View source for Candela

{{Short description|SI unit of luminous intensity}}
{{About|the unit of luminous intensity}}
{{Use dmy dates|date=March 2021}}
{{Infobox Unit
| name          = candela
| image         = [[File:Luminosity.svg|290px]]
| caption       = [[Photopic vision|Photopic]] (black) and [[scotopic vision|scotopic]]<ref>{{cite web| url = http://www.cvrl.org/database/text/lum/scvl.htm| title = CIE Scotopic luminosity curve (1951)}}</ref> (green) luminous efficiency functions. The photopic includes the CIE 1931 standard<ref>{{cite web| url = http://www.cvrl.org/database/text/cmfs/ciexyz31.htm| title = CIE (1931) 2-deg colour matching functions}}</ref> (solid), the Judd–Vos 1978 modified data<ref>{{cite web| url = http://www.cvrl.org/database/text/lum/vljv.htm | title = Judd–Vos modified CIE 2-deg photopic luminosity curve (1978)}}</ref> (dashed), and the Sharpe, Stockman, Jagla & Jägle 2005 data<ref name="Sharpe">[http://www.cvrl.org/database/text/lum/ssvl2.htm Sharpe, Stockman, Jagla &amp; Jägle (2005) 2-deg V*(l) luminous efficiency function] {{webarchive|url=https://web.archive.org/web/20070927222337/http://www.cvrl.org/database/text/lum/ssvl2.htm |date=27 September 2007 }}</ref> (dotted). The horizontal axis is wavelength in&nbsp;nm.
| standard      = [[SI]]
| quantity      = [[luminous intensity]]
| symbol        = cd
| namedafter    = 
| units1        = international candles
| inunits1      = ≈ {{val|1.02}} [[candlepower|cp]] 
| units2        = Hefnerkerze
| inunits2      = ≈ {{val|1.11}} [[hefner lamp|HK]] 
}}

'''Candela''' (symbol: '''cd''') is the [[International System of Units|SI]] unit of [[luminous intensity]].<ref name="SIBrochure9thEd">{{citation |title=The International System of Units (SI) |author=International Bureau of Weights and Measures |author-link=New SI |date=20 May 2019  |edition=9th |isbn=978-92-822-2272-0 |url=https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9.pdf| archive-url = https://web.archive.org/web/20211018184555/https://www.bipm.org/documents/20126/41483022/SI-Brochure-9.pdf/fcf090b2-04e6-88cc-1149-c3e029ad8232 |archive-date=18 October 2021 |url-status=live}}</ref><ref>{{cite book |last1=CIE |title=CIE S 017:2020 ILV: International Lighting Vocabulary, 2nd edition. |date=2020 |publisher=CIE |edition=2nd |url=https://cie.co.at/eilvterm/17-21-083}}</ref> It measures the luminous power per unit [[solid angle]] emitted in a particular direction. A common wax [[candle]] has a luminous intensity of roughly 1 cd. 

The word ''candela'' is [[Latin language|Latin]] for ''candle''. The old name "candle" is still sometimes used, as in ''[[foot-candle]]'' and the modern definition of ''[[candlepower]]''.<ref name=Webster>{{cite web|url=http://m-w.com/dictionary/candlepower |title=Candlepower – Definition |work=Merriam-Webster Dictionary|access-date=15 February 2015}}</ref>

== Definition ==
The 26th [[General Conference on Weights and Measures]] (CGPM) redefined the candela in 2018.<ref>{{cite web |title=Convocation of the General Conference on Weights and Measures (26th meeting) |location=Versailles |date=13 November 2018 |publisher=Bureau International des Poids et Mesures |url=https://www.bipm.org/utils/en/pdf/CGPM/Convocation-2018.pdf#page=25 |access-date=10 February 2019 |archive-date=19 September 2019 |archive-url=https://web.archive.org/web/20190919050548/https://www.bipm.org/utils/en/pdf/CGPM/Convocation-2018.pdf#page=25 }}</ref><ref>{{Cite web|last=BIPM|date=22 March 2021|title=Mise en pratique for the definition of the candela in the SI|url=https://www.bipm.org/documents/20126/41489685/SI-App2-candela.pdf/1603b2e8-64a3-1fda-d9b4-7b748bad9c01?version=1.7&t=1637237944393&download=false|website=BIPM}}</ref> The new definition, which took effect on 20 May 2019, is:

