Stockman and Sharpe (2000) 2-deg cone fundamentals

Data key

Columns

Quantal

Logarithmic

  1. Wavelength (nm)
  2. log L-cone spectral sensitivity, log L2(λ)
  3. log M-cone spectral sensitivity, log M2(λ)
  4. log S-cone spectral sensitivity,  log S2(λ)

Energy

Logarithmic

  1. Wavelength (nm)
  2. log L-cone spectral sensitivity, log L2(λ)
  3. log M-cone spectral sensitivity, log M2(λ)
  4. log S-cone spectral sensitivity,  log S2(λ)

Linear

  1. Wavelength (nm)
  2. L-cone spectral sensitivity, L2(λ)
  3. M-cone spectral sensitivity, M2(λ)
  4. S-cone spectral sensitivity,  S2(λ)

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.

References

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.