Luminous efficacy

Luminous efficacy is a measure of how well a light source produces visible light. 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, 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 lumens per watt, or "efficacies" expressed as a percentage.

The luminous coefficient is luminous efficiency expressed as a value between zero and one, with one corresponding to an efficacy of 683 lm/W.

Luminous efficacy of radiation

Explanation

The response of a typical human eye to light, as standardized by the CIE in 1924. The horizontal axis is wavelength in nm

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 lumens 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

$\frac{ \int^\infin_0 y_\lambda J_\lambda d\lambda } { \int^\infin_0 J_\lambda d\lambda },$

where

y_λ is the standard luminosity function,

J_λ 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 $\int^\infin_0 y_\lambda J_\lambda d\lambda$ is an inner product between y_λ and J_λ and that $\int^\infin_0 J_\lambda d\lambda$ is the one-norm of J_λ.

Examples

Spectral radiance of a black body. Energy outside the visible wavelength range (~380–750 nm, shown by grey dotted lines) reduces the luminous efficiency.

Type	Luminous efficacy of radiation (lm/W)	Luminous efficiency[note 1]
Typical tungsten light bulb at 2800 K	15[7]	2%
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	93[7]	13.6%
ideal black-body radiator at 7000 K	95[8]	14%
ideal 5800 K black-body, truncated to 400–700 nm (ideal "white" source)	251[7][note 2]	37%
ideal monochromatic 555 nm source	683[9]	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[note 1]
Combustion	candle	0.3[note 3]	0.04%
	gas mantle	1–2[10]	0.15–0.3%
Incandescent	100–200 W tungsten incandescent (230 V)	13.8[11]–15.2[12]	2.0–2.2%
	100–200–500 W tungsten glass halogen (230 V)	16.7[13]–17.6[12]–19.8[12]	2.4–2.6–2.9%
	5–40–100 W tungsten incandescent (120 V)	5–12.6[14]–17.5[14]	0.7–1.8–2.6%
	2.6 W tungsten glass halogen (5.2 V)	19.2[15]	2.8%
	tungsten quartz halogen (12–24 V)	24	3.5%
	photographic and projection lamps	35[16]	5.1%
Light-emitting diode	white LED (raw, without power supply)	4.5–150 [17][18][19][20]	0.66–22.0%
	4.1 W LED screw base lamp (120 V)	58.5–82.9[21]	8.6–12.1%
	5.4 W LED screw base lamp (100 V 50/60Hz)	101.9[22]	14.9%
	6.9 W LED screw base lamp (120 V)	55.1–81.9[21]	8.1–12.0%
	7 W LED PAR20 (120 V)	28.6[23]	4.2%
	7 W LED PAR20 (110-230 V)	60.0[24]	8.8%
	8.7 W LED screw base lamp (120 V)	69.0–93.1[21][25]	10.1–13.6%
	Theoretical limit (white LED)	260.0–300.0[26]	38.1–43.9%
Arc lamp	xenon arc lamp	30–50[27][28]	4.4–7.3%
	mercury-xenon arc lamp	50–55[27]	7.3–8.0%
Fluorescent	T12 tube with magnetic ballast	60[29]	9%
	9–32 W compact fluorescent	46–75[30][31][12]	8–11.45%[32]
	T8 tube with electronic ballast	80–100[29]	12–15%
	PL-S 11 W U-tube, excluding ballast loss	82[33]	12%
	T5 tube	70–104.2[34][35]	10–15.63%
Gas discharge	1400 W sulfur lamp	100[36]	15%
	metal halide lamp	65–115[37]	9.5–17%
	high pressure sodium lamp	85–150[12]	12–22%
	low pressure sodium lamp	100–200[38][39][12]	15–29%
Cathodoluminescence	electron stimulated luminescence	30[40]	5%
Ideal sources	Truncated 5800 K blackbody[note 2]	251[7]	37%
	Green light at 555 nm (maximum possible luminous efficacy)	683.002[9]	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.”^[16] At temperatures where the tungsten filament of an ordinary light bulb remains solid (below 3683 kelvins), most of its emission is in the infrared.^[16]

