Editing Luminous efficiency function (section)

==Details==
[[File:Fluorescence in beer @ 450nm illumination.jpg|thumb|[[Fluorescence]] in beer. The one watt laser appears much dimmer than the fluorescence it produces, because the camera, like the human eye, is much more sensitive between 500 and 600 nm than at the laser's 450 nm wavelength.]]
There are two luminous efficiency functions in common use. For everyday light levels, the [[photopic vision|photopic]] luminosity function best approximates the response of the human eye. For low light levels, the response of the human eye changes, and the [[scotopic vision|scotopic]] curve applies. The photopic curve is the CIE standard curve used in the CIE 1931 color space.

The luminous flux (or visible power) in a light source is defined by the photopic luminosity function (assuming it is bright enough to activate photopic vision in the eyes). The following equation calculates the total luminous flux in a source of light:
: <math>\Phi_\mathrm{v} = 683.002\ (\mathrm{lm/W}) \cdot \int^\infin_0 \overline{y}(\lambda) \Phi_{\mathrm{e},\lambda}(\lambda)\, \mathrm{d}\lambda,</math>
where
* Φ<sub>v</sub> is the [[luminous flux]], in lumens;
* Φ<sub>e,λ</sub> is the [[Radiant flux#Spectral flux|spectral radiant flux]], in watts per nanometre;
* {{overline|''y''}}(''λ''), also known as ''V''(''λ''), is the luminosity function, dimensionless;
* ''λ'' is the wavelength, in nanometres.

Formally, the [[integral]] is the [[inner product]] of the luminosity function with the [[spectral power distribution]].<ref name="Charles2003"/> In practice, the integral is replaced by a sum over discrete wavelengths for which tabulated values of the luminous efficiency function are available. The [[International Commission on Illumination|CIE]] distributes standard tables with luminosity function values at {{nowrap|5 nm}} intervals from {{nowrap|380 nm}} to {{nowrap|780 nm}}.<ref name="CIEdocs" group=cie/>

The standard luminous efficiency function is normalized to a peak value of unity at {{nowrap|555 nm}} (see [[luminous coefficient]]). The value of the constant in front of the integral is usually rounded off to {{val|683|u=lm/W}}. The small excess fractional value comes from the slight mismatch between the definition of the lumen and the peak of the luminosity function. The lumen is defined to be unity for a radiant energy of {{nowrap|1/683 W}} at a frequency of {{nowrap|540 THz}}, which corresponds to a standard air wavelength of {{nowrap|555.016 nm}} rather than {{val|555|u=nm}}, which is the peak of the luminosity curve. The value of {{overline|''y''}}(''λ'') is {{val|0.999997}} at {{val|555.016|u=nm}}, so that a value of 683/{{val|0.999997}} = 683.002 is the multiplicative constant.<ref name="Wyszecki2000"/>

The number 683 is connected to the modern (1979) definition of the [[candela]], the unit of [[luminous intensity]].<ref name="candela" group=cie/> This arbitrary number made the new definition give numbers equivalent to those from the old definition of the candela.