Photographic granularity : mathematical formulation and effect of impenetrability of grains

We develop a new and general formula for the granularity of a wide class of anisotropic media (for apertures of arbitrary shape) that exactly accounts for the microstructure. Using this formula, we compute for the first time to our knowledge, the granularity of a two-dimensional distribution of impenetrable, opaque circular disks for a wide range of densities and aperture sizes. These results are compared with the much-investigated, random-dot model. The effect of impenetrability of the grains for a fixed aperture area is to reduce the granularity relative to that of the random-dot model, especially at high densities.