photographic emulsion, this in turn is determined by the energy,
E(x,y) to which it has been exposed. Thus an emulsion is best
characterized experimentally by the transmittance versus exposure (Ta-
E) response curve. This is in contrast to the typical H & D curve
provided by most film manufacturers. The curves are, of course,
related. The amplitude transmission (ignoring any phase shift) is the
square root of the intensity transmission measured experimentally.
The exposure is the same as in the H & D curve but is not plotted
logarithmically. These curves also display an "s" shape due to the
saturation at low and high exposures. The Ta-E curves have the
opposite slope as the H & D curve because the transmission decreases
with exposure while the density increases with exposure.
For the matched filter to be recorded linearly, the recording
media must have transmittance directly proportional to exposure,
Ta=cE, for all values of E. Recall from the previous discussion of
optical matched filters that the hologram is created from the
interference of the Fourier transform wave and a reference wave. A
lens forms the Fourier transform of the reference image
S(u)=So(u)exp{i6(u)}, and a uniform reference beam R(u)=Roexp{iau} is
introduced at an angle i to the optical axis (a=ksin c). A
photographic film placed at the focal plane of the Fourier lens
receives an exposure
E(u) = !S(u) + R(u)12 t (6.1)
where t is the exposure time. Substituting for S(u) and R(u),
E(u) = [Ro+So(u)]t + tRoSo(u)[exp(ie)exp(-iau) + exp(-io)exp(iau)]
= Edc + Eac
(6.2)