A queueing model for reciprocity failure in the photographic grain

Abstract

Under normal conditions, the developed density in a photographic emulsion depends on the incident light only through the product of the intensity and the duration of the exposure. This is called the Law of Reciprocity. However, under extreme conditions such a very low or high intensities, this law of reciprocity breaks down, with a resulting loss in efficiency of the photographic process. This paper presents a probabilistic model for reciprocity failure in photographic materials. The model is based on the Gurney-Mott hypothesis for the photographic process, and in addition to combining both low and high intensity reciprocity failure, allows for the formation of electron pools and recombination with holes. The analysis is similar to, but not derived from, the corresponding transient analysis for an enhanced M/G/1 queueing system.