Candela
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| candela | |
|---|---|
| General information | |
| Unit system | SI |
| Unit of | luminous intensity |
| Symbol | cd |
| Conversions | |
| 1 cd in ... | ... is equal to ... |
| international candles | ≈ 1.02 cp |
| Hefnerkerze | ≈ 1.11 HK |
Candela (symbol: cd) is the SI unit of luminous intensity.[5][6] 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 for candle. The old name "candle" is still sometimes used, as in foot-candle and the modern definition of candlepower.[7]
Definition
[edit]The 26th General Conference on Weights and Measures (CGPM) redefined the candela in 2018.[8][9] The new definition, which took effect on 20 May 2019, is:
The candela [...] is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540×1012 Hz,[a] Kcd, to be 683 when expressed in the unit lm W−1, which is equal to cd sr W−1, or cd sr kg−1 m−2 s3, where the kilogram, metre and second are defined in terms of h, c and ΔνCs.[10]
Explanation
[edit]
The frequency chosen is in the visible spectrum near green, corresponding to a wavelength of about 555 nanometres. The human eye, when 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 where Iv(λ) is the luminous intensity, Ie(λ) is the radiant intensity and 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 weighted by the luminous efficiency function, the model of the sensitivity of the human eye to different wavelengths, standardized by the CIE and ISO.[11][4][12]
Examples
[edit]- 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.
- A 25 W compact fluorescent light bulb puts out around 1700 lumens; if that light is radiated equally in all directions (i.e. over 4π steradians), it will have an intensity of
- Focused into a 20° beam (0.095 steradians), the same light bulb would have an intensity of around 18,000 cd or 18 kcd within the beam.
History
[edit]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 grains per hour. Germany, Austria and Scandinavia used the Hefnerkerze, a unit based on the output of a Hefner lamp.[13]

A better standard for luminous intensity was needed. In 1884, Jules Violle had proposed a standard based on the light emitted by 1 cm2 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.[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, realizing 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 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:
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.[15]
It was then ratified in 1948 by the 9th CGPM[16] 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.[17]
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 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 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, 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 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.[21]
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
[edit]
| Quantity | Unit | Dimension [nb 1] |
Notes | ||
|---|---|---|---|---|---|
| Name | Symbol[nb 2] | Name | Symbol | ||
| Luminous energy | Qv[nb 3] | lumen second | lm⋅s | T⋅J | The lumen second is sometimes called the talbot. |
| Luminous flux, luminous power | Φv[nb 3] | 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[nb 3] | 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: | |||||
- ^ The symbols in this column denote dimensions; "L", "T" and "J" are for length, time and luminous intensity respectively, not the symbols for the units litre, tesla and joule.
- ^ Standards organizations recommend that photometric quantities be denoted with a subscript "v" (for "visual") to avoid confusion with radiometric or photon quantities. For example: USA Standard Letter Symbols for Illuminating Engineering USAS Z7.1-1967, Y10.18-1967
- ^ a b c Alternative symbols sometimes seen: W for luminous energy, P or F for luminous flux, and ρ for luminous efficacy of a source.
Relationships between luminous intensity, luminous flux, and illuminance
[edit]If a source emits a known luminous intensity Iv (in candelas) in a well-defined cone, the total luminous flux Φv in lumens is given by where A is the radiation 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. 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 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 idealized 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/m2 (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 ri is the position of the ith source of uniform intensity Ii, and â is the unit vector normal to the illuminated elemental opaque area dA 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 intensity Iv, at a distance r and normally incident, this reduces to
SI multiples
[edit]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 10−3 candela.
Notes
[edit]- ^ This frequency corresponds to a wavelength of 555 nm in air, which is yellowish-green light approximately at the peak of human visual response. The color can be approximated on an sRGB display with CSS color value
rgb(120,255,0)or hex#78ff00.
References
[edit]- ^ "CIE Scotopic luminosity curve (1951)".
- ^ "CIE (1931) 2-deg color matching functions".
- ^ "Judd–Vos modified CIE 2-deg photopic luminosity curve (1978)".
