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 scalein accordance with Mansfield's (1985) proposal. See also Lamb (1995) and Stockman and Sharpe (2000) for further details.
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.