Candela

For other uses, see the unit of luminous intensity.

Photopic (black) and scotopic (green) luminosity 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.

The candela (Template:Pron-en or /kænˈdiːlə/, symbol: cd) is the SI base unit of luminous intensity; that is, power emitted by a light source in a particular direction, weighted by the luminosity function (a standardized model of the sensitivity of the human eye to different wavelengths, also known as the luminous efficiency function). A common 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.

Definition

Like other SI base units, the candela has an operational definition—it is defined by a description of a physical process that will produce one candela of luminous intensity. Since the 16th General Conference on Weights and Measures (CGPM) in 1979, the candela has been defined as:

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×10¹² hertz and that has a radiant intensity in that direction of ¹/₆₈₃ watt per steradian.

The definition describes how to produce a light source that (by definition) emits one candela. Such a source could then be used to calibrate instruments designed to measure luminous intensity, for example.

The candela is sometimes still called by the old name candle [1], such as in foot-candle and the modern definition of candlepower.

Explanation

The frequency chosen is in the visible spectrum near green, corresponding to a wavelength of about 555 nanometers. The human eye is most sensitive to this frequency, when adapted for bright conditions. 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 $\lambda$ is given by

$I_{v}(\lambda )=683.002\,{\overline {y}}(\lambda )I(\lambda )$

where $I_{v}(\lambda )$ is the luminous intensity in candelas, $I(\lambda )$ is the radiant intensity in W/sr and ${\overline {y}}(\lambda )$ is the standard luminosity function. If more than one wavelength is present (as is usually the case), one must sum or integrate over the spectrum of wavelengths present to get the total luminous intensity.

A common candle emits roughly 1 cd. A 100 W incandescent lightbulb emits about 120 cd.

Origin

Prior to 1948, there existed a variety of standards for luminous intensity in use in various 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 standards was the English standard: 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 grains per hour. Germany, Austria, and Scandinavia used the hefnerkerze, a unit based on the output of a Hefner lamp.

It became clear that a better-defined unit was needed. The Commission internationale de l'éclairage (International Commission on Illumination) and the CIPM proposed a “new candle” based on the luminance of a Planck radiator (a black body) at the temperature of freezing platinum. The value of the new unit was chosen to make it similar to the earlier unit candlepower. The decision was promulgated by the CIPM in 1946:

The value of the new candle is such that the brightness of the full radiator at the temperature of solidification of platinum is 60 new candles per square centimetre.

It was then ratified in 1948 by the 9th CGPM 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:

The candela is the luminous intensity, in the perpendicular direction, of a surface of 1/600 000 square metre of a black body at the temperature of freezing platinum under a pressure of 101 325 newtons per square metre.

In 1979, because of the difficulties in realizing a Planck radiator at high temperatures and the new possibilities offered by radiometry, the 16th CGPM adopted the modern definition of the candela. The arbitrary (1/683) term was chosen so that the new definition would exactly match the old definition. Although the candela is now defined partly in terms of the watt, which is a derived SI unit of power, the candela remains a base unit of the SI system, by definition.[2]

SI photometric light units

SI photometry quantities

Quantity		Unit		Dimension	Notes
Name	Symbol	Name	Symbol
Luminous energy	Qv	lumen second	lm⋅s	T⋅J	The lumen second is sometimes called the talbot.
Luminous flux, luminous power	Φv	lumen (= candela steradian)	lm (= cd⋅sr)	J	Luminous energy per unit time
Luminous intensity	Iv	candela (= lumen per steradian)	cd (= lm/sr)	J	Luminous flux per unit solid angle
Luminance	Lv	candela per square metre	cd/m2 (= lm/(sr⋅m2))	L−2⋅J	Luminous flux per unit solid angle per unit projected source area. The candela per square metre is sometimes called the nit.
Illuminance	Ev	lux (= lumen per square metre)	lx (= lm/m2)	L−2⋅J	Luminous flux incident on a surface
Luminous exitance, luminous emittance	Mv	lumen per square metre	lm/m2	L−2⋅J	Luminous flux emitted from a surface
Luminous exposure	Hv	lux second	lx⋅s	L−2⋅T⋅J	Time-integrated illuminance
Luminous energy density	ωv	lumen second per cubic metre	lm⋅s/m3	L−3⋅T⋅J
Luminous efficacy (of radiation)	K	lumen per watt	lm/W	M−1⋅L−2⋅T3⋅J	Ratio of luminous flux to radiant flux
Luminous efficacy (of a source)	η	lumen per watt	lm/W	M−1⋅L−2⋅T3⋅J	Ratio of luminous flux to power consumption
Luminous efficiency, luminous coefficient	V			1	Luminous efficacy normalized by the maximum possible efficacy
See also: SI Photometry Radiometry

Relationship between luminous intensity and luminous flux

If a source emits a known intensity (in candelas) in a well-defined cone, the total luminous flux in lumens can be calculated by taking the number of candelas, and dividing it by the number in the table below that corresponds to the "radiation angle" of the lamp (the full vertex angle of the emission cone). See MR16 for emission angles of some common lamps. Theory Formulas Online converter

• Example: A lamp that emits 590 cd with a radiation angle of 40°:
  590/2.64 = approximately 223 lumens.

Radiation angle	Divide by
5°	167.22
10°	41.82
15°	18.50
20°	10.48
25°	6.714
30°	4.671
35°	3.439
40°	2.639
45°	2.091
50°	1.699
55°	1.409
60°	1.188
65°	1.016
70°	0.8800
75°	0.7702
80°	0.6803
85°	0.6058
90°	0.5434
95°	0.4906
100°	0.4455
105°	0.4068
110°	0.3732
115°	0.3440
120°	0.3183

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 12.6 lumens.

External links

• Candela: The SI Unit of Luminous Intensity
• "The Unit of Luminous Intensity: Candela (cd)". Retrieved 2008-02-08.