunately,
this does not permit accurate modeling in the saturation regions.
When modeling an absorption hologram, where only the linear region is
utilized, the cubic polynomial will suffice. The cubic polynomial
loses accuracy when modeling holograms whose response extends into the
non-linear regions, such as phase holograms. This problem is greatly
relieved by using a 5th order polynomial. This gives a more accurate
fit to the t-E curve over the entire useful range of the film.
In order to model accurately the film response, a set of
experimental training points must be established. This is
accomplished by exposing the film to varying irradiances of light and