Bilinear system analysis for microdensitometers

Abstract

Partial coherence theory and the bilinear system method are applied to analyze a typical microdensitometer. Both the coherence of the illumination on a sample and the film-grain noise are taken into account. A bilinear transfer function for a microdensitometer, which is unambiguously defined, is determined by the influx, the efflux optics, and the illumination on the source-slit plane but is independent of the sample being measured. The expression for the mean measured value of light-intensity transmittance is obtained, in which the response to the mean amplitude transmittance of a sample can be linearized while the response to film-grain noise remains bilinear as the Callier effect term. Because of this, the consistency of light-intensity transmittance for the same photographic sample on different optical systems exists only when these systems have the same bilinear transfer function.