Recent work by Jones and Higgins has led to an objective method for evaluating the granular structure of the developed photographic image by which materials of widely differing granularity can be ordered in correspondence with subjective graininess measurements. The present paper gives the theoretical calculations of statistical fluctuations of density and syzygetic density differences (<i>S</i>Δ<i>D</i>) for simplified density patterns when scanned with varied-size apertures. Average syzygetic density values, 〈<i>S</i>Δ<i>D</i>〉<sub><i>AV</i></sub>, <i>versus</i> density curves are derived first for square, checkerboard density patterns and second for circular patterns containing uniform-size grains with random arrangement. By combining the experimental, threshold, visual, gradient sensitivity curve (〈<i>S</i>Δ<i>D</i>〉<sub><i>AV</i></sub><i>versus</i> density for critical aperture), obtained by Jones and Higgins, with theoretical curves of 〈<i>S</i>Δ<i>D</i>〉<sub><i>AV</i></sub><i>versus</i> density calculated here, it is shown how the graininess-density curve can be obtained.
J. H. WEBB, "Some Theoretical Considerations on Photographic Graininess and Granularity," J. Opt. Soc. Am. 45, 379-386 (1955)