- ^ a b Sharpe, Stockman, Jagla & Jägle (2005) 2-deg V*(l) luminous efficiency function Archived 27 September 2007 at the Wayback Machine
- ^ International Bureau of Weights and Measures (20 May 2019), The International System of Units (SI) (PDF) (9th ed.), ISBN 978-92-822-2272-0, archived from the original on 18 October 2021
- ^ CIE (2020). CIE S 017:2020 ILV: International Lighting Vocabulary, 2nd edition (2nd ed.). CIE.
- ^ "Candlepower – Definition". Merriam-Webster Dictionary. Retrieved 15 February 2015.
- ^ "Convocation of the General Conference on Weights and Measures (26th meeting)" (PDF). Versailles: Bureau International des Poids et Mesures. 13 November 2018. Archived from the original (PDF) on 19 September 2019. Retrieved 10 February 2019.
- ^ BIPM (22 March 2021). "Mise en pratique for the definition of the candela in the SI". BIPM.
- ^ The International System of Units (PDF), V3.01 (9th ed.), International Bureau of Weights and Measures, August 2024, p. 135, ISBN 978-92-822-2272-0
- ^ 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.
- ^ Wyszecki, G.; Stiles, W.S. (1982). Color Science: Concepts and Methods, Quantitative Data and Formulae (2nd ed.). Wiley-Interscience. ISBN 0-471-02106-7.
- ^ "Hefner unit, or Hefner candle". Sizes.com. 30 May 2007. Retrieved 25 February 2009.
- ^ a b Cottington, Ian E. (1986). "Platinum and the Standard of Light: A Selective Review of Proposals Which Led to an International Unit of Luminous Intensity". Platinum Metals Review. 30 (2): 84.
- ^ Barry N. Taylor (1992). The Metric System: The International System of Units (SI). U. S. Department of Commerce. p. 18. ISBN 0-941375-74-9. (NIST Special Publication 330, 1991 ed.)
- ^ Proceedings of the 9th CGPM, 1948, page 54 (French)
- ^ 13th CGPM Resolution 5, CR, 104 (1967), and Metrologia, 4, 43–44 (1968).
- ^ 16th CGPM Resolution 3, CR, 100 (1979), and Metrologia, 16, 56 (1980).
- ^ "Base unit definitions: Candela". The NIST Reference on Constants, Units, and Uncertainty. Retrieved 27 September 2010.
- ^ "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)". SI Brochure Appendix 2. Bureau International des Poids et Mesures. 22 March 2021. Retrieved 7 October 2023.
- ^ "Units for photochemical and photobiological quantities". SI Brochure Appendix 3. Bureau International des Poids et Mesures. 22 March 2021. Retrieved 7 October 2023.
Candela
View on GrokipediaDefinition and Fundamentals
Formal Definition
The candela (symbol: cd) is the SI base unit of luminous intensity in a given direction.[1] It is defined as the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency $ 540 \times 10^{12} $ Hz (corresponding to green light at a wavelength of 555 nm) and that has a radiant intensity in that direction of $ \frac{1}{683} $ watt per steradian (W/sr).[1] This definition fixes the luminous efficacy $ K_{cd} $ of such radiation exactly at 683 lm/W.[1] The relationship between luminous intensity $ I_v $ (in cd) and radiant intensity $ I_e $ (in W/sr) for this monochromatic source is given byVisual Basis
The candela, as the SI unit of luminous intensity, quantifies the power of visible light emitted by a source in a given direction, weighted according to the average sensitivity of the human visual system under photopic conditions. This weighting is provided by the spectral luminous efficiency function V(λ), which describes the relative effectiveness of different wavelengths in stimulating human vision, with a peak sensitivity at 555 nm, corresponding to a frequency of 540 × 10¹² Hz.[8] By focusing on this monochromatic green light at maximum sensitivity, the definition standardizes measurements to align with human perceptual response, ensuring photometric quantities reflect perceived brightness rather than total energy.[9] Photopic vision refers to the normal functioning of the human eye in well-lit, daylight conditions, where cone cells in the retina dominate and enable color perception and high acuity. The eye's sensitivity curve V(λ) is normalized to a maximum value of 1 at 555 nm, dropping sharply outside the visible spectrum from approximately 380 nm to 780 nm, emphasizing that only light in this range contributes to luminous intensity. This physiological basis justifies the candela's emphasis on the peak wavelength for standardization, as it captures the green-yellow region where the human eye is most efficient, avoiding over- or underestimation of brightness for broadband sources.[8][9] The International Commission on Illumination (CIE) established the photopic luminosity function V(λ) as part of its 1931 standard observer model, derived from experimental data on human color matching and spectral sensitivity for a 2° field of view. This V(λ) curve serves as the foundational weighting function in photometry, transforming radiometric spectral power distributions into luminous quantities by integrating over wavelength with V(λ) as the kernel. In contrast, radiometry measures unweighted electromagnetic radiation across all wavelengths, focusing on physical energy flux without regard to human perception, such as in watts per steradian for radiant intensity.[8][9]Historical Development
