In order to determine the relation between the visual impression of graininess and the objectively determined granularity of a wide range of granularity types, a series of samples was prepared containing uniformly exposed black-and-white materials and prints (transparencies) containing varying degrees of mottle. These samples were judged by the method of paired comparisons at different magnifications and scanned to obtain the standard deviation σ(D) for a wide range of scanning apertures. The psychophysical relationship between the two functions, (1) graininess versus magnification and (2) granularity σ(D) versus the square root of the scanning area, depends on the character of the scanning operation performed by the eye. An estimate of the size of the effective scanning spot of the eye can be obtained from these data.
KEITH F. STULTZ and HANS J. ZWEIG, "Relation between Graininess and Granularity for Black-and-White Samples with Nonuniform Granularity Spectra," J. Opt. Soc. Am. 49, 693-701 (1959)