Luminous efficacy
Luminous efficacy is a figure of merit for light sources. It is the ratio of luminous flux to power. Depending on context, the power can be either the radiant flux of the source's output, or it can be the total electric power consumed by the source.[1][2][3] 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 source.
The luminous efficacy of a source is a measure of the efficiency with which the source provides visible light from electricity.[4] The luminous efficacy of radiation describes how well a given quantity of electromagnetic radiation from a source produces visible light: the ratio of luminous flux to radiant flux.[5] Not all wavelengths of light are equally visible, or equally effective at stimulating human vision, due to the spectral sensitivity of the human eye; radiation in the infrared and ultraviolet parts of the spectrum is useless for illumination. The overall luminous efficacy of a source is the product of how well it converts energy to electromagnetic radiation, and how well the emitted radiation is detected by the human eye.
Efficacy and efficiency
In some systems of units, luminous flux has the same units as radiant flux. The luminous efficacy of radiation is then dimensionless. In this case, it is often instead called the luminous efficiency or luminous coefficient and may be expressed as a percentage. A common choice is to choose units such that the maximum possible efficacy, 683 lm/W, corresponds to an efficiency of 100%. The distinction between efficacy and efficiency is not always carefully maintained in published sources, so it is not uncommon to see "efficiencies" expressed in lumen per watt, or "efficacies" expressed as percentages.
Luminous efficacy of radiation
Explanation
Wavelengths of light outside of the visible spectrum are not useful for illumination because they cannot be seen by the human eye. Furthermore, the eye responds more to some wavelengths of light than others, even within the visible spectrum. This response of the eye is represented by the luminosity function. This is a standardized function which represents the response of a "typical" eye under bright conditions (photopic vision). One can also define a similar curve for dim conditions (scotopic vision). When neither is specified, photopic conditions are generally assumed.
Luminous efficacy of radiation measures the fraction of electromagnetic power which is useful for lighting. It is obtained by dividing the luminous flux by the radiant flux. Light with wavelengths outside the visible spectrum reduces luminous efficacy, because it contributes to the radiant flux while the luminous flux of such light is zero. Wavelengths near the peak of the eye's response contribute more strongly than those near the edges.
In SI, luminous efficacy has units of lumen per watt (lm/W). Photopic luminous efficacy of radiation has a maximum possible value of 683 lm/W, for the case of monochromatic light at a wavelength of 555 nm (green). Scotopic luminous efficacy of radiation reaches a maximum of 1700 lm/W for narrowband light of wavelength 507 nm.
Mathematical definition
The dimensionless luminous efficiency measures the integrated fraction of the radiant power that contributes to its luminous properties as evaluated by means of the standard luminosity function.[6] The luminous coefficient is
where
- yλ is the standard luminosity function,
- Jλ is the spectral power distribution of the radiant intensity.
The luminous coefficient is unity for a narrow band of wavelengths at 555 nanometres.
Note that is an inner product between and and that is the one-norm of .
Examples
Type |
Luminous efficacy of radiation (lm/W) |
Luminous efficiency[7] |
---|---|---|
Class M star (Antares, Betelgeuse), 3000 K | 30 | 4% |
ideal black-body radiator at 4000 K | 47.5 [8] | 7.0% |
Class G star (Sun, Capella), 5800 K | 80 | 12% |
ideal black-body radiator at 7000 K | 95 [8] | 14% |
ideal 5800 K black-body, truncated to 400–700 nm (ideal "white" source) | 251 [9] | 37% |
ideal monochromatic 555 nm source | 683 [10] | 100% |
Lighting efficiency
Artificial light sources are usually evaluated in terms of luminous efficacy of a source, also sometimes called overall luminous efficacy. This is the ratio between the total luminous flux emitted by a device and the total amount of input power (electrical, etc.) it consumes. It is also sometimes referred to as the wall-plug luminous efficacy or simply wall-plug efficacy. The overall luminous efficacy is a measure of the efficiency of the device with the output adjusted to account for the spectral response curve (the “luminosity function”). When expressed in dimensionless form (for example, as a fraction of the maximum possible luminous efficacy), this value may be called overall luminous efficiency, wall-plug luminous efficiency, or simply the lighting efficiency.
The main difference between the luminous efficacy of radiation and the luminous efficacy of a source is that the latter accounts for input energy that is lost as heat or otherwise exits the source as something other than electromagnetic radiation. Luminous efficacy of radiation is a property of the radiation emitted by a source. Luminous efficacy of a source is a property of the source as a whole.
