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 power (electric power, chemical energy, or others) 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

$\frac{ \int^\infty_0 y_\lambda J_\lambda d\lambda } { \int^\infty_0 J_\lambda d\lambda },$

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 $\int^\infty_0 y_\lambda J_\lambda d\lambda$ is an inner product between $y_\lambda$ and $J_\lambda$ and that $\int^\infty_0 J_\lambda d\lambda$ is the one-norm of $J_\lambda$.

Examples

Photopic vision

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	54.7[8]	8%
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) [note 2]	251[7][note 3][9]	37%
5800 K black-body truncated to ≥2% photopic sensitivity range[note 4]	292[10][9]	43%
2800 K black-body truncated to ≥2% photopic sensitivity range[note 4]	299[10][9]	44%
2800 K black-body truncated to ≥5% photopic sensitivity range[note 5]	343[10][9]	50%
5800 K black-body truncated to ≥5% photopic sensitivity range[note 5]	348[10][9]	51%
Ideal monochromatic 555 nm source	683[11]	100%

Scotopic vision

Type	Luminous efficacy of radiation (lm/W)	Luminous efficiency[note 1]
Ideal monochromatic 507 nm source	1699 lm/W[12] or 1700 lm/W[13]	100%

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

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. Note that all lamps requiring electrical/electronic ballast are unless noted (see also voltage) listed without losses for that, reducing total efficiency.

Category	Type	Overall luminous efficacy (lm/W)	Overall luminous efficiency[note 1]
Combustion	candle	0.3[note 6]	0.04%
	gas mantle	1–2[14]	0.15–0.3%
Incandescent	100–200 W tungsten incandescent (230 V)	13.8[15]–15.2[16]	2–2.2%
	100–200–500 W tungsten glass halogen (230 V)	16.7[17]–17.6[16]–19.8[16]	2.4–2.6–2.9%
	5–40–100 W tungsten incandescent (120 V)	5–12.6[18]–17.5[18]	0.7–1.8–2.6%
	2.6 W tungsten glass halogen (5.2 V)	19.2[19]	2.8%
	tungsten quartz halogen (12–24 V)	24	3.5%
	photographic and projection lamps	35[20]	5.1%
Light-emitting diode	white LED (raw, without power supply)	4.5–150 [21][22][23][24]	0.66–22%
	4.1 W LED screw base lamp (120 V)	58.5–82.9[25]	8.6–12%
	5.4 W LED screw base lamp (100 V 50/60 Hz)	101.9[26]	14.9%
	6.9 W LED screw base lamp (120 V)	55.1–81.9[25]	8.1–12%
	7 W LED PAR20 (120 V)	28.6[27]	4.2%
	7 W LED PAR30 (110-230 V)	60[28]	8.8%
	8.7 W LED screw base lamp (120 V)	69–93.1[25][29]	10.1–13.6%
	Theoretical limit for a white LED with phosphorescence color mixing	260–300[30]	38.1–43.9%
Arc lamp	carbon arc lamp	2-7[31]	0.29-1.0%
	xenon arc lamp	30–50[32][33]	4.4–7.3%
	mercury-xenon arc lamp	50–55[32]	7.3–8%
	UHP – ultra-high-pressure mercury-vapor arc lamp: initial, free mounted	58–78[34]	8.5–11.4%
	UHP – ultra-high-pressure mercury-vapor arc lamp: rated, with reflector for projectors	30–50[35]	4.4–7.3%
Fluorescent	very low pressure mercury-vapor gas-discharge lamp with fluorescence as T12 tube with magnetic ballast	60[36]	9%
	9–32 W compact fluorescent (with ballast)	46–75[16][37][38]	8–11.45%[39]
	T8 tube with electronic ballast	80–100[36]	12–15%
	PL-S 11 W U-tube, excluding ballast loss	82[40]	12%
	T5 tube	70–104.2[41][42]	10–15.63%
	70-150W Inductively Coupled Electrodeless Lighting System	71-84[43]	10-12%
Gas discharge	1400 W sulfur lamp	100[44]	15%
	metal halide lamp	65–115[45]	9.5–17%
	high pressure sodium lamp	85–150[16]	12–22%
	low pressure sodium lamp	100–200[16][46][47]	15–29%
	Plasma display panel	2-10[48]	0.3–1.5%
Cathodoluminescence	electron stimulated luminescence	30	5%
Ideal sources	Truncated 5800 K blackbody[note 3]	251[7]	37%
	Green light at 555 nm (maximum possible luminous efficacy)	683.002[11]	100%

