It is shown that, when a photographic image of uniform density is viewed under such conditions that graininess is just perceptible, the average spatial luminance gradient on the cones of the eye is a function of the density of the sample alone if the illuminance on the sample is held constant. This function, which bears a logarithmic relation to net density and is independent of the nature of the photographic image, is herein termed the threshold gradient sensitivity function of the eye for graininess. Granularity is defined in terms of the diameter of the scanning aperture that will produce this threshold gradient on the cones of the eye for the density of the sample in question. It is shown that granularity as thus expressed can be multiplied by a constant factor to give the same numerical value of threshold graininess that would be obtained by measuring the sample visually under standard conditions.
L. A. JONES, G. C. HIGGINS, and K. F. STULTZ, "Photographic Granularity and Graininess. VIII. A Method of Measuring Granularity in Terms of the Scanning Area Giving a Threshold Luminance Gradient," J. Opt. Soc. Am. 45, 107-110 (1955)