Convergence of experimental multiple Rayleigh matches to peak L- and M-photopigment sensitivity estimates

Shift in the wavelength of peak sensitivity of the cone photo pigments is a major cause of inter-individual variations in the Rayleigh match. Normal color observers performed multiple Rayleigh matches (i.e., a series of seven Rayleigh-type color matches using various sets of test and primary lights) in order to derive estimates of the M- and L-photo pigment wavelengths of maximum absorbance. We predicted the ratio of incident radiances Pr/Pg for a range of plausible values in terms of wavelength of the peak sensitivity of the M-cone and L-cone. An algorithm allowed us to adjust the values of the peak wavelength of the cone photo pigments in order to minimize the sum of squared differences between predicted and real results of matches. To create candidate M-cone and L-cone photo pigments that best predict the set of equation values, we used the low density spectral absorbance curves of the M-cone and L-cone photo pigments respectively, as tabulated by Stockman and Sharpe (2000), and shifted each template along a logarithmic wavelength scale. For all observers, the system of seven Rayleigh-like equations converges to a unique solution. M- and L-cone photo pigments are estimated separately. The distribution of the wavelength of maximum sensitivity of the photo pigments includes a cluster. Only a few women's results lie outside the cluster. The choice of the template has a considerable influence on the convergence of the algorithm.