**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**)*

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 D_{65} 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}(*

*V _{Fq}(*

where *V
_{Fq}(*

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}(*

*V _{Fe}(*

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}(*

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*.