Luminous efficiency function

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Photopic (black) and scotopic (green) luminous efficiency functions. The photopic includes the CIE 1931 standard (solid), the Judd-Vos 1978 modified data (dashed), and the Sharpe, Stockman, Jagla & Jagle 2005 data (dotted). The horizontal axis is wavelength in nm. Luminosity.svg
Photopic (black) and scotopic (green) luminous efficiency functions. The photopic includes the CIE 1931 standard (solid), the Judd–Vos 1978 modified data (dashed), and the Sharpe, Stockman, Jagla & Jägle 2005 data (dotted). The horizontal axis is wavelength in nm.

A luminous efficiency function or luminosity function represents the average spectral sensitivity of human visual perception of 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 wavelengths. It is not an absolute reference to any particular individual, but is a standard observer representation of visual sensitivity of theoretical human eye. It is valuable as a baseline for experimental purposes, and in colorimetry. Different luminous efficiency functions apply under different lighting conditions, varying from photopic in brightly lit conditions through mesopic to scotopic under low lighting conditions. When not specified, the luminous efficiency function generally refers to the photopic luminous efficiency function.

Contents

The CIE photopic luminous efficiency function y(λ) or V(λ) is a standard function established by the Commission Internationale de l'Éclairage (CIE) and standardized in collaboration with the ISO, [1] 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.

Details

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. Fluorescence in beer @ 450nm illumination.jpg
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 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 spectral 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. The CIE distributes standard tables with luminosity function values at 5 nm intervals from 380 nm to 780 nm. [cie 1]

The standard luminous efficiency 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 0.999997 at 555.016 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 the candela, the unit of luminous intensity. [cie 2] 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, [cie 3] which is included in the CIE 1931 color-matching functions as the y(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 CIE VM(λ). [6] More recently, Sharpe, Stockman, Jagla & Jägle (2005) developed a function consistent with the Stockman & 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 of chromatic adaptation under daylight. [8] Their work in 2008 [9] has revealed that "luminous efficiency or V(l) functions change dramatically with chromatic adaptation". [10]

ISO standard

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]

Scotopic luminosity

For very low levels of intensity (scotopic vision), the sensitivity of the eye is mediated by rods, not cones, and shifts toward the violet, peaking around 507 nm for young eyes; the sensitivity is equivalent to 1699 lm/W [13] or 1700 lm/W [14] 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). [15]

Luminosity for mesopic 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

Protanopic (red, dotted) and deuteranopic (green, dashed) luminosity functions. For comparison, the standard photopic curve is shown (black, solid). LuminosityCurve3.svg
Protanopic (red, dotted) and deuteranopic (green, dashed) luminosity functions. For comparison, the standard photopic curve is shown (black, solid).

Color blindness changes the sensitivity of the eye as a function of wavelength. For people with protanopia, the peak of the eye's response is shifted toward the short-wave part of the spectrum (approximately 540 nm), while for people with deuteranopia, 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.

Most non-primate mammals 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. [18]

For older people with normal color vision, the crystalline lens may become slightly yellow due to cataracts, which moves the maximum of sensitivity to the red part of the spectrum and narrows the range of perceived wavelengths.[ citation needed ]

See also

Related Research Articles

<span class="mw-page-title-main">Candela</span> SI unit of luminous intensity

The candela is the unit of luminous intensity in the International System of Units (SI). It measures luminous power per unit solid angle emitted by a light source in a particular direction. Luminous intensity is analogous to radiant intensity, but instead of simply adding up the contributions of every wavelength of light in the source's spectrum, the contribution of each wavelength is weighted by the luminous efficiency function, the model of the sensitivity of the human eye to different wavelengths, standardized by the CIE and ISO. A common wax candle emits light with a luminous intensity of roughly one candela. If emission in some directions is blocked by an opaque barrier, the emission would still be approximately one candela in the directions that are not obscured.

