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A luminous efficiency function or luminosity function represents the average
spectral sensitivity Spectral sensitivity is the relative efficiency of detection, of light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that can be visual perception, perceived by the human eye. Visible ...
of human
visual perception Visual perception is the ability to interpret the surrounding environment (biophysical), environment through photopic vision (daytime vision), color vision, scotopic vision (night vision), and mesopic vision (twilight vision), using light in ...
of
light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that is visual perception, perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nan ...

light
. 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
wavelength In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...

wavelength
s. It is not an absolute reference to any particular individual, but is a standard observer representation of visual sensitivity of theoretical
human eye The human eye is a sense organ A sense is a biological system A biological system is a complex biological network, network which connects several biologically relevant entities. Biological organization spans several scales and are determined ...

human eye
. It is valuable as a baseline for experimental purposes, and in
colorimetry Colorimetry is "the science and technology used to quantify and describe physically the human ". It is similar to , but is distinguished by its interest in reducing spectra to the physical correlates of color perception, most often the and re ...
. Different luminous efficiency functions apply under different lighting conditions, varying from
photopic
photopic
in brightly lit conditions through mesotopic to
scotopic
scotopic
under low lighting conditions. When not specified, ''the luminous efficiency function'' generally refers to the photopic luminous efficiency function. The CIE photopic luminous efficiency function or is a standard function established by the Commission Internationale de l'Éclairage (CIE) and may be used to convert
radiant energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succ ...
into luminous (i.e., visible) energy. It also forms the central color matching function in the
CIE 1931 color space The CIE 1931 color spaces are the first defined quantitative links between distributions of wavelengths in the electromagnetic visible spectrum The visible spectrum is the portion of the that is to the . in this range of s is called ' or ...
.


Details

There are two luminous efficiency 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: : \Phi_\mathrm = 683.002\ \mathrm \cdot \int^\infin_0 \overline(\lambda) \Phi_(\lambda)\, \mathrm\lambda, where * Φv is the
luminous flux In photometryPhotometry can refer to: * Photometry (optics), the science of measurement of visible light in terms of its perceived brightness to human vision * Photometry (astronomy), the measurement of the flux or intensity of an astronomical ...

luminous flux
, in lumens; * Φe,λ is the spectral radiant flux, in watts per nanometre; * (''λ''), also known as ''V''(''λ''), is the luminosity function, dimensionless; * ''λ'' is the wavelength, in nanometres. Formally, the
integral In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities a ...

integral
is the
inner product In mathematics, an inner product space or a Hausdorff space, Hausdorff pre-Hilbert space is a vector space with a binary operation called an inner product. This operation associates each pair of vectors in the space with a Scalar (mathematics), ...
of the luminosity function with the
spectral power distribution In radiometry, photometry (optics), photometry, and color science, a spectral power distribution (SPD) measurement describes the Power (physics), power per unit area per unit wavelength of an illumination (lighting), illumination (radiant exitance ...
. In practice, the integral is replaced by a sum over discrete wavelengths for which tabulated values of the luminous efficiency function are available. The
CIE CIE may refer to: Organizations * Cambridge International Examinations, an international examination board * Center for International Education at the University of Massachusetts-Amherst * Cleveland Institute of Electronics, a private technical an ...
distributes standard tables with luminosity function values at intervals from to . The standard luminous efficiency function is normalized to a peak value of unity at (see luminous coefficient). The value of the constant in front of the integral is usually rounded off to . 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 at a frequency of , which corresponds to a standard air wavelength of rather than , which is the peak of the luminosity curve. The value of (''λ'') is at , so that a value of 683/ = 683.002 is the multiplicative constant. The number 683 is connected to the modern (1979) definition of the
candela The candela ( or ; symbol: cd) is the of in the (SI); that is, luminous power per unit emitted by a point light source in a particular direction. Luminous intensity is analogous to , but instead of simply adding up the contributions of ever ...

candela
, the unit of
luminous intensity In photometryPhotometry can refer to: * Photometry (optics), the science of measurement of visible light in terms of its perceived brightness to human vision * Photometry (astronomy), the measurement of the flux or intensity of an astronomical o ...
. This arbitrary number made the new definition give numbers equivalent to those from the old definition of the candela.


