Luminous efficacy

Luminous efficacy
Common symbols	K
SI unit	lm⋅W−1
In SI base units	cd⋅s3⋅kg−1⋅m−2
Dimension	<math>\mathsf J \mathsf{T}^{3} \mathsf{M}^{-1} \mathsf{L}^{-2}</math>

Luminous efficacy is a measure of how well a light source produces visible light. It is the ratio of luminous flux to power, measured in lumens per watt in the International System of Units (SI). 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.<ref>Allen Stimson (1974). Photometry and Radiometry for Engineers. New York: Wiley and Son. Bibcode:1974wi...book.....S.</ref><ref>Franc Grum; Richard Becherer (1979). Optical Radiation Measurements, Vol 1. New York: Academic Press.</ref><ref>Robert Boyd (1983). Radiometry and the Detection of Optical Radiation. New York: Wiley and Son.</ref> 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,<ref name="IEC_845-21-090">International Electrotechnical Commission (IEC): International Electrotechnical Vocabulary, ref. 845-21-090, Luminous efficacy of radiation (for a specified photometric condition)</ref> and the latter luminous efficacy of a light source<ref name="IEC_845-21-089">International Electrotechnical Commission (IEC): International Electrotechnical Vocabulary, ref. 845-21-089, Luminous efficacy (of a light source)</ref> or overall luminous efficacy.<ref>Roger A. Messenger; Jerry Ventre (2004). Photovoltaic systems engineering (2 ed.). CRC Press. p. 123. ISBN 978-0-8493-1793-4.</ref><ref>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.</ref>

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 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

Luminous efficacy can be normalized by the maximum possible luminous efficacy to a dimensionless quantity called luminous efficiency. 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.

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 nanometers.<ref>ISO (2005). ISO 23539:2005 Photometry — The CIE system of physical photometry (Report). Retrieved 2022-01-05.</ref>

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.<ref name="IEC_845-21-090" /> 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.

Photopic luminous efficacy of radiation has a maximum possible value of 683.002 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 monochromatic light at a wavelength of 507 nm.

Mathematical definition

Luminous efficacy (of radiation), denoted K, is defined as<ref name="IEC_845-21-090" />

<math>K = \frac{\Phi_\mathrm{v}}{\Phi_\mathrm{e}} = \frac{\int_0^\infty K(\lambda) \Phi_{\mathrm{e},\lambda}\,\mathrm{d}\lambda}{\int_0^\infty \Phi_{\mathrm{e},\lambda}\,\mathrm{d}\lambda},</math>

where

• Φ_v is the luminous flux;
• Φ_e is the radiant flux;
• Φ_e,λ is the spectral radiant flux;
• K(λ) = K_mV(λ) is the spectral luminous efficacy.

Examples

Photopic vision

Type	Luminous efficacy of radiation (lm/W)	Luminous efficiency<ref name="max" group="note">Defined such that the maximum possible luminous efficacy corresponds to a luminous efficiency of 100%.</ref>
Tungsten light bulb, typical, 2800 K	15<ref name="ideal-white">"Maximum Efficiency of White Light" (PDF). Retrieved 2011-07-31.</ref>	2%
Class M star (Antares, Betelgeuse), 3300 K	30	4%
Black body, 4000 K, ideal	54.7<ref name="blackbody" group="note">Black body visible spectrum</ref>	8%
Class G star (Sun, Capella), 5800 K	93<ref name="ideal-white" />	13.6%
Black-body, 7000 K, ideal	95<ref name="blackbody" group="note"></ref>	14%
Black-body, 5800 K, truncated to 400–700 nm (ideal "white" source)<ref group="note">Most efficient source that mimics the solar spectrum within range of human visual sensitivity.</ref>	251<ref name="ideal-white" /><ref name="ideal_white" group="note">Integral of truncated Planck function times photopic luminosity function times 683.002 lm/W.</ref><ref name="max-eff-truncated-1" />	37%
Black-body, 5800 K, truncated to ≥ 2% photopic sensitivity range<ref name="max-eff-truncated" group="note">Omits the part of the spectrum where the eye's sensitivity is very poor.</ref>	292<ref name="max-eff-truncated-1"> Murphy, Thomas W. (2012). "Maximum spectral luminous efficacy of white light". Journal of Applied Physics. 111 (10): 104909–104909–6. arXiv:1309.7039. Bibcode:2012JAP...111j4909M. doi:10.1063/1.4721897. S2CID 6543030.</ref>	43%
Black-body, 2800 K, truncated to ≥ 2% photopic sensitivity range<ref name="max-eff-truncated" group="note"></ref>	299<ref name="max-eff-truncated-1" />	44%
Black-body, 2800 K, truncated to ≥ 5% photopic sensitivity range<ref name="max-eff-truncated-1" group="note">Omits the part of the spectrum where the eye's sensitivity is low (≤ 5% of the peak).</ref>	343<ref name="max-eff-truncated-1" />	50%
Black-body, 5800 K, truncated to ≥ 5% photopic sensitivity range<ref name="max-eff-truncated-1" group="note"></ref>	348<ref name="max-eff-truncated-1" />	51%
Ideal monochromatic source: 555 nm	683.002<ref name=SI-statement> "BIPM statement: Information for users about the proposed revision of the SI" (PDF). Archived (PDF) from the original on 21 January 2018. Retrieved 5 May 2018. </ref>	100%