<blockquote>The candela [...] is defined by taking the fixed numerical value of the [[luminous efficacy]] of monochromatic radiation of frequency {{val|540e12|u=Hz}},{{Refn|This frequency corresponds to a [[wavelength]] of 555&nbsp;nm in air, which is yellowish-green light approximately at the peak of human visual response. The colour can be approximated on an [[sRGB]] display with [[CSS]] colour value <code>rgb(120,255,0)</code> or hex <code>#78ff00</code> {{Colorsample|#78ff00|border=#55b900}}. |group=lower-alpha}} ''K''<sub>cd</sub>, to be 683 when expressed in the unit lm&nbsp;W<sup>−1</sup>, which is equal to {{nowrap|cd sr W<sup>−1</sup>}}, or {{nowrap|cd sr kg<sup>−1</sup> m<sup>−2</sup> s<sup>3</sup>}}, where the kilogram, metre and second are defined in terms of ''[[Planck constant|h]]'', ''[[Speed of light in vacuum|c]]'' and [[unperturbed ground state hyperfine transition frequency of the caesium 133 atom|Δ''ν''<sub>Cs</sub>]].<ref>{{SIbrochure9th|page=135}}</ref></blockquote>

=== Explanation ===
[[File:Linear visible spectrum.svg|thumb|right|upright=1.5]]
The frequency chosen is in the [[visible light|visible spectrum]] near [[green]], corresponding to a wavelength of about 555&nbsp;nanometres. The [[human eye]], when [[Adaptation (eye)|adapted]] for bright conditions, is most sensitive near this frequency. Under these conditions, [[photopic vision]] dominates the visual perception of our eyes over the [[scotopic vision]]. At other frequencies, more radiant intensity is required to achieve the same luminous intensity, according to the frequency response of the human eye. The luminous intensity for light of a particular wavelength ''λ'' is given by
<math display="block">I_\mathrm{v}(\lambda)= 683.002\ \mathrm{lm/W} \cdot \overline{y}(\lambda) \cdot I_\mathrm{e}(\lambda) ,</math>
where {{math|''I''<sub>v</sub>(''λ'')}} is the [[luminous intensity]], {{math|''I''<sub>e</sub>(''λ'')}} is the [[radiant intensity]] and <math display="inline">\textstyle \overline{y}(\lambda)</math> is the [[photopic]] [[luminous efficiency function]]. If more than one wavelength is present (as is usually the case), one must integrate over the [[spectrum]] of wavelengths to get the total luminous intensity.

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 [[weighting|weighted]] by the [[luminous efficiency function]], the model of the sensitivity of the human eye to different wavelengths, standardised by the CIE and [[International Organization for Standardization|ISO]].<ref>{{cite book | url=https://www.iso.org/standard/83178.html | title=ISO/CIE 23539:2023 CIE TC 2-93 Photometry — The CIE system of physical photometry | publisher=ISO/CIE | date=2023 | language=en | doi=10.25039/IS0.CIE.23539.2023}}</ref><ref name="Sharpe"/><ref>{{cite book |last=Wyszecki |first=G. |author-link1=Günter Wyszecki |last2=Stiles |first2=W.S. |year=1982 |edition=2nd |title=Color Science: Concepts and Methods, Quantitative Data and Formulae | isbn = 0-471-02106-7 |publisher=Wiley-Interscience}}</ref>

=== Examples ===
* A common candle emits light with roughly 1&nbsp;cd luminous intensity. 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.
* A 25&nbsp;W [[compact fluorescent light bulb]] puts out around 1700&nbsp;[[lumen (unit)|lumens]]; if that light is radiated equally in all directions (i.e. over 4{{pi}} [[steradian]]s), it will have an intensity of <math>I_\text{V} = \frac{1700\ \text{lm}}{4 \pi\ \text{sr}} \approx 135\ \text{lm}/\text{sr} = 135\ \text{cd}.</math>
* Focused into a 20° beam (0.095 steradians), the same light bulb would have an intensity of around 18,000&nbsp;cd or 18 kcd within the beam.