SI photometry units

SI photometry unitsv · d · e

Quantity	Symbol[nb 1]	SI unit	Symbol	Dimension	Notes
Luminous energy	Qv [nb 2]	lumen second	lm⋅s	T⋅J	units are sometimes called talbots
Luminous flux	Φv [nb 2]	lumen (= cd⋅sr)	lm	J	also called luminous power
Luminous intensity	Iv	candela (= lm/sr)	cd	J [nb 3]	an SI base unit, luminous flux per unit solid angle
Luminance	Lv	candela per square metre	cd/m2	L−2⋅J	units are sometimes called nits
Illuminance	Ev	lux (= lm/m2)	lx	L−2⋅J	used for light incident on a surface
Luminous emittance	Mv	lux (= lm/m2)	lx	L−2⋅J	used for light emitted from a surface
Luminous exposure	Hv	lux second	lx⋅s	L−2⋅T⋅J
Luminous energy density	ωv	lumen second per metre3	lm⋅s⋅m−3	L−3⋅T⋅J
Luminous efficacy	η [nb 2]	lumen per watt	lm/W	M−1⋅L−2⋅T3⋅J	ratio of luminous flux to radiant flux
Luminous efficiency	V			1	also called luminous coefficient
See also: SI · Photometry · Radiometry

1. ^ Standards organizations recommend that photometric quantities be denoted with a suffix "v" (for "visual") to avoid confusion with radiometric or photon quantities.
2. ^ ^{a b c} Alternative symbols sometimes seen: W for luminous energy, P or F for luminous flux, and ρ or K for luminous efficacy.
3. ^ "J" is the recommended symbol for the dimension of luminous intensity in the International System of Units.

See also

• Photometry
• Light pollution
• Wall-plug efficiency - a related principle, but slightly different
• Coefficient of utilization

Notes

1. ^ ^{a b} Defined such that the maximum value possible is 100%.
2. ^ ^{a b} Integral of truncated Planck function times photopic luminosity function times 683 W/sr, according to the definition of the candela.^{[original research?]}
3. ^ 1 candela*4π steradians/40 W

