CIE (2008) physiologically-relevant 10-deg V(λ) luminous efficiency functions

Data key

Columns

Quantal

Logarithmic

1.      Wavelength (nm)

2.      log 10-deg photopic luminous efficiency, V_F,10q(λ)

Energy

Logarithmic

1.      Wavelength (nm)

2.      log 10-deg photopic luminous efficiency, V_F,10e(λ)

Linear

1.      Wavelength (nm)

2.      10-deg photopic luminous efficiency, V_F,10e(λ)

Notes

  Based on the linear combination of the Stockman and Sharpe (2000) M- and L-cone spectral sensitivities that best fits experimentally-determined 25-Hz, 2° diameter, heterochromatic (minimum) flicker photometric data obtained from 40 observers (35 males, 5 females) of known genotype. The same L- and M-cone weights are assumed to apply at 10 deg as at 2 deg.

NOTE THAT THE CIE FUNCTIONS ARE CORRECTED VERSIONS OF THE SHARPE et al. 2005 FUNCTIONS. The correction, which is described in Stockman, Jägle, Pirzer & Sharpe (2008), takes into account the fact that the targets used to measure the flicker photometric matches change the adapting chromaticity. See also CIE (2006). The coefficients are now defined to 8 dp for consistency with the CIE physiologically-relevant LMS to XYZ transformation.

 The quantal luminous efficiency function is therefore:

V_F,10q(λ) = (1.89  +  / 2.80455017          or

V_F,10q(λ) = 0.67390486  + 0.35656342  

where V _Fq,10(λ) is the proposed relative spectral sensitivity at 10 deg and  and  are quantal 10 deg fundamentals normalized to unity peak sensitivities. The value 2.804550 is needed for normalization of the luminosity function to unity peak.  Functions are tabulated 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 a cubic spline.  Functions are normalized to peak at unity at the nearest 0.1 nm step. The λ_max for quantal efficiencies is 544.8 nm.

The same function, but energy based, and given in terms of the energy-based cone fundamentals  and  renormalized to unity peak sensitivities:

 

When the photopic sensitivity curve and the cone fundamentals are defined on energy basis, then the following equation holds:

 

V_F,10e(λ) = [1.981377  +  ] / 2.85979294            or

 

V_F,10e(λ) = 0.69283932  +  0.34967567  

 

Note: The energy ratio 1.981377 is simply 1.89 multiplied by 566.704036 (the factor required to renormalize  [=  times  λ] to unity peak) divided by 540.568754, the factor required to renormalize  [=  times  λ] to unity peak). The value 2.85979294 is needed for normalization of V_F,10e(λ) to unity peak (which means normalization at the nearest 0.1 nm to the maximum value at 555.7 nm).

 

References

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.

Sharpe, L. T., Stockman, A., Jagla, W. & Jägle, H.(2005). A luminous efficiency function, V*(λ), for daylight adaptation. Journal of Vision, 5, 948-968.

CIE (2006). Fundamental chromaticity diagram with physiological axes  Parts 1 and 2. Technical Report 170-1. Vienna: Central Bureau of the Commission Internationale de l' Éclairage.

Stockman, A., Jägle, H., Pirzer, M., & Sharpe, L. T. (2008). The dependence of luminous efficiency on chromatic adaptation. Journal of Vision, 8, 16:1, 1-26.