Effect of background lightness and crispening phenomena in relation between lightness and brightness

The relation between lightness and brightness is one of the psychophysical relations, which has been discussed by the late nineteenth century and early twentieth century. Two types of equations have been suggested for this Logarithmic model and Power-law model. The results of curve fitting of these two general models versus experimental data showed acceptable performance for both logarithmic and power-law equations. However it seems that mathematical basic of logarithmic model, by assuming that visual steps in the different levels of lightness are the same, is more acceptable. One of the most important parameters which affects the relation between lightness and brightness, is the lightness of the background on which the samples were presented. When the lightness of the sample is closed to the lightness of the background, on which the sample is observed, the human visual system is more sensitive to the changes of sample's lightness; this effect is called Crispening. Among different logarithmic functions, Whittle's equation, which considers this effect and other important parameters, is superior to other logarithmic functions. Till now, the comparison between Whittle's model and other power-law's model (for example: L*) has been given no definitive answer. The aim of this paper is to review the studies about “crispening effect”- from the beginning till now-and the models proposed for predicting this effect.