<span class="mw-page-title-main">Visible spectrum</span> Portion of the electromagnetic spectrum that is visible to the human eye

The visible spectrum is the band of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called visible light. The optical spectrum is sometimes considered to be the same as the visible spectrum, but some authors define the term more broadly, to include the ultraviolet and infrared parts of the electromagnetic spectrum as well.

<span class="mw-page-title-main">International Commission on Illumination</span> International authority on light, illumination, color, and color spaces

The International Commission on Illumination is the international authority on light, illumination, colour, and colour spaces. It was established in 1913 as a successor to the Commission Internationale de Photométrie, which was founded in 1900, and is today based in Vienna, Austria.

<span class="mw-page-title-main">Lux</span> SI derived unit of illuminance

The lux is the unit of illuminance, or luminous flux per unit area, in the International System of Units (SI). It is equal to one lumen per square metre. In photometry, this is used as a measure of the intensity, as perceived by the human eye, of light that hits or passes through a surface. It is analogous to the radiometric unit watt per square metre, but with the power at each wavelength weighted according to the luminosity function, a model of human visual brightness perception, standardized by the CIE and ISO. In English, "lux" is used as both the singular and plural form. The word is derived from the Latin word for "light", lux.

In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model of the sensitivity of the human eye. The SI unit of luminous intensity is the candela (cd), an SI base unit.

<span class="mw-page-title-main">Photometry (optics)</span> Science of the measurement of visible light

Photometry is the science of the measurement of light, in terms of its perceived brightness to the human eye. It is distinct from radiometry, which is the science of measurement of radiant energy in terms of absolute power. In modern photometry, the radiant power at each wavelength is weighted by a luminosity function that models human brightness sensitivity. Typically, this weighting function is the photopic sensitivity function, although the scotopic function or other functions may also be applied in the same way. The weightings are standardized by the CIE and ISO.

<span class="mw-page-title-main">Cone cell</span> Photoreceptor cells responsible for color vision made to function in bright light

Cone cells or cones are photoreceptor cells in the retinas of vertebrates' eyes. They respond differently to light of different wavelengths, and the combination of their responses is responsible for color vision. Cones function best in relatively bright light, called the photopic region, as opposed to rod cells, which work better in dim light, or the scotopic region. Cone cells are densely packed in the fovea centralis, a 0.3 mm diameter rod-free area with very thin, densely packed cones which quickly reduce in number towards the periphery of the retina. Conversely, they are absent from the optic disc, contributing to the blind spot. There are about six to seven million cones in a human eye, with the highest concentration being towards the macula.

<span class="mw-page-title-main">Luminous flux</span> Perceived luminous power

In photometry, luminous flux or luminous power is the measure of the perceived power of light. It differs from radiant flux, the measure of the total power of electromagnetic radiation, in that luminous flux is adjusted to reflect the varying sensitivity of the human eye to different wavelengths of light.

The lumen is the unit of luminous flux, a measure of the total quantity of visible light emitted by a source per unit of time, in the International System of Units (SI). Luminous flux differs from power in that radiant flux includes all electromagnetic waves emitted, while luminous flux is weighted according to a model of the human eye's sensitivity to various wavelengths, this weighting is standardized by the CIE and ISO. One lux is one lumen per square metre.

<span class="mw-page-title-main">Spectral power distribution</span>

In radiometry, photometry, and color science, a spectral power distribution (SPD) measurement describes the power per unit area per unit wavelength of an illumination. More generally, the term spectral power distribution can refer to the concentration, as a function of wavelength, of any radiometric or photometric quantity.

<span class="mw-page-title-main">Purkinje effect</span> Tendency for sight to shift toward blue colors at low light levels

The Purkinje effect or Purkinje phenomenon is the tendency for the peak luminance sensitivity of the eye to shift toward the blue end of the color spectrum at low illumination levels as part of dark adaptation. In consequence, reds will appear darker relative to other colors as light levels decrease. The effect is named after the Czech anatomist Jan Evangelista Purkyně. While the effect is often described from the perspective of the human eye, it is well established in a number of animals under the same name to describe the general shifting of spectral sensitivity due to pooling of rod and cone output signals as a part of dark/light adaptation.

