Crowded Emulsions: Granularity Theory for Monolayers*

Abstract

Photographic grains do not always behave like Poisson-distributed disks, as the random-dot model assumes. Because real grains cannot occupy the same space at the same time, they crowd one another out at high densities, imposing constraints on their locations, which, consequently, cannot be completely random. The theory presented here takes this into account for nonscattering grains illuminated by collimated light. It predicts rms density fluctuations that can sometimes reach a peak at a mean density less than dmax and then decrease beyond this point. This is explained by granularity spectra that, at high densities, have their greatest power per unit bandwidth at high frequencies that are strongly attenuated by the aperture. These results, markedly different from those predicted by the familiar random-dot model of grains overlapping in multilayers, are by no means universally true; for crowded monolayers, in which grains tend to stick to one another, can have granularity curves so similar to those for uncrowded multilayers as to be virtually indistinguishable in practice.