Pre-SI Standards
The unit of luminous intensity known as the "candle" was standardized in the 19th century, with the British standard candle adopted in 1860 based on the light emitted by a standard candle made from spermaceti wax derived from sperm whale oil, burning at a specified rate of approximately 7.776 grams per hour. This definition provided a practical reference tied to a common source of illumination. However, early implementations varied, as the flame's output depended on factors like wick composition and environmental conditions.[3] In the 19th century, refinements addressed these inconsistencies through national standards. The British standard candle specified the luminous intensity produced by a spermaceti candle weighing one-sixth of a pound (about 76 grams) and consuming 120 grains (7.8 grams) of wax per hour, with the flame maintained at a height of 3.048 cm above the wick tip. Other national standards included the French bougie décimale, defined as one-tenth of the bougie (the light from a Carcel lamp), and the German Hefnerkerze, introduced in 1893, which emitted approximately 0.9 cd.[10] This British definition aimed for reproducibility but still faced challenges from material purity variations. By 1909, international collaboration led to the "international candle," defined as the average luminous intensity of a group of carbon-filament incandescent lamps operated at a color temperature of around 1800 K under standardized voltage and current conditions, calibrated against the British standard. This shift from flame to electric sources marked progress toward uniformity among nations like France, the United Kingdom, and the United States.[11][12][10] The name "candela" was formally adopted in 1948 by the 9th Conférence Générale des Poids et Mesures (CGPM), based on a proposal from the International Commission on Illumination (CIE), replacing the "international candle" with a definition based on thermal radiation: one candela equaled the luminous intensity, in the perpendicular direction, of a surface area of 1/600,000 square meter of a blackbody radiator at the freezing temperature of platinum (2042 K) under a pressure of 101,325 Pa. This standard, while more physically grounded than prior artifact-based ones, retained a reliance on a reproducible thermal source rather than direct electrical or frequency measures.[10][2] Artifact-based pre-SI standards, from spermaceti candles to carbon-filament lamps and blackbody radiators, were limited by inherent variabilities in materials and construction, such as inconsistent flame heights or filament degradation, which caused discrepancies up to 10% between national realizations. These issues necessitated repeated international conferences for calibration and agreement, highlighting the need for a more invariant definition to support global photometry.[3][10]SI Adoption
The candela was formally established as one of the six base units of the International System of Units (SI) by the 11th Conférence Générale des Poids et Mesures (CGPM) in 1960, alongside the metre, kilogram, second, ampere, and degree Kelvin.[13] This adoption, detailed in Resolution 12, integrated the candela into the newly named Système International d'Unités, replacing the earlier "new candle" unit and standardizing luminous intensity as a fundamental quantity independent of other units.[14] At that time, the candela was defined as 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 (2042 K) under a pressure of 101 325 Pa.[14] The International Committee for Weights and Measures (CIPM), through its Consultative Committee for Photometry, played a key role in recommending this inclusion to ensure international consistency in photometric measurements. In 1979, the 16th CGPM redefined the candela to enhance precision and reproducibility, shifting from the blackbody-based standard to a source of monochromatic radiation. Resolution 3 specified: "The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 10^{12} Hz and that has a radiant intensity in that direction of 1/683 watt per steradian."[15] This change, proposed by the CIPM based on advancements in laser technology and radiometry, eliminated dependencies on physical artifacts like platinum blackbody sources, allowing more accurate realizations using tunable lasers.[14] National metrology institutes, such as those affiliated with the Consultative Committee for Photometry and Radiometry (CCPR), validated this redefinition through intercomparisons, ensuring global alignment in luminous intensity standards.