Abstract

A well-known, simple theory predicts that, for a given grain size, the granularity of a developed photographic image is proportional to the square root of the density. In this paper, it is shown that, in the case of a two-dimensional grain model consisting of randomly placed opaque disks (dots), this simple relation progressively underestimates granularity as density is increased. The disparity exists because, with the random-dot model, density is not solely proportional to the number of dots in the aperture, but may vary at random according to the amount of overlap among the dots. It is suggested that the effect of random overlap may be relatively small in a developed photographic image, which differs from a random-dot model in that the grains are distributed in depth.

© 1964 Optical Society of America

Correlation between Random-Dot Samples and the Photographic Emulsion*

J. C. Marchant and P. L. P. Dillon
J. Opt. Soc. Am. 51(6) 641-644 (1961)

Density and granularity of clustered distributions of monosized opaque dots

J. C. Dainty and R. Shaw
J. Opt. Soc. Am. 72(5) 662-665 (1982)

Relation between Granularity and Autocorrelation*

A. Marriage and E. Pitts
J. Opt. Soc. Am. 46(12) 1019-1027 (1956)

Extended random-dot model

Kazuo Tanaka and Suguru Uchida
J. Opt. Soc. Am. 73(10) 1312-1319 (1983)

Crowded Emulsions: Granularity Theory for Multilayers*

William H. Lawton, Eugene A. Trabka, and Donald R. Wilder
J. Opt. Soc. Am. 62(5) 659-667 (1972)