Examples
The following table lists luminous efficacy of a source and efficiency for various light sources:
Category |
Type |
Overall luminous efficacy (lm/W) |
Overall luminous efficiency[7] |
---|---|---|---|
Combustion | candle | 0.3 [11] | 0.04% |
gas mantle | 1–2 [12] | 0.15–0.3% | |
Incandescent | 100–200 W tungsten incandescent (230 V) | 13.8[13]–15.2[14] | 2.0–2.2% |
100–200–500 W tungsten glass halogen (230 V) | 16.7[15]–17.6[14]–19.8[14] | 2.4–2.6–2.9% | |
5–40–100 W tungsten incandescent (120 V) | 5–12.6[16]–17.5[16] | 0.7–1.8–2.6% | |
2.6 W tungsten glass halogen (5.2 V) | 19.2 [17] | 2.8% | |
tungsten quartz halogen (12–24 V) | 24 | 3.5% | |
photographic and projection lamps | 35 [18] | 5.1% | |
Light-emitting diode | white LED (raw, without power supply) | 4.5–150 [19][20][21][22] | 0.66–22.0% |
4.1 W LED screw base lamp (120 V) | 58.5–82.9 [23] | 8.6–12.1% | |
6.9 W LED screw base lamp (120 V) | 55.1–81.9 [23] | 8.1–12.0% | |
7 W LED PAR20 (120 V) | 28.6 [24] | 4.2% | |
8.7 W LED screw base lamp (120 V) | 69.0–93.1 [23][25] | 10.1–13.6% | |
Arc lamp | xenon arc lamp | 30–50 [26][27] | 4.4–7.3% |
mercury-xenon arc lamp | 50–55 [26] | 7.3–8.0% | |
Fluorescent | T12 tube with magnetic ballast | 60 [28] | 9% |
9–32 W compact fluorescent | 46–75 [29][30][14] | 8–11.45% [31] | |
T8 tube with electronic ballast | 80–100 [28] | 12–15% | |
T5 tube | 70–104.2 [32] [33] | 10–15.63% | |
Spiral tube with electronic ballast | 114-124.3 [34] | 15–18% | |
Gas discharge | 1400 W sulfur lamp | 100 [35] | 15% |
metal halide lamp | 65–115 [36] | 9.5–17% | |
high pressure sodium lamp | 85–150 [14] | 12–22% | |
low pressure sodium lamp | 100–200 [37][38][14] | 15–29% | |
Ideal sources | Truncated 5800 K blackbody [9] | 251 [citation needed] | 37% |
Green light at 555 nm (maximum possible LER) | 683.002 [10] | 100% |
Sources that depend on thermal emission from a solid filament, such as incandescent light bulbs, tend to have low overall efficacy compared to an ideal blackbody source because, as explained by Donald L. Klipstein, “An ideal thermal radiator produces visible light most efficiently at temperatures around 6300 °C (6600 K or 11,500 °F). Even at this high temperature, a lot of the radiation is either infrared or ultraviolet, and the theoretical luminous [efficacy] is 95 lumens per watt. Of course, nothing known to any humans is solid and usable as a light bulb filament at temperatures anywhere close to this. The surface of the sun is not quite that hot.”[18] At temperatures where the tungsten filament of an ordinary light bulb remains solid (below 3683 kelvins), most of its emission is in the infrared.[18]
SI photometry units
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.
See also
- Luminous coefficient
- Photometry
- Light pollution
- Wall-plug efficiency - a related principle, but slightly different
References
- ^ Stimson, Allen (1974). Photometry and Radiometry for Engineers. New York: Wiley and Son.
- ^
Grum, Franc and Becherer, Richard (1979). Optical Radiation Measurements Vol 1. New York: Academic Press.
{{cite book}}
: CS1 maint: multiple names: authors list (link) - ^ Boyd, Robert (1983). Radiometry and the Detection of Optical Radiation. New York: Wiley and Son.
- ^ Roger A. Messenger and Jerry Ventre (2004). Photovoltaic systems engineering (Second ed.). CRC Press. p. 123. ISBN 9780849317934.
- ^
Erik Reinhard, Erum Arif Khan, Ahmet Oğuz Akyüz, and Garrett Johnson (2008). Color imaging: fundamentals and applications. A K Peters, Ltd. p. 338. ISBN 9781568813448.