[8] The 2019 revision of the SI, approved by the 26th CGPM in 2018 and effective from 20 May 2019, left the candela's core definition intact but explicitly linked it to the system's seven fixed constants, including the Planck constant and speed of light . The updated definition states: "The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 × 10^{12} Hz, , to be 683 lm/W, where the kilogram, metre, and second are defined in terms of , , and the caesium hyperfine transition frequency ." This integration emphasized exactness without artifact references, as the watt (used in the radiant intensity) derives from base units now anchored to invariants. The CIPM, advised by the CCPR and metrology institutes worldwide, coordinated extensive validation experiments to confirm the revised framework's stability and equivalence across laboratories.[14][8]Photometric System Integration
Core Relationships
The candela (cd), as the SI unit of luminous intensity , quantifies the luminous flux emitted by a point source in a particular direction per unit solid angle, expressed as in candelas, where is in lumens (lm) and is the solid angle in steradians (sr).[8] For an isotropic point source emitting uniformly over a solid angle , this simplifies to .[2] The steradian (sr) is the SI derived unit of solid angle, defined as the solid angle subtended at the center of a sphere by a portion of its surface area equal to the square of the sphere's radius, given by , where is the surface area in square meters and is the radius in meters. This unit is dimensionless but retained for clarity in photometric and radiometric contexts, with the full sphere encompassing sr. Luminous efficacy relates the total luminous flux (in lm) to the total radiant flux (in watts, W) as (lm/W), representing the efficiency of converting radiant energy into visible light as perceived by the human eye.[9] The maximum luminous efficacy of radiation is 683 lm/W for monochromatic radiation at a wavelength of 555 nm under photopic (daylight) vision conditions, as defined by the International Commission on Illumination (CIE).[9] The candela connects luminous intensity to its radiometric counterpart, radiant intensity (in W/sr), through spectral integration weighted by the human visual response: , where is the spectral radiant intensity at wavelength and is the spectral luminous efficiency function (photopic luminosity function) standardized by the CIE.[16] This formulation ensures that luminous intensity accounts for the eye's sensitivity peak near 555 nm, transforming physical power per solid angle into a perceptually weighted measure.[16]Derived Quantities
Illuminance, denoted , quantifies the amount of luminous flux incident on a surface per unit area and is a key derived quantity from the candela. For an isotropic point source with luminous intensity , the illuminance at a perpendicular distance obeys the inverse square law, given by , where the unit is the lux (lx), equivalent to one lumen per square meter (lm/m²).[17][18] Luminance, , extends luminous intensity to surface properties by measuring it per unit projected area, thereby characterizing perceived brightness. It is defined as , with representing the projected area of the source perpendicular to the direction of observation, and has the unit candela per square meter (cd/m²).[19][20] Luminous exitance, , describes the total luminous flux leaving a surface per unit area and is particularly relevant for diffuse emitters. For Lambertian sources, which follow Lambert's cosine law for uniform angular distribution, , relating it directly to luminance; this assumes the source's emission is weighted by the human visual response function inherent in the candela definition.[21] These quantities facilitate applications in lighting design, such as optimizing workspace visibility and energy efficiency, by incorporating geometric and perceptual factors absent in purely radiometric measures like irradiance.[22]Practical Aspects
SI Prefixes
The candela (cd), as an SI base unit of luminous intensity, can be scaled using standard SI prefixes to express multiples and submultiples, facilitating the description of light sources with varying intensities. These prefixes follow the decimal system and are applied uniformly across SI units, including those in photometry, to denote factors of powers of ten.[23] The following table lists the SI prefixes from micro- to giga-, along with their symbols and scaling factors relative to the candela:| Prefix | Symbol | Factor | Unit Example |
|---|---|---|---|
| micro- | μ | 10⁻⁶ | microcandela (μcd) |
| milli- | m | 10⁻³ | millicandela (mcd) |
| centi- | c | 10⁻² | centicandela (ccd) |
| deci- | d | 10⁻¹ | decicandela (dcd) |
| (none) | - | 10⁰ | candela (cd) |
| deca- | da | 10¹ | decacandela (dacd) |
| hecto- | h | 10² | hectocandela (hcd) |
| kilo- | k | 10³ | kilocandela (kcd) |
| mega- | M | 10⁶ | megacandela (Mcd) |
| giga- | G | 10⁹ | gigacandela (Gcd) |