References

1. ^ Stimson, Allen (1974). Photometry and Radiometry for Engineers. New York: Wiley and Son. 
2. ^ Grum, Franc and Becherer, Richard (1979). Optical Radiation Measurements Vol 1. New York: Academic Press. 
3. ^ Boyd, Robert (1983). Radiometry and the Detection of Optical Radiation. New York: Wiley and Son. 
4. ^ Roger A. Messenger and Jerry Ventre (2004). Photovoltaic systems engineering (Second ed.). CRC Press. p. 123. ISBN 9780849317934. http://books.google.com/?id=XiOeYrhyVlEC&pg=PA123&dq=%22luminous+efficacy+of+a+source%22#v=onepage&q=%22luminous%20efficacy%20of%20a%20source%22&f=false. 
5. ^ 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. http://books.google.com/?id=79-V0_TElg4C&pg=PA338&dq=luminous+efficacy+of+radiation#v=onepage&q=luminous%20efficacy%20of%20radiation&f=false. 
6. ^ Van Nostrand's Scientific Encyclopedia, 3rd Edition. Princeton, New Jersey, Toronto, London, New York: D. Van Nostrand Company, Inc.. January 1958. 
7. ^ ^{a b c d} ""Maximum Efficiency of White Light"". http://physics.ucsd.edu/~tmurphy/papers/lumens-per-watt.pdf. Retrieved 2011-07-31. 
8. ^ ^{a b} Black body visible spectrum
9. ^ ^{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. 
10. ^ Westermaier, F. V. (1920). "Recent Developments in Gas Street Lighting". The American City (New York: Civic Press) 22 (5): 490. http://books.google.com/?id=rWxLAAAAMAAJ&dq=mantle%20lamp&pg=PA490#v=onepage&q=mantle%20lamp. 
11. ^ Bulbs: Gluehbirne.ch: Philips Standard Lamps (German)
12. ^ ^{a b c d e f} Philips Product Catalog (German)
13. ^ "Osram halogen" (in German) (PDF). www.osram.de. Archived from the original on November 7, 2007. http://web.archive.org/web/20071107054500/http://www.osram.de/_global/pdf/osram_de/tools_services/downloads/allgemeinbeleuchtung/halogenlampen/haloluxhalopar.pdf. Retrieved 2008-01-28. 
14. ^ ^{a b} Keefe, T.J. (2007). "The Nature of Light". http://www.ccri.edu/physics/keefe/light.htm. Retrieved 2007-11-05. 
15. ^ "Osram Miniwatt-Halogen". www.ts-audio.biz. http://www.ts-audio.biz/tsshop/WGS/411/PRD/LFH0324408/Osram_6406330_500mA_52V_E10_BLK1_MINIWATT-Halogen-Gluehlampe_f.Taschenl..htm. Retrieved 2008-01-28. ^{[dead link]}
16. ^ ^{a b c} Klipstein, Donald L. (1996). "The Great Internet Light Bulb Book, Part I". http://freespace.virgin.net/tom.baldwin/bulbguide.html. Retrieved 2006-04-16. 
17. ^ White LED Offers Broad Temp Range And Color Yield Electronicdesign (HTTP cookies required) Otherwise see:Google Cache
18. ^ "Nichia NSPWR70CSS-K1 specifications" (pdf). Nichia Corp.. http://www.nichia.co.jp/specification/led_09/NSPWR70CSS-K1-E.pdf. Retrieved April 26, 2009. ^{[dead link]}
19. ^ Klipstein, Donald L.. "The Brightest and Most Efficient LEDs and where to get them". Don Klipstein's Web Site. http://members.misty.com/don/led.html#ln. Retrieved 2008-01-15. 
20. ^ "Cree XLamp XP-G LEDs Data Sheet". http://www.cree.com/Products/pdf/XLampXP-G.pdf.  Claims 132 lm/W.
21. ^ ^{a b c} Toshiba E-CORE LED Lamp
22. ^ Toshiba E-CORE LED Lamp LDA5N-E17
23. ^ GE 73716 7-Watt Energy Smart PAR20 LED Light Bulb
24. ^ Lite Gear LED PAR 30 7W Light Bulb
25. ^ Toshiba to release 93 lm/W LED bulb Ledrevie
26. ^ White LEDs with super-high luminous efficacy physorg.com
27. ^ ^{a b} "Technical Information on Lamps" (pdf). Optical Building Blocks. http://www.pti-nj.com/products/High-Speed-Spectrofluorometer/TechNotes/TechnicalInformationLamps.pdf. 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.
28. ^ OSRAM Sylvania Lamp and Ballast Catalog. 2007. 
29. ^ ^{a b} Federal Energy Management Program (December 2000). How to buy an energy-efficient fluorescent tube lamp. U.S. Department of Energy. http://www1.eere.energy.gov/femp/procurement/eep_fluortube_lamp.html. 
30. ^ "Low Mercury CFLs". Energy Federation Incorporated. http://www.energyfederation.org/consumer/default.php/cPath/25_44_3006. Retrieved 2008-12-23. 
31. ^ "Conventional CFLs". Energy Federation Incorporated. http://www.energyfederation.org/consumer/default.php/cPath/25_44_784. Retrieved 2008-12-23. 
32. ^ "Global bulbs". 1000Bulbs.com accessdate=2010-2-20. http://www.1000bulbs.com/32-Watt-Compact-Fluorescents/37889/. |
33. ^ Phillips. "Phillips Master". http://skinflint.co.uk/a416644.html. Retrieved 2010-12-21. 
34. ^ Department of the Environment, Water, Heritage and the Arts, Australia. "Energy Labelling—Lamps". http://www.energyrating.gov.au/appsearch/download.asp. Retrieved 2008-08-14. 
35. ^ "1000bulbs.com". 1000Bulbs.com. http://www.1000bulbs.com/F35T5-6500K/39598/. Retrieved 2010-2-20. 
36. ^ "1000-watt sulfur lamp now ready". IAEEL newsletter (IAEEL) (1). 1996. Archived from the original on Aug. 18, 2003. http://web.archive.org/web/20030818061414/195.178.164.205/IAEEL/iaeel/newsl/1996/ett1996/LiTech_b_1_96.html. 
37. ^ "The Metal Halide Advantage". Venture Lighting. 2007. http://www.venturelighting.com/TechCenter/Metal-Halide-TechIntro.html. Retrieved 2008-08-10. 
38. ^ "LED or Neon? A scientific comparison". http://www.signweb.com/index.php/channel/12/id/138/. 
39. ^ "Why is lightning coloured? (gas excitations)". http://webexhibits.org/causesofcolor/4.html. 
40. ^ ""Vu1 ESL™ R-30 Energy Efficient Light Bulb Specifications"". http://www.vu1corporation.com/eslupdate/. 

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