Variation of Absorptance-Curve Shape With Changes in Pigment Concentration.

Abstract

A complete quantitative analysis is presented of changes in the shape of the spectral absorptance curve of any Beer's-law pigment solution (or other Bouguer's-law material) as concentration of the pigment, or thickness of the solution layer, is varied. The relative absorptance curve, normalized to unit maximum, is taken as defining the shape of the absolute absorptance curve, and the index of shape change is taken to be the difference between the normalized curves. All concentration changes from infinite decrease to infinite increase are covered, with some extreme cases requiring limit methods. Formulas and graphs are given for determining, as a function of concentration change and peak absolute absorptance of the original curve, where along the curve the shape change is greatest, and how large the maximum change is. Implications for color vision theory are discussed and it is shown that the assumption of low peak absorptances (< 10%) for the visual photopigments accounts for the constancy of the color-matching functions for moderate luminances, but not, in itself, for the breakdown of matches at high luminances; while the assumption of high peak absorptances (≈ 80%), although it contradicts recent microspectrophotometric measurements, seems to account for both phenomena.