CHAPTER VI

 MATCHED FILTER LINEARITY

 Optical matched filters are almost always produced on some type of

film or photosensitive surface. The pattern recorded is typically the

Fourier transform of the reference scene or some pattern related to

the transform. The assumption of the previous chapters was that the

film responds as a square-law device. This implies that the

transmission of the film responds linearly with the irradiance or

exposure on the plate. However, photographic materials are rarely

linear, but rather, respond with a typical "s" curve response. The

study of the relationships between the irradiance of the light falling

on the film and the resulting blackening produced after development is

known as sensitometry. The sensitometry of any photographic material

is a crucial link in producing and optimizing a matched filter.

 Sensitometry is based upon plotting the density (blackening) of a

photographic material as a function of exposure. The blackening of a

photographic emulsion is measured in terms of optical density. Light

striking a developed photographic negative is partially absorbed by

the metallic silver in the emulsion. Opacity is defined as the the

ratio of the irradiance of light incident on a film to the irradiance

of the light passing through the film. This ratio is always greater

than unity. The intensity transmittance is defined as the reciprocal

of the opacity and thus has a value less than 1. The density of a

photographic material is the logarithm (base 10) of the opacity.