== History ==
Prior to 1948, various standards for luminous intensity were in use in a number of countries. These were typically based on the brightness of the flame from a "standard candle" of defined composition, or the brightness of an incandescent filament of specific design. One of the best-known of these was the English standard of candlepower. One candlepower was the light produced by a pure [[spermaceti]] candle weighing one sixth of a pound and burning at a rate of 120&nbsp;[[Grain (unit)|grains]] per hour. Germany, Austria and Scandinavia used the [[Hefnerkerze]], a unit based on the output of a [[Hefner lamp]].<ref>{{cite web |url=http://www.sizes.com/units/hefner.htm |title=Hefner unit, or Hefner candle |work=Sizes.com |date=30 May 2007 |access-date=25 February 2009}}</ref>

[[File:BlackBody.jpg|thumb|150px|1=radiating tube of thorium dioxide; 2=melting pot; 3=solidifying platinum]]
A better standard for luminous intensity was needed. In 1884, [[Jules Violle]] had proposed a standard based on the light emitted by 1&nbsp;cm<sup>2</sup> of [[platinum]] at its melting point (or freezing point). The resulting unit of intensity, called the "violle", was roughly equal to 60 English candlepower. Platinum was convenient for this purpose because it had a high enough melting point, was not prone to [[oxidation]], and could be obtained in pure form.<ref name=Cottington>{{cite journal |journal=Platinum Metals Review |year=1986 |volume=30 |issue=2 |page=84 |title=Platinum and the Standard of Light: A Selective Review of Proposals Which Led to an International Unit of Luminous Intensity |first=Ian E. |last=Cottington |url=https://technology.matthey.com/article/30/2/84-95/}}</ref> Violle showed that the intensity emitted by pure platinum was strictly dependent on its temperature, and so platinum at its melting point should have a consistent luminous intensity. 

In practice, realising a standard based on Violle's proposal turned out to be more difficult than expected.<ref name=Cottington/> Impurities on the surface of the platinum could directly affect its emissivity, and in addition impurities could affect the luminous intensity by altering the melting point. Over the following half century various scientists tried to make a practical intensity standard based on incandescent platinum. The successful approach was to suspend a hollow shell of [[thorium dioxide]] with a small hole in it in a bath of molten platinum. The shell (cavity) serves as a [[black body]], producing [[black-body radiation]] that depends on the temperature and is not sensitive to details of how the device is constructed.

In 1937, the ''[[Commission Internationale de l'Éclairage]]'' (International Commission on Illumination) and the CIPM proposed a "new candle" based on this concept, with value chosen to make it similar to the earlier unit candlepower. The decision was promulgated by the CIPM in 1946:
<blockquote>The value of the '''new candle''' is such that the brightness of the full radiator at the temperature of solidification of platinum is 60&nbsp;new candles per [[square centimetre]].<ref>{{cite book |title = The Metric System: The International System of Units (SI) |author = Barry N. Taylor |publisher = U. S. Department of Commerce |year = 1992 |isbn = 0-941375-74-9 |page = 18 |url = https://books.google.com/books?id=y2-BDaoBVnwC&pg=PA18 }} (NIST Special Publication 330, 1991 ed.)</ref></blockquote>

It was then ratified in 1948 by the 9th&nbsp;CGPM<ref>
[http://www.bipm.org/utils/common/pdf/CGPM/CGPM9.pdf#page=54 Proceedings of the 9th CGPM], 1948, page 54 (French)</ref> which adopted a new name for this unit, the ''candela''. In 1967 the 13th CGPM removed the term "new candle" and gave an amended version of the candela definition, specifying the atmospheric pressure applied to the freezing platinum:
<blockquote>The candela is the luminous intensity, in the perpendicular direction, of a surface of {{nowrap|1 / 600,000}} square&nbsp;metre of a black body at the temperature of freezing platinum under a pressure of {{nowrap|101,325}}&nbsp;newtons per square&nbsp;metre.<ref>13th CGPM Resolution 5, CR, 104 (1967), and ''Metrologia'', '''4''', 43–44 (1968).</ref></blockquote>

In 1979, because of the difficulties in realising a Planck radiator at high temperatures and the new possibilities offered by [[radiometry]], the 16th&nbsp;CGPM adopted a new definition of the candela:<ref>16th CGPM Resolution 3, CR, 100 (1979), and ''Metrologia'', '''16''', 56 (1980).</ref><ref>{{cite web
|title = Base unit definitions: Candela
|work = The [[NIST]] Reference on Constants, Units, and Uncertainty
|url = http://physics.nist.gov/cuu/Units/candela.html
|access-date =27 September 2010}}</ref>

<blockquote>
The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency {{val|540|e=12|ul=hertz}} and that has a [[radiant intensity]] in that direction of {{sfrac|683}}&nbsp;[[watt]] per [[steradian]].
</blockquote>

