Luminosity function

The luminosity function or luminous efficiency function describes the average spectral sensitivity of human visual perception of brightness. It is based on subjective judgements of which of a pair of different-colored lights is brighter, to describe relative sensitivity to light of different wavelengths. It should not be considered perfectly accurate in every case, but it is a very good representation of visual sensitivity of the human eye and it is valuable as a baseline for experimental purposes.

The CIE luminosity function y(λ) or V(λ) is a standard function established by the Commission Internationale de l'Éclairage (CIE) and may be used to convert radiant energy into luminous (i.e., visible) energy. It also forms the central color matching function in the CIE 1931 color space.

There are two luminosity functions in common use. For everyday light levels, the 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 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. The following equation calculates the total luminous flux in a source of light:

where

Formally, the integral is the inner product of the luminosity function with the light spectrum. In practice, the integral is replaced by a sum over discrete wavelengths for which tabulated values of the luminosity function are available. The CIE distributes standard tables with luminosity function values at 5 nm intervals from 380 nm to 780 nm.

The standard luminosity function is normalized to a peak value of unity at 555 nm (see luminous coefficient). The value of the constant in front of the integral is usually rounded off to 683 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 1/683 W at a frequency of 540 THz, which corresponds to a standard air wavelength of 555.016 nm rather than 555 nm, which is the peak of the luminosity curve. The value of y(λ) is 0.999,997 at 555.016 nm, so that a value of 683/0.999,997 = 683.002 is the multiplicative constant.

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