The common or average template for the three logarithmic photopigment optical density spectra, log10[A(x)], for the log wavelength scale is:
where x is log10(nm), a = -188862.970810906644, b = 90228.966712600282, c = -2483.531554344362, d = -6675.007923501414, e = 1813.525992411163, f = -215.177888526334, g = 12.487558618387, and h = -0.289541500599.
The template was derived iteratively by aligning the S-cone and M-cone photopigment with the L-cone photopigment spectra and then finding the best-fitting polynomial to describe the aligned spectra. The mean template has a λmax of 558.0 nm.
For other λmax values the
template should be shifted along a log wavelength scale. In general, then:
x=log10(λ) - log10(λmax/558).
The λmax values of the fitted templates that best fits the original Stockman and Sharpe (2000) S-, M- and L-cone photopigment spectra are 420.7, 530.3 and 558.9 nm for the S-, M- and L-cones, respectively;
The above equation produces a fixed template shape on a log wavelength,
log frequency, or normalized frequency scale
Lamb, T. D. (1995). Photoreceptor spectral sensitivities: common shape in the long-wavelength region. Vision Research, 35, 3083-3091.
Mansfield, R. J. W. (1985). Primate photopigments and cone mechanisms. In A. Fein, & J. S. Levine (Ed.), The visual system New York: Alan R. Liss.
Stockman, A., & Sharpe, L. T. (2000). Spectral sensitivities of the middle- and long-wavelength sensitive cones derived from measurements in observers of known genotype. Vision Research, 40, 1711-1737.