This article is about the unit of luminous intensity. For other uses, seeCandela (disambiguation).
candela
Photopic (black) andscotopic[1] (green) luminous efficiency functions. The photopic includes the CIE 1931 standard[2] (solid), the Judd–Vos 1978 modified data[3] (dashed), and the Sharpe, Stockman, Jagla & Jägle 2005 data[4] (dotted). The horizontal axis is wavelength in nm.
Candela (symbol:cd) is theSI unit ofluminous intensity.[5][6] It measures the luminous power per unitsolid angle emitted in a particular direction. A common waxcandle has a luminous intensity of roughly 1 cd.
The wordcandela isLatin forcandle. The old name "candle" is still sometimes used, as infoot-candle and the modern definition ofcandlepower.[7]
The candela [...] is defined by taking the fixed numerical value of theluminous efficacy of monochromatic radiation of frequency540×1012 Hz,[a]Kcd, to be 683 when expressed in the unit lm W−1, which is equal tocd sr W−1, orcd sr kg−1 m−2 s3, where the kilogram, metre and second are defined in terms ofh,c andΔνCs.[10]
The frequency chosen is in thevisible spectrum neargreen, corresponding to a wavelength of about 555 nanometres. Thehuman eye, whenadapted for bright conditions, is most sensitive near this frequency. Under these conditions,photopic vision dominates the visual perception of our eyes overscotopic 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 wavelengthλ is given bywhereIv(λ) is theluminous intensity,Ie(λ) is theradiant intensity and is thephotopicluminous efficiency function. If more than one wavelength is present (as is usually the case), one must integrate over thespectrum of wavelengths to get the total luminous intensity.
Luminous intensity is analogous toradiant intensity, but instead of simply adding up the contributions of everywavelength of light in the source's spectrum, the contribution of each wavelength isweighted by theluminous efficiency function, the model of the sensitivity of the human eye to different wavelengths, standardised by the CIE andISO.[11][4][12]
A common candle emits light with roughly 1 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.
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 purespermaceti candle weighing one sixth of a pound and burning at a rate of 120 grains per hour. Germany, Austria and Scandinavia used theHefnerkerze, a unit based on the output of aHefner lamp.[13]
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 cm2 ofplatinum 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 tooxidation, and could be obtained in pure form.[14] 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.[14] 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 ofthorium dioxide with a small hole in it in a bath of molten platinum. The shell (cavity) serves as ablack body, producingblack-body radiation that depends on the temperature and is not sensitive to details of how the device is constructed.
In 1937, theCommission 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:
The value of thenew candle is such that the brightness of the full radiator at the temperature of solidification of platinum is 60 new candles persquare centimetre.[15]
It was then ratified in 1948 by the 9th CGPM[16] which adopted a new name for this unit, thecandela. 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:
The candela is the luminous intensity, in the perpendicular direction, of a surface of1 / 600,000 square metre of a black body at the temperature of freezing platinum under a pressure of101,325 newtons per square metre.[17]
In 1979, because of the difficulties in realising a Planck radiator at high temperatures and the new possibilities offered byradiometry, the 16th CGPM adopted a new definition of the candela:[18][19]
The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency540×1012hertz and that has aradiant intensity in that direction of1/683watt persteradian.
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[20] 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 thesecond (an SI base unit) and the watt (a derived SI unit), the candela remains a base unit of the SI system, by definition.[21]
The 26th CGPM approved the modern definition of the candela in 2018 as part of the2019 revision of the SI, which redefined the SI base units in terms of fundamental physical constants.
^The symbols in this column denotedimensions; "L", "T" and "J" are for length, time, and luminous intensity respectively, not the symbols for theunits litre, tesla, and joule.
^Standards organizations recommend that photometric quantities be denoted with a subscript "v" (for "visual") to avoid confusion with radiometric orphoton quantities. For example:USA Standard Letter Symbols for Illuminating Engineering USAS Z7.1-1967, Y10.18-1967
^abcAlternative symbols sometimes seen:W for luminous energy,P orF for luminous flux, andρ for luminous efficacy of a source.
Relationships between luminous intensity, luminous flux, and illuminance
If a source emits a known luminous intensityIv (in candelas) in a well-defined cone, the totalluminous fluxΦv inlumens is given bywhereA is theradiation angle of the lamp—the full vertex angle of the emission cone. For example, a lamp that emits 590 cd with a radiation angle of 40° emits about 224 lumens. SeeMR16 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 4π: a uniform 1 candela source emits 4π lumens (approximately 12.566 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 alight meter is incident light on a sensor of finite area, i.e.illuminance in lm/m2 (lux). However, if designing illumination from many point light sources, like light bulbs, of known approximate omnidirectionally uniform intensities, the contributions to illuminance fromincoherent light being additive, it is mathematically estimated as follows. Ifri is the position of theith source of uniform intensityIi, andâ is the unit vectornormal to the illuminated elemental opaque areadA being measured, and provided that all light sources lie in the same half-space divided by the plane of this area,In the case of a single point light source of intensityIv, at a distancer and normally incident, this reduces to
Like other SI units, the candela can also be modified by adding ametric prefix that multiplies it by apower of 10, for example millicandela (mcd) for 10−3 candela.
^This frequency corresponds to awavelength of 555 nm in air, which is yellowish-green light approximately at the peak of human visual response. The colour can be approximated on ansRGB display withCSS colour valuergb(120,255,0) or hex#78ff00.
