where Edd = t[Ro + So2]
and Eac = tRoSo[exp(ie)exp(-iau) + exp(-ie)exp(iau)]
are the local average exposure and the varying components
respectively. Note that dc (direct current) and ac (alternating
current) subscripts apply here to the slowly varying terms and the
high spatial frequency terms respectively.
The ideal recording medium would have a transmittance directly
proportional to exposure, Ta = cE, for all values of E. For such a
linear material the transmittance would be
Ta(u) = c[Edc + Eac]. (6.3)
When such a transparency is illuminated with a collimated beam, light
is diffracted by the film. The first term in equation 6.3 is real and
gives rise to wavefronts propagating near the optical axis. The ac
term includes the factor exp(iau), a linear phase shift, which will
diffract light waves at angles plus and minus ( to the optical axis.
Thus if a is chosen appropriately, or the recording angle properly
chosen, each of these wavefronts will be separated from the other and
from those which propagate on axis. One of the off-axis beams
contains the term So(u) exp{-ie(u)} which is the complex conjugate of
the reference Fourier transform, and thus has the desired optimal
filter characteristic.
Unfortunately, photographic emulsions do not exhibit this ideal
linear response described above. Rather, they saturate at high and
low exposures. To understand the effect of this non-linearity, it is
important to describe the actual film response at all exposures and