Improvements to the standard

The CIE 1924 photopic ''V''(''λ'') luminosity function, which is included in the CIE 1931 color-matching functions as the (''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, improved by Vos in 1978, resulted in a function known as CIE ''V''M(''λ''). More recently, Sharpe, Stockman, Jagla & Jägle (2005) developed a function consistent with th
Stockman & Sharpe cone fundamentals
their curves are plotted in the figure above.


ISO standard

The ISO standard is ISO 11664-1:2007, soon to be replaced by ISO/CIE FDIS 11664-1. The standard provides an incremental table by nm of each value in the visible range.


Scotopic luminosity

For very low levels of intensity (
scotopic vision Scotopic vision is the vision of the eye under low-light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that can be visual perception, perceived by the human eye. Visible light is usual ...
), the sensitivity of the eye is mediated by rods, not cones, and shifts toward the
violet Violet may refer to: Common meanings * Violet (color), a spectral color with wavelengths shorter than blue * One of a list of plants known as violet, particularly: ** Viola (plant), ''Viola'' (plant), a genus of flowering plants Places United ...
, peaking around for young eyes; the sensitivity is equivalent to or at this peak. The standard scotopic luminous efficiency function or ''V''(''λ'') was adopted by the CIE in 1951, based on measurements by Wald (1945) and by Crawford (1949).


Color blindness

Color blindness Color blindness (color vision deficiency) is the decreased ability to see color or differences in color Color (American English American English (AmE, AE, AmEng, USEng, en-US), sometimes called United States English or U.S. Eng ...

Color blindness
changes the sensitivity of the eye as a function of wavelength. For people with
protanopia Color blindness (color vision deficiency) is the decreased ability to see color or differences in color Color ( American English), or colour ( Commonwealth English), is the characteristic of visual perception described through color ...
, the peak of the eye's response is shifted toward the short-wave part of the spectrum (approximately 540 nm), while for people suffering
deuteranopia Color blindness (color vision deficiency) is the decreased ability to see color or differences in color Color ( American English), or colour ( Commonwealth English), is the characteristic of visual perception described through color ...
, there is a slight shift in the peak of the spectrum, to about 560 nm. People with protanopia have essentially no sensitivity to light of wavelengths more than 670 nm. Most non-
primate A primate ( ) (from Latin , from 'prime, first rank') is a eutherian mammal constituting the Taxonomy (biology), taxonomic order (biology), order Primates (). Primates arose 85–55 million years ago first from small Terrestrial animal, ...

primate
mammals Mammals (from Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of the R ...
have the same luminous efficiency function as people with protanopia. Their insensitivity to long-wavelength red light makes it possible to use such illumination while studying the nocturnal life of animals. For older people with normal color vision, the
crystalline lens The lens is a transparent biconvex structure in the eye that, along with the cornea, helps to refract light to be focused on the retina The retina (from la, rete) is the innermost, light-sensitive layer of tissue of the eye of most verte ...
may become slightly yellow due to
cataract A cataract is a cloudy area in the lens A lens is a transmissive optical Optics is the branch of physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physic ...
s, which moves the maximum of sensitivity to the red part of the spectrum and narrows the range of perceived wavelengths.


See also

* *
Color vision Color vision, a feature of visual perception Visual perception is the ability to interpret the surrounding environment (biophysical), environment through photopic vision (daytime vision), color vision, scotopic vision (night vision), and ...

Color vision
*
Quantum efficiency In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through ...
, the image sensor equivalent *
A-weighting A-weighting is the most commonly used of a family of curves defined in the International standard IECIEC may refer to: Businesses and organisations * International Electrotechnical Commission The International Electrotechnical Commission ...
and
equal-loudness contour An equal-loudness contour is a measure of sound pressure level Sound pressure or acoustic pressure is the local pressure deviation from the ambient (average or equilibrium) atmospheric pressure, caused by a sound wave. In air, sound press ...
, related sound concepts


References


CIE documents


Curve data


External links


Color and Research Vision Laboratory - luminous efficiency data tables
{{Authority control Physical quantities Photometry