Properties of Granularity Wiener Spectra

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Abstract
The description of the random-dot model for photographic granularity by independent and identical grain-location statistics allows the average transmittance and transmittance autocorrelation function to be determined in a few straightforward steps. Here, the analysis is applied to the case of uniform exposures and arbitrarily shaped opaque grains, although the formalism allows nonopaque phase-retarding grains and the result of image exposures to be described. The results are interpreted in terms of the granularity Wiener spectrum, giving simple bounds on the low-frequency noise level, an inverse-third-power form for high frequencies, and bounds on a spectrum width that increase monotonically with decreasing average transmittance.