Exploiting colorimetric relationships in characterizing the spectral response functions of the human visual system directly from colour matching functions

Abstract

AbstractThe linear relationship between the spectral response functions (SRFs) of a three‐colour response system and the set of the corresponding colour matching functions (CMFs) for a particular set of primaries, in the form of three simultaneous equations, is the principal fundamental approach adopted in this article in determining the characteristics of the former. After reviewing, evaluating, and where necessary processing the three sets of 2° field CMFs derived by the historic researchers, Guild, Wright, and Stiles & Burch, they were used with three sets of CMFs to SRFs transforms with adjustable matrix coefficients, respectively, to provide three closely matched sets of SRFs. These close matches then formed the basis for the three sets of potential human visual system (HVS) SRFs, which with three further transforms, whose coefficients are based upon the response of the SRFs at the primary wavelengths, then generate, respectively, a close match to each of the historic sets of CMFs. The precept adopted is that given the relative trichromatic sensitivity of the HVS SRFs and a set of three spectral primaries of defined wavelength and known luminosities, a mathematical relationship may be derived between them that produces a corresponding set of CMFs related to the wavelengths of the primaries selected. In an ideal situation then the three sets of SRFs obtained which each produce a match of the derived CMFs to the original CMFs, should also produce a match with each other and represent the SRFs of the HVS. The same procedure was also applied to the Stiles & Burch 10° SMFs to obtain a 10° version of the HVS SRFs. This article outlines the structure of the mathematical tool evolved and the design of the spreadsheet used to derive and build the various relationships, together with the reasoning for each of the steps in the process. The resulting tool is then used with processed forms of the CMFs of the historic researchers, to show that, within the limits of the experimental errors of the original works, the resulting derived CMFs compare favorably with those originally established by experiment, and furthermore, the three associated individual sets of SRFs match, providing strong evidence that they do indeed represent the SRFs of the human vision system.