Sources that depend on thermal emission from a solid filament, such as incandescent light bulbs, tend to have low overall efficacy 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. No substance 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.”^[20] At temperatures where the tungsten filament of an ordinary light bulb remains solid (below 3683 kelvins), most of its emission is in the infrared.^[20]

SI photometry units

SI photometry quantities

Quantity		Unit		Dimension	Notes
Name	Symbol[nb 1]	Name	Symbol	Symbol
Luminous energy	Qv [nb 2]	lumen second	lm⋅s	T⋅J [nb 3]	Units are sometimes called talbots.
Luminous flux / luminous power	Φv [nb 2]	lumen (= cd⋅sr)	lm	J [nb 3]	Luminous energy per unit time.
Luminous intensity	Iv	candela (= lm/sr)	cd	J [nb 3]	Luminous power per unit solid angle.
Luminance	Lv	candela per square metre	cd/m^2	L^−2⋅J	Luminous power per unit solid angle per unit projected source area. Units are sometimes called nits.
Illuminance	Ev	lux (= lm/m^2)	lx	L^−2⋅J	Luminous power incident on a surface.
Luminous exitance / luminous emittance	Mv	lux	lx	L^−2⋅J	Luminous power emitted from a surface.
Luminous exposure	Hv	lux second	lx⋅s	L^−2⋅T⋅J
Luminous energy density	ωv	lumen second per cubic metre	lm⋅s⋅m^−3	L^−3⋅T⋅J
Luminous efficacy	η [nb 2]	lumen per watt	lm/W	M^−1⋅L^−2⋅T^3⋅J	Ratio of luminous flux to radiant flux or power consumption, depending on context.
Luminous efficiency / luminous coefficient	V			1
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. For example: USA Standard Letter Symbols for Illuminating Engineering USAS Z7.1-1967, Y10.18-1967
2. Alternative symbols sometimes seen: W for luminous energy, P or F for luminous flux, and ρ or K for luminous efficacy.
3. "J" here is the symbol for the dimension of luminous intensity, not the symbol for the unit joules.

See also

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

Notes

1. Defined such that the maximum value possible is 100%.
2. most efficient source you can do that mimics solar spectrum only within range of visual sensitivity
3. Integral of truncated Planck function times photopic luminosity function times 683 W/sr, according to the definition of the candela.
4. Truncates the very poor sensitivity (≤2% of the peak) and as such insignificant parts of the visible spectrum
5. Truncates the very poor sensitivity (≤5% of the peak) and as such insignificant parts of the visible spectrum
6. 1 candela*4π steradians/40 W