The definition describes how to produce a light source that (by definition) emits one candela, but does not specify the luminous efficiency function for weighting radiation at other frequencies.  Such a source could then be used to calibrate instruments designed to measure luminous intensity with reference to a specified luminous efficiency function. An appendix to the SI Brochure<ref>{{cite web |url=http://www.bipm.org/en/publications/mises-en-pratique |title=''Mise en pratique'' for the definition of the candela and associated derived units for photometric and radiometric quantities in the International System of Units (SI) |work=SI Brochure Appendix 2 |date=22 March 2021 |publisher=Bureau International des Poids et Mesures |access-date=2023-10-07 }}</ref> makes it clear that the luminous efficiency function is not uniquely specified, but must be selected to fully define the candela.

The arbitrary (1/683) term was chosen so that the new definition would precisely match the old definition. Although the candela is now defined in terms of the [[second]] (an SI base unit) and the watt (a derived SI unit), the candela remains a base unit of the SI system, by definition.<ref>{{cite web |url=https://www.bipm.org/en/publications/si-brochure |title=Units for photochemical and photobiological quantities |work=SI Brochure Appendix 3 |date=22 March 2021 |publisher=Bureau International des Poids et Mesures |access-date=2023-10-07 }}</ref>

The 26th CGPM approved the modern definition of the candela in 2018 as part of the [[2019 revision of the SI]], which redefined the SI base units in terms of fundamental physical constants.

== SI photometric light units ==
{{SI light units}}

=== Relationships between luminous intensity, luminous flux, and illuminance ===
If a source emits a known luminous intensity {{math|''I''<sub>v</sub>}} (in candelas) in a well-defined cone, the total [[luminous flux]] {{math|''Φ''<sub>v</sub>}} in [[lumen (unit)|lumens]] is given by
<math display="block">\Phi_\mathrm{v} = I_\mathrm{v} 2 \pi [1 - \cos(A/2)]</math>
where {{math|''A''}} is the ''radiation angle'' of the lamp—the full vertex angle of the emission cone. For example, a lamp that emits 590&nbsp;cd with a radiation angle of 40° emits about 224&nbsp;lumens. See [[MR16]] for emission angles of some common lamps.

If the source emits light uniformly in all directions, the flux can be found by multiplying the intensity by 4{{pi}}: a uniform 1&nbsp;candela source emits 4{{pi}} lumens (approximately 12.566&nbsp;lumens).

For the purpose of measuring illumination, the candela is not a practical unit, as it only applies to idealised point light sources, each approximated by a source small compared to the distance from which its luminous radiation is measured, also assuming that it is done so in the absence of other light sources. What gets directly measured by a [[light meter]] is incident light on a sensor of finite area, i.e. [[illuminance]] in lm/m<sup>2</sup> (lux). However, if designing illumination from many point light sources, like light bulbs, of known approximate omnidirectionally uniform intensities, the contributions to illuminance from [[incoherent light]] being additive, it is mathematically estimated as follows. If {{math|'''r'''<sub>''i''</sub>}} is the position of the ''i''th source of uniform intensity {{math|''I<sub>i</sub>''}}, and {{math|'''â'''}} is the unit vector [[normal (geometry)|normal]] to the illuminated elemental opaque area {{math|''dA''}} being measured, and provided that all light sources lie in the same half-space divided by the plane of this area,
<math display="block"> \text{illuminance at point } \mathbf{r}\text{ on } dA\text{, } E_\mathrm v(\mathbf{r}) = \sum _{i}{ \frac{|\mathbf{\hat{a}}\cdot(\mathbf{r}-\mathbf{r}_i)|}{|\mathbf{r}-\mathbf{r}_i|^3} I_i }.</math>
In the case of a single point light source of intensity ''I<sub>v</sub>'', at a distance ''r'' and normally incident, this reduces to
<math display="block"> E_\mathrm{v} (r) = \frac{I_\mathrm v}{r^2}.</math>

== SI multiples ==
Like other SI units, the candela can also be modified by adding a [[metric prefix]] that multiplies it by a [[power of 10]], for example millicandela (mcd) for 10<sup>−3</sup> candela.

== Notes ==
{{reflist|group=lower-alpha}} 

== References ==
{{reflist|30em}}

{{SI units}}
{{Authority control}}

[[Category:SI base units]]
[[Category:Units of luminous intensity]]