The perceived magnitude of a stimulus detected by the human visual system is, according to Fechner's Law, proportional to the logarithm of its physical intensity. This suggests that the perceived mottle in a printed image depends not only on the reflectance variation of the image, but also on its mean reflectance level. One possible approach is therefore to use the reflectance variation divided by the mean reflectance level, dR/R, as an estimate of the perceived mottle in an image. However, practical use of this method indicates that perceived mottle may be overestimated in dark and underestimated in light images. The present study therefore attempts to establish a better relationship between perceived mottle and mean reflectance level. A set of halftone patches was constructed by digital simulation, and then visually evaluated. Results suggest that the measured variation should be divided by a power function, with an exponent less than 1, of the mean reflectance to obtain the best correlation between visual and instrumental evaluation. The highest correlation was attained using the inverse square root, i.e., an exponent equal to 0.5.
Carl-Magnus Fahlcrantz, Per-Åke Johansson, Peter Åslund, "The Influence of Mean Reflectance on Perceived Print Mottle" in Journal of Imaging Science and Technology, 2003, pp 54 - 59, https://doi.org/10.2352/J.ImagingSci.Technol.2003.47.1.art00010