Aluminous efficiency function orluminosity function represents the averagespectral sensitivity of humanvisual perception oflight. It is based on subjective judgements of which of a pair of different-colored lights is brighter, to describe relative sensitivity to light of differentwavelengths. It is not an absolute reference to any particular individual, but is a standard observer representation of visual sensitivity of a theoreticalhuman eye. It is valuable as a baseline for experimental purposes, and incolorimetry. Different luminous efficiency functions apply under different lighting conditions, varying fromphotopic in brightly lit conditions throughmesopic toscotopic under low lighting conditions. When not specified,the luminous efficiency function generally refers to the photopic luminous efficiency function.

The CIE photopic luminous efficiency functiony(λ) orV(λ) is a standard function established by theCommission Internationale de l'Éclairage (CIE) and standardized in collaboration with theISO,^[1] and may be used to convertradiant energy into luminous (i.e., visible) energy. It also forms the centralcolor matching function in theCIE 1931 color space.

There are two luminous efficiency functions in common use. For everyday light levels, thephotopic luminosity function best approximates the response of the human eye. For low light levels, the response of the human eye changes, and thescotopic 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:

${\displaystyle {\mathrm{\Phi }}_{\mathrm{v}}=683.002(\mathrm{l}\mathrm{m}/\mathrm{W})\cdot {\int }_0^{\mathrm{\infty }}\overline{y}(\lambda ){\mathrm{\Phi }}_{\mathrm{e},\lambda }(\lambda )\mathrm{d}\lambda ,}$

where

• Φ_v is theluminous flux, in lumens;
• Φ_e,λ is thespectral radiant flux, in watts per nanometre;
• y(λ), also known asV(λ), is the luminosity function, dimensionless;
• λ is the wavelength, in nanometres.

Formally, theintegral is theinner product of the luminosity function with thespectral power distribution.^[2] In practice, the integral is replaced by a sum over discrete wavelengths for which tabulated values of the luminous efficiency function are available. TheCIE distributes standard tables with luminosity function values at5 nm intervals from380 nm to780 nm.^{[cie 1]}

The standard luminous efficiency function is normalized to a peak value of unity at555 nm (seeluminous coefficient). The value of the constant in front of the integral is usually rounded off to683 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 of1/683 W at a frequency of540 THz, which corresponds to a standard air wavelength of555.016 nm rather than555 nm, which is the peak of the luminosity curve. The value ofy(λ) is0.999997 at555.016 nm, so that a value of 683/0.999997 = 683.002 is the multiplicative constant.^[3]

The number 683 is connected to the modern (1979) definition of thecandela, the unit ofluminous intensity.^{[cie 2]} This arbitrary number made the new definition give numbers equivalent to those from the old definition of the candela.

The CIE 1924 photopicV(λ) luminosity function,^{[cie 3]} which is included in the CIE 1931 color-matching functions as they(λ) function, has long been acknowledged to underestimate the contribution of the blue end of the spectrum to perceived luminance. There have been numerous attempts to improve the standard function, to make it more representative of human vision. Judd in 1951,^[4] improved by Vos in 1978,^[5] resulted in a function known as CIEV_M(λ).^[6] More recently, Sharpe, Stockman, Jagla & Jägle (2005) developed a function consistent with theStockman & Sharpe cone fundamentals;^[7] their curves are plotted in the figure above.

Stockman & Sharpe has subsequently produced an improved function in 2011, taking into account the effects ofchromatic adaptationunder daylight.^[8] Their work in 2008^[9] has revealed that "luminous efficiency or V(l) functions change dramatically with chromatic adaptation".^[10]

The ISO standard is ISO/CIE FDIS 11664-1. The standard provides an incremental table by nm of each value in the visible range for the CIE 1924 function.^[11][12]

For very low levels of intensity (scotopic vision), the sensitivity of the eye is mediated by rods, not cones, and shifts toward theviolet, peaking around507 nm for young eyes; the sensitivity is equivalent to1699 lm/W^[13] or1700 lm/W^[14] at this peak. The standard scotopic luminous efficiency function orV′(λ) was adopted by the CIE in 1951, based on measurements by Wald (1945) and by Crawford (1949).^[15]

Luminosity formesopic vision, a wide transitioning band between scotopic and phototic vision, is more poorly standardized. The consensus is that this luminous efficiency can be written as a weighted average of scotopic and mesopic luminosities, but different organizations provide different weighting factors.^[16]

Color blindness changes the sensitivity of the eye as a function of wavelength. For people withprotanopia, the peak of the eye's response is shifted toward the short-wave part of the spectrum (approximately 540 nm), while for people withdeuteranopia, there is a slight shift in the peak of the spectrum, to about 560 nm.^[17] People with protanopia have essentially no sensitivity to light of wavelengths more than 670 nm.

For older people with normal color vision, thecrystalline lens may become slightly yellow due tocataracts, which moves the maximum of sensitivity to the red part of the spectrum and narrows the range of perceived wavelengths.^[18] A method for estimating the transmittance of the human crystalline lens depending on age is standardized as CIE 203:2012,^[19] though further improvement has been proposed.^[20] For a few more lens transmission functions, see the Lucas (2014) Irradiance Toolbox.^[21]

The wavelength-dependent effect of light is seen not only with vision, but also (in humans) in thecircadian rhythm viamelanopsin. For reporting the effect of light on the human circadian rhythm, a value calledmelanopic illuminance is used, defined using a luminous efficiency function specific to the melanopsin. The unit is lux (lx) used in a non-SI-compliant fashion. With CIE S 026:2018, the system has become SI-compliant, with the melanopic equivalent daylight illuminance (M-EDI, unitlx) being derived from melanopic irradiance (unit W/m²). A human being subject to 100 lx of M-EDI of light should have the same alternation to their circadian rhythm as if they are being exposed to 100 lx of daylight.^[22]

Lucas (2014) and the later CIE S 026 also define luminous efficiency function specific to four other human opsins. Lucas uses non-SI-compliant lux while CIE uses SI-compliant EDI lux.^[22] Although the CIE standard requires payment, the associated toolbox and its user guide is available for free.^[23]

Most non-primatemammals have the a similar luminous efficiency function to people with protanopia. Their insensitivity to long-wavelength red light makes it possible to use such illumination while studying the nocturnal life of animals.^[24]

Definition ofmelanopic illuminance and opsin-specific illuminances in the sense of Lucas (2014) are available for rodents. There is a significant difference at short wavelengths (< 420 nm) because the rodent eye filters light differently before the retina compared to the human eye.^[22] A 2024 article by Lucas's Group and international researchers calls for better standardization of light levels used in animal experiments using these species-adjusted illuminance measurements, both to improve the reproducibility of light-related experiments and to improve animal welfare. The article includes αopic data for mice, brown rats, macaques, cats, and dogs. It links to two separate toolboxes, one for calculating the species-specific EDI from aspectral power distribution, the other for estimating the species-specific EDI for a given amount of photonic lux and a light source of known spectrum.^[25]

The wavelength-dependent attractive effect on bees and moths have been quantified with a relative arbitrary unit of "attraction". These data have been used to designwhite LED light sources with lower arthopod attraction at night.^[26]

• Apparent magnitude
• Color vision
• Quantum efficiency, the image sensor equivalent
• A-weighting andequal-loudness contour, related sound concepts

• Color and Research Vision Laboratory - luminous efficiency data tables

• Physical quantities
• Photometry

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