{{cite book}}
: CS1 maint: multiple names: authors list (link) - ^ Van Nostrand's Scientific Encyclopedia, 3rd Edition. Princeton, New Jersey, Toronto, London, New York: D. Van Nostrand Company, Inc. 1958.
{{cite book}}
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ignored (help) - ^ a b Defined such that the maximum value possible is 100%.
- ^ a b Black body visible spectrum
- ^ a b Integral of truncated Planck function times photopic luminosity function times 683 W/sr, according to the definition of the candela.[original research?]
- ^ a b Wyszecki, Günter and Stiles, W.S. (2000). Color Science - Concepts and Methods, Quantitative Data and Formulae (2nd ed.). Wiley-Interscience. ISBN 0-471-39918-3.
{{cite book}}
: CS1 maint: multiple names: authors list (link) - ^ 1 candela*4π steradians/40 W
- ^ Westermaier, F. V. (1920). "Recent Developments in Gas Street Lighting". The American City. 22 (5). New York: Civic Press: 490.
- ^ Bulbs: Gluehbirne.ch: Philips Standard Lamps (German)
- ^ a b c d e f Philips Product Catalog (German)
- ^ "Osram halogen" (PDF). www.osram.de (in German). Archived from the original (PDF) on November 7, 2007. Retrieved 2008-01-28.
- ^ a b Keefe, T.J. (2007). "The Nature of Light". Retrieved 2007-11-05.
- ^ "Osram Miniwatt-Halogen". www.ts-audio.biz. Retrieved 2008-01-28.[dead link]
- ^ a b c Klipstein, Donald L. (1996). "The Great Internet Light Bulb Book, Part I". Retrieved 2006-04-16.
- ^ White LED Offers Broad Temp Range And Color Yield Electronicdesign (HTTP cookies required) Otherwise see:Google Cache
- ^ "Nichia NSPWR70CSS-K1 specifications" (pdf). Nichia Corp. Retrieved April 26, 2009. [dead link]
- ^ Klipstein, Donald L. "The Brightest and Most Efficient LEDs and where to get them". Don Klipstein's Web Site. Retrieved 2008-01-15.
- ^ "Cree XLamp XP-G LEDs Data Sheet" (PDF). Claims 132 lm/W.
- ^ a b c Toshiba E-CORE LED Lamp
- ^ GE 73716 7-Watt Energy Smart PAR20 LED Light Bulb
- ^ Toshiba to release 93 lm/W LED bulb Ledrevie
- ^ a b "Technical Information on Lamps" (pdf). Optical Building Blocks. Retrieved 2010-05-01. Note that the figure of 150 lm/W given for xenon lamps appears to be a typo. The page contains other useful information.
- ^ OSRAM Sylvania Lamp and Ballast Catalog. 2007.
- ^ a b Federal Energy Management Program (December 2000). "How to buy an energy-efficient fluorescent tube lamp". U.S. Department of Energy.
{{cite journal}}
: Cite journal requires|journal=
(help) - ^ "Low Mercury CFLs". Energy Federation Incorporated. Retrieved 2008-12-23.
- ^ "Conventional CFLs". Energy Federation Incorporated. Retrieved 2008-12-23.
- ^ "Global bulbs". 1000Bulbs.com accessdate=2010-2-20.
{{cite web}}
: Missing pipe in:|publisher=
(help)| - ^ Department of the Environment, Water, Heritage and the Arts, Australia. "Energy Labelling—Lamps". Retrieved 2008-08-14.
{{cite web}}
: CS1 maint: multiple names: authors list (link) - ^ "1000bulbs.com". 1000Bulbs.com. Retrieved 2010-2-20.
{{cite web}}
: Check date values in:|accessdate=
(help) - ^ Panasonic. "Panasonic Spiral Fluorescent". Retrieved 2010-09-27.
- ^ "1000-watt sulfur lamp now ready". IAEEL newsletter. No. 1. IAEEL. 1996. Archived from the original on Aug. 18, 2003.
{{cite news}}
: Check date values in:|archivedate=
(help) - ^ "The Metal Halide Advantage". Venture Lighting. 2007. Retrieved 2008-08-10.
- ^ "LED or Neon? A scientific comparison".
- ^ "Why is lightning coloured? (gas excitations)".
External links
- Hyperphysics has these graphs of efficacy that do not quite comply with the standard definition
- Energy Efficient Light Bulbs
- Other Power
- CIPCO Energy Library