The common or average template for the three logarithmic photopigment
optical density spectra, log_{10}[*A*(*x*)], for the log wavelength scale is:

,

where *x* is log_{10}(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 *λ*_{max} of 558.0 nm.

For other *λ*_{max} values the
template should be shifted along a log wavelength scale. In general, then:

*x*=log_{10}(*λ*) - log_{10}(*λ*_{max}/558).

The *λ*_{max} 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.