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Comparative Analysis of Brightness and Lightness Functions

A study is reported of twelve chromatic functions and one achromatic function of brightness, and fourteen chromatic functions and one achromatic function of lightness with the aim of establishing the change in the exponent of the functions, a phenomenon considered as being related to: (a) the brightness or lightness response of a subject; (b) the influence of hue and saturation; (c) the level of the background surrounding the stimulus; (d) the Helmholtz - Kohlrausch effect. Different authors agree that these differences are produced by specific contributions of the tristimulus value Y and of chromaticity, the complexity of the problem arising from the fact that chromaticity would be expected to play a different role in each hue. They also agree that the Helmholtz - Kohlrausch effect is independent of the appearance of colour. We show that the variation due to hue and saturation does not prevent the lightness and brightness functions from showing a specific response that permits differentiation between them and other functions, for instance the saturation functions. Finally, we correlate chromatic and achromatic functions by means of the quadratic fluctuation function which allows us to define a self-correlation function. This mathematical analysis extends to all the samples without taking into account their variation in wavelength and purity. It shows the existence of a solid and stable coding system for luminance, a system that achieves stability through its instability, reflected in the variation of the exponent of the functions.