Columns
Quantal
Logarithmic
Energy
Logarithmic
Linear
Notes
2° cone
spectral sensitivities: log L2(λ) or log ,
log M2(λ) or log
and log S2(λ) or log
at 0.1, 1 or 5 nm steps. The 0.1
and 1 nm functions were obtained by the interpolation of the 5 nm functions
using the cubic spline method. The functions are normalized to peak at
unity at the nearest 0.1 nm step.
The cone spectral sensitivities
are defined as linear combinations of the Stiles
and Burch (1959) 10-deg CMFs, ,
and
.
Their derivation requires a knowledge of the five unknowns,
,
,
,
and
,
in the following equations:
Stockman, Sharpe & Fach
(1999) and Stockman and Sharpe (2000) estimated the five unknowns from L- and
M-cone spectral sensitivity measurements in single-gene red-green dichromats,
S-cone spectral sensitivity measurements in blue
cone monochromats and normals, and from existing color matching
data. The estimates are =0.010600 for S;
=0.168926 and
=8.265895 for M and
=2.846201 and
=11.092490 for L. For the adjustment
from 10-deg to 2-deg, it was assumed (i) that the macular pigment density
changes from a peak of 0.095 to a peak of 0.35 and (ii) that the peak
photopigment optical density changes from 0.38 to 0.50 (for L and M) or from
0.30 to 0.40 (for S). In making the calculations, the Stockman, Sharpe
and Fach (1999) lens and macular pigment density spectra were used.
The values of
,
,
and
,
the absolute values of which are unknown, were chosen so that the three functions
peak at one.
For further details, see Stockman, Sharpe & Fach (1999) and Stockman & Sharpe (2000). Stockman, Sharpe & Fach (1999) were unable to measure S-cone spectral sensitivity data after 615 nm, after which S(λ) is so small that it can reasonably, for most purposes, be set to zero.
Stiles, W. S. & Burch, J. M. (1959). NPL colour-matching investigation: Final report. Optica Acta, 6, 1-26.
Stockman, A., Sharpe, L. T., & Fach, C. C. (1999). The spectral sensitivity of the human short-wavelength cones. Vision Research, 39, 2901-2927.
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.