References

1. Allen Stimson (1974). Photometry and Radiometry for Engineers. New York: Wiley and Son.
2. Franc Grum, Richard Becherer (1979). Optical Radiation Measurements, Vol 1. New York: Academic Press.
3. Robert Boyd (1983). Radiometry and the Detection of Optical Radiation. New York: Wiley and Son.
4. Roger A. Messenger; Jerry Ventre (2004). Photovoltaic systems engineering (2 ed.). CRC Press. p. 123. ISBN 978-0-8493-1793-4.
5. Erik Reinhard, Erum Arif Khan, Ahmet Oğuz Akyüz, Garrett Johnson (2008). Color imaging: fundamentals and applications. A K Peters, Ltd. p. 338. ISBN 978-1-56881-344-8.
6. Van Nostrand's Scientific Encyclopedia, 3rd Edition. Princeton, New Jersey, Toronto, London, New York: D. Van Nostrand Company, Inc. January 1958.
7. "Maximum Efficiency of White Light" (PDF). Retrieved 2011-07-31.
8. Black body visible spectrum
9. Murphy, Thomas W. (2012). "Maximum spectral luminous efficacy of white light". Journal of Applied Physics 111 (10): 104909. doi:10.1063/1.4721897.
10. Murphy Jr, T. W. (2013). "Maximum Spectral Luminous Efficacy of White Light". Journal of Applied Physics 111 (10): 104909. arXiv:1309.7039. doi:10.1063/1.4721897.
11. 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.
12. Kohei Narisada; Duco Schreuder (2004). Light Pollution Handbook. Springer. ISBN 1-4020-2665-X.
13. Casimer DeCusatis (1998). Handbook of Applied Photometry. Springer. ISBN 1-56396-416-3.
14. Westermaier, F. V. (1920). "Recent Developments in Gas Street Lighting". The American City (New York: Civic Press) 22 (5): 490.
15. "Bulbs: Gluehbirne.ch: Philips Standard Lamps (German)". Bulbs.ch. Retrieved 2013-05-17.
16. Philips Product Catalog (German) Archived July 15, 2011, at the Wayback Machine.
17. "Osram halogen" (PDF). osram.de (in German). Archived from the original (PDF) on November 7, 2007. Retrieved 2008-01-28.
18. Keefe, T.J. (2007). "The Nature of Light". Archived from the original on 2012-01-18. Retrieved 2016-04-15.
19. "Osram 6406330 Miniwatt-Halogen 5.2V". bulbtronics.com. Retrieved 2013-04-16.
20. Klipstein, Donald L. (1996). "The Great Internet Light Bulb Book, Part I". Retrieved 2006-04-16.
21. "White LED Offers Broad Temp Range And Color Yield". Electronicdesign. 2001-04-02. Retrieved 2013-05-16.
22. "Nichia NSPWR70CSS-K1 specifications" (PDF). Nichia Corp. Retrieved 2013-05-16.
23. Klipstein, Donald L. "The Brightest and Most Efficient LEDs and where to get them". Don Klipstein's Web Site. Retrieved 2008-01-15.
24. "Cree XLamp XP-G LEDs Data Sheet" (PDF).
25. "Toshiba E-CORE LED Lamp". item.rakuten.com. Retrieved 2013-05-17.
26. "Toshiba E-CORE LED Lamp LDA5N-E17". Archived from the original on 2011-07-19.
27. "GE 73716 7-Watt Energy Smart PAR20 LED Light Bulb". Amazon.com. 2008-12-12. Retrieved 2013-05-17.
28. "Lite Gear LED PAR 30 7W Light Bulb". Bax-shop.nl. 2010-07-01. Retrieved 2013-05-17.
29. Toshiba to release 93 lm/W LED bulb Ledrevie
30. White LEDs with super-high luminous efficacy physorg.com
31. "Arc Lamps". Edison Tech Center. Retrieved 2015-08-20.
32. "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.
33. OSRAM Sylvania Lamp and Ballast Catalog. 2007.
34. REVIEW ARTICLE: UHP lamp systems for projection applications Journal of Physics D: Applied Physics
35. OSRAM P-VIP PROJECTOR LAMPS Osram
36. Federal Energy Management Program (December 2000). "How to buy an energy-efficient fluorescent tube lamp". U.S. Department of Energy.
37. "Low Mercury CFLs". Energy Federation Incorporated. Archived from the original on October 13, 2008. Retrieved 2008-12-23.
38. "Conventional CFLs". Energy Federation Incorporated. Archived from the original on October 14, 2008. Retrieved 2008-12-23.
39. "Global bulbs". 1000Bulbs.com accessdate=2010-2-20.|
40. Phillips. "Phillips Master". Retrieved 2010-12-21.
41. Department of the Environment, Water, Heritage and the Arts, Australia. "Energy Labelling—Lamps". Archived from the original on July 23, 2008. Retrieved 2008-08-14.
42. "BulbAmerica.com". Bulbamerica.com. Archived from the original on December 1, 2012. Retrieved 2010-02-20.
43. SYLVANIA. "SYLVANIA ICETRON® QUICKTRONIC® Design Guide" (PDF). Retrieved 2015-06-10.
44. "1000-watt sulfur lamp now ready". IAEEL newsletter (1) (IAEEL). 1996. Archived from the original on 2003-08-18.
45. "The Metal Halide Advantage". Venture Lighting. 2007. Retrieved 2008-08-10.
46. "LED or Neon? A scientific comparison".
47. "Why is lightning coloured? (gas excitations)". webexhibits.org.
48. "Future Looks Bright for Plasma TVs" (PDF). Panasonic. 2007. Retrieved 2013-02-10.

External links

• Hyperphysics has these graphs of efficacy that do not quite comply with the standard definition
• Energy Efficient Light Bulbs
• Other Power