Luminous efficacy is a measure of how well a light source produces visible light. It is the ratio of luminous flux to power, measured in lumens per watt in the International System of Units (SI). Depending on context, the power can be either the radiant flux of the source's output, or it can be the total power consumed by the source. Which sense of the term is intended must usually be inferred from the context, and is sometimes unclear. The former sense is sometimes called luminous efficacy of radiation, and the latter luminous efficacy of a light source or overall luminous efficacy.

<span class="mw-page-title-main">Photopic vision</span> Visual perception under well-lit conditions

Photopic vision is the vision of the eye under well-lit conditions (luminance levels from 10 to 108 cd/m2). In humans and many other animals, photopic vision allows color perception, mediated by cone cells, and a significantly higher visual acuity and temporal resolution than available with scotopic vision.

In the study of human visual perception, scotopic vision is the vision of the eye under low-light conditions. The term comes from Greek skotos, meaning "darkness", and -opia, meaning "a condition of sight". In the human eye, cone cells are nonfunctional in low visible light. Scotopic vision is produced exclusively through rod cells, which are most sensitive to wavelengths of around 498 nm (blue-green) and are insensitive to wavelengths longer than about 640 nm (red-orange). This condition is called the Purkinje effect.

<span class="mw-page-title-main">CIE 1931 color space</span> Color space defined by the CIE in 1931

The CIE 1931 color spaces are the first defined quantitative links between distributions of wavelengths in the electromagnetic visible spectrum, and physiologically perceived colors in human color vision. The mathematical relationships that define these color spaces are essential tools for color management, important when dealing with color inks, illuminated displays, and recording devices such as digital cameras. The system was designed in 1931 by the "Commission Internationale de l'éclairage", known in English as the International Commission on Illumination.

<span class="mw-page-title-main">LMS color space</span> Color space represented by the response of the three types of cones of the human eye

LMS, is a color space which represents the response of the three types of cones of the human eye, named for their responsivity (sensitivity) peaks at long, medium, and short wavelengths.

In photometry, luminous energy is the perceived energy of light. This is sometimes called the quantity of light. Luminous energy is not the same as radiant energy, the corresponding objective physical quantity. This is because the human eye can only see light in the visible spectrum and has different sensitivities to light of different wavelengths within the spectrum. When adapted for bright conditions, the eye is most sensitive to light at a wavelength of 555 nm. Light with a given amount of radiant energy will have more luminous energy if the wavelength is 555 nm than if the wavelength is longer or shorter. Light whose wavelength is well outside the visible spectrum has a luminous energy of zero, regardless of the amount of radiant energy present.

<span class="mw-page-title-main">Duplex retina</span>

A duplex retina is a retina consisting of both rod cells and cone cells, which are the photoreceptor cells for two parallel but mostly separate visual systems. The rods enable the scotopic visual system, which is active in dim light. The cones enable the photopic visual system, which is active in bright light. While one is active, the other is generally inactive; either the rods are photobleached, or oversaturated, in bright light, or the cones are not sensitive enough to hyperpolarize, or instigate the phototrasduction cascade, in dim light. However, at mesopic (twilight) conditions, both visual systems are active. In this region of overlap, both systems are active and combine to contribute to mesopic vision.

Mesopic vision, sometimes also called twilight vision, is a combination of photopic and scotopic vision under low-light conditions. Mesopic levels range approximately from 0.01 to 3.0 cd/m2 in luminance. Most nighttime outdoor and street lighting conditions are in the mesopic range.

<span class="mw-page-title-main">Spectral sensitivity</span> Relative efficiency of detection of a signal as a function of its frequency or wavelength

Spectral sensitivity is the relative efficiency of detection, of light or other signal, as a function of the frequency or wavelength of the signal.

