Stockman and Sharpe's (2000) photopigment template

The common or average template for the three photopigment optical density spectra () for the log wavelength scale is:

,

where x is log₁₀(l), and l is the wavelength in 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 lmax of 558.0 nm.

For other lmax values the template should be shifted along a log wavelength scale. In general, then:
x=log10(l) - log10(lmax/558).

The lmax 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;

For further details, please see Equation 8 and the discussion in Stockman and Sharpe (2000).

Notes

The above equation produces a fixed template shape on a log wavelength, log frequency, or normalized frequency scale--in accordance with Mansfield's (1985) proposal.  See also Lamb (1995).  See Stockman and Sharpe (2000).

References

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.

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