## 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*.