References

  1. ↑ ISO/CIE 23539:2023 CIE TC 2-93 Photometry — The CIE system of physical photometry. ISO/CIE. 2023. doi:10.25039/IS0.CIE.23539.2023.
  2. ↑ Charles A. Poynton (2003). Digital Video and HDTV: Algorithms and Interfaces. Morgan Kaufmann. ISBN   1-55860-792-7.
  3. ↑ Wyszecki, Günter & Stiles, W.S. (2000). Color Science - Concepts and Methods, Quantitative Data and Formulae (2nd ed.). Wiley-Interscience. ISBN   0-471-39918-3.
  4. ↑ Judd, Deane B. & Wyszecki, Günter (1975). Color in Business, Science and Industry (3rd ed.). John Wiley. ISBN   0-471-45212-2.
  5. ↑ Vos, J. J. (1978). "Colorimetric and photometric properties of a 2° fundamental observer". Color Research and Application. 3 (3): 125–128. doi:10.1002/col.5080030309.
  6. ↑ Stiles, W. S.; Burch, J. M. (1955). "Interim report to the Commission Internationale de l'Eclairage Zurich 1955, on the National Physical Laboratory's investigation of colour-matching". Optica Acta. 2 (4): 168–181. Bibcode:1955AcOpt...2..168S. doi:10.1080/713821039.
  7. ↑ Sharpe, L. T.; Stockman, A.; Jagla, W.; Jägle, H. (2005). "A luminous efficiency function, V*(λ), for daylight adaptation" (PDF). Journal of Vision. 5 (11): 948–968. doi: 10.1167/5.11.3 . PMID   16441195. Archived from the original (PDF) on April 26, 2012.
  8. ↑ Sharpe, L.T.; Stockman, A.; et al. (February 2011). "A Luminous Efficiency Function, V*D65(λ), for Daylight Adaptation: A Correction". COLOR Research and Application. 36 (1): 42–46. doi: 10.1002/col.20602 .
  9. ↑ Stockman, A; Jägle, H; Pirzer, M; Sharpe, LT (15 December 2008). "The dependence of luminous efficiency on chromatic adaptation". Journal of vision. 8 (16): 1.1-26. doi: 10.1167/8.16.1 . PMID   19146268.
  10. ↑ Stockman, Andrew (December 2019). "Cone fundamentals and CIE standards" (PDF). Current Opinion in Behavioral Sciences. 30: 87–93. Retrieved 27 October 2023.
  11. ↑ "Colorimetry -- Part 1: CIE standard colorimetric observers" . Retrieved December 9, 2018.
  12. ↑ "Kay & Laby;tables of physical & chemical constants;General physics;SubSection: 2.5.3 Photometry". National Physical Laboratory; UK. Archived from the original on May 1, 2019. Retrieved December 9, 2018.
  13. ↑ Kohei Narisada; Duco Schreuder (2004). Light Pollution Handbook. Springer. ISBN   1-4020-2665-X.
  14. ↑ Casimer DeCusatis (1998). Handbook of Applied Photometry. Springer. ISBN   1-56396-416-3.
  15. ↑ "Scotopic luminosity function".
  16. ↑ Photopic and Scotopic lumens - 4: When the photopic lumen fails us
  17. 1 2 Judd, Deane B. (1979). Contributions to Color Science. Washington D.C. 20234: NBS. p. 316.{{cite book}}: CS1 maint: location (link)
  18. ↑ I. S. McLennan & J. Taylor-Jeffs (2004). "The use of sodium lamps to brightly illuminate mouse houses during their dark phases" (PDF). Laboratory Animals. 38 (4): 384–392. doi:10.1258/0023677041958927. PMID   15479553. S2CID   710605.[ permanent dead link ]

CIE documents

  1. ↑ "CIE Selected Colorimetric Tables". Archived from the original on 2017-01-31.
  2. ↑ 16th Conférence générale des poids et mesures Resolution 3, CR, 100 (1979), and Metrologia, 16, 56 (1980).
  3. ↑ CIE (1926). Commission internationale de l'Eclairage proceedings, 1924. Cambridge University Press, Cambridge.

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