CIE (2008) physiologically-relevant 2-deg V(λ) luminous efficiency functions

Data key

Columns

Quantal

Logarithmic

1.      Wavelength (nm)

2.      log 2-deg photopic luminous efficiency, V_Fq(λ)

Energy

Logarithmic

1.      Wavelength (nm)

2.      log 2-deg photopic luminous efficiency, V_Fe(λ)

Linear

1.      Wavelength (nm)

2.      2-deg photopic luminous efficiency, V_Fe(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, 22 with the serine variant L(ser180), 16 with the alanine L(ala180) variant, and 2 with both variants of the L-cone photopigment. The matches, from 425 to 675 nm in 5-nm steps, were made on a 3 log troland xenon white (correlated color temperature of 5586 K, but tritanopically metameric with CIE D₆₅ standard daylight for the Stockman & Sharpe (2000) L- and M-cone fundamentals) adapting field of 16° angular subtense, relative to a 560 nm standard. Both the reference standard and test lights were kept near flicker threshold so that, in the region of the targets, the total retinal illuminance averaged 3.19 log trolands. The new function is extrapolated to wavelengths shorter than 425 nm and longer than 675 nm using the Stockman & Sharpe (2000) cone fundamentals. See Sharpe, Stockman, Jagla & Jägle (2005).

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:

V_Fq(λ) = [1.89  +  ] / 2.80360572    or

V_Fq(λ) = 0.67413188  + 0.35668354  

 where V _Fq(λ) is the proposed relative quantal spectral sensitivity, the index F meaning “fundamental”, and    and  are the quantal 2 deg fundamentals normalized to unity peak sensitivities. The value 2.80360572 is needed for normalization of V_Fq(λ)  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, which is at 546.1 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_Fe(λ) = [1.980647  +  ] / 2.87090767        or

 

V_Fe(λ) = 0.68990272  + 0.34832189  

 

Note: The energy ratio 1.980647 is simply 1.89 multiplied by 568.051059 (the factor required to renormalize   [=  times  λ] to unity peak) divided by 542.053485 (the factor required to renormalize   [=  times λ] to unity peak).  The value 2.87090767 is needed for normalization of V_Fe(λ) to unity peak (which means normalization at the nearest 0.1 nm to the maximum value at 556.1 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.