A crowded photographic emulsion is viewed as a sandwich of stacked, crowded monolayers. An earlier renewal model of granularity in a crowded monolayer, combined with a new analysis of the general way in which granularity propagates through layers, leads to predictions of the granularity of the multilayer sandwich as a function of the number of layers. For a fixed concentration of grains per unit projected area in the sandwich, rms density fluctuations increase as the number of layers decreases because rms transmittance fluctuations decrease at a slower rate than mean transmittance. These changes are similar to the entropy decrease of grain configurations in the emulsion. For sandwiches consisting of at least 15 layers having a maximum density not greater than 2, the change of rms density fluctuations vs mean density for n exposure series is accurately predicted by the honest random-dot model. Any discrepancy between the theoretical predictions of the honest random-dot model and experimental data for normal emulsions cannot be attributed solely to the neglect of crowding constraints by that model.
WILLIAM H. LAWTON, EUGENE A. TRABKA, and DONALD R. WILDER, "Crowded Emulsions: Granularity Theory for Multilayers," J. Opt. Soc. Am. 62, 659-667 (1972)