Scotopic vision

Type	Luminous efficacy of radiation (lm/W)	Luminous efficiency<ref name="max" group="note"></ref>
Ideal monochromatic 507 nm source	1699<ref name="Kohei20042">Kohei Narisada; Duco Schreuder (2004). Light Pollution Handbook. Springer. ISBN 1-4020-2665-X.</ref> or 1700<ref name="Casimer19982">Casimer DeCusatis (1998). Handbook of Applied Photometry. Springer. ISBN 1-56396-416-3.</ref>	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

Main article: Wall-plug efficiency

Artificial light sources are usually evaluated in terms of luminous efficacy of the source, also sometimes called wall-plug 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. The luminous efficacy of the source 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 luminous efficiency of a source, overall luminous efficiency or 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<ref name="max" group="note"></ref>
Combustion	Gas mantle	1–2<ref>Westermaier, F. V. (1920). "Recent Developments in Gas Street Lighting". The American City. New York: Civic Press. 22 (5): 490.</ref>	0.15–0.3%
Incandescent	15, 40, 100 W tungsten incandescent (230 V)	8.0, 10.4, 13.8<ref>"Philips Classictone Standard 15 W clear".</ref><ref>"Philips Classictone Standard 40 W clear".</ref><ref>"Bulbs: Gluehbirne.ch: Philips Standard Lamps (German)". Bulbs.ch. Retrieved 2013-05-17.</ref><ref name="philc">Philips Product Catalog (German)</ref>	1.2, 1.5, 2.0%
	5, 40, 100 W tungsten incandescent (120 V)	5.0, 12.6, 17.5<ref name="incandescent">Keefe, T.J. (2007). "The Nature of Light". Archived from the original on 2012-01-18. Retrieved 2016-04-15.</ref>	0.7, 1.8, 2.6%
Halogen incandescent	100, 200, 500 W tungsten halogen (230 V)	16.7, 17.6, 19.8<ref>"Osram halogen" (PDF). osram.de (in Deutsch). Archived from the original (PDF) on November 7, 2007. Retrieved 2008-01-28.</ref><ref name="philc" />	2.4, 2.6, 2.9%
	2.6 W tungsten halogen (5.2 V)	19.2<ref>"Osram 6406330 Miniwatt-Halogen 5.2V". bulbtronics.com. Archived from the original on 2016-02-13. Retrieved 2013-04-16.</ref>	2.8%
	Halogen-IR (120 V)	17.7–24.5<ref>"GE Lighting HIR Plus Halogen PAR38s" (PDF). ge.com. Retrieved 2017-11-01.</ref>	2.6–3.5%
	Tungsten quartz halogen (12–24 V)	24	3.5%
	Photographic and projection lamps	35<ref name="bulbguide">Klipstein, Donald L. (1996). "The Great Internet Light Bulb Book, Part I". Archived from the original on 2001-09-09. Retrieved 2006-04-16.</ref>	5.1%
Light-emitting diode	LED screw base lamp (120 V)	102<ref name="Toshiba-LED">"Toshiba E-CORE LED Lamp". item.rakuten.com. Retrieved 2013-05-17.</ref><ref name="Toshiba-LED LDA5N-E17">"Toshiba E-CORE LED Lamp LDA5N-E17". Archived from the original on 2011-07-19.</ref><ref>Toshiba to release 93 lm/W LED bulb Ledrevie</ref>	14.9%
	5–16 W LED screw base lamp (230 V)	null"]. www.lighting.philips.co.uk. Retrieved 2021-09-26.</ref>	11–30%
	21.5 W LED retrofit for T8 fluorescent tube (230 V)	172<ref>"MAS LEDtube 1500mm UE 21.5W 840 T8". Retrieved 2018-01-10.</ref>	25%
	Theoretical limit for a white LED with phosphorescence color mixing	260–300<ref name="physorg.com_LED_efficacy">Zyga, Lisa (2010-08-31). "White LEDs with super-high luminous efficacy could satisfy all general lighting needs". Phys.org. Retrieved 17 November 2021.</ref>	38.1–43.9%
Arc lamp	Carbon arc lamp	2–7<ref name="carbon">"Arc Lamps". Edison Tech Center. Retrieved 2015-08-20.</ref>	0.29–1.0%
	Xenon arc lamp	OSRAM Automotive"]. www.osram.com. Retrieved 2021-09-30.</ref>	4.4–13.5%
	Mercury-xenon arc lamp	50–55<ref name="xenon" />	7.3–8%
	Ultra-high-pressure (UHP) mercury-vapor arc lamp, free mounted	58–78<ref>REVIEW ARTICLE: UHP lamp systems for projection applications Journal of Physics D: Applied Physics</ref>	8.5–11.4%
	Ultra-high-pressure (UHP) mercury-vapor arc lamp, with reflector for projectors	30–50<ref>OSRAM P-VIP PROJECTOR LAMPS Osram</ref>	4.4–7.3%
Fluorescent	32 W T12 tube with magnetic ballast	60<ref name=FEMP>Federal Energy Management Program (December 2000). "How to buy an energy-efficient fluorescent tube lamp". U.S. Department of Energy. Archived from the original on 2007-07-02. {{cite journal}}: Cite journal requires |journal= (help)</ref>	9%
	9–32 W compact fluorescent (with ballast)	46–75<ref name="philc" /><ref name="cf">"Low Mercury CFLs". Energy Federation Incorporated. Archived from the original on October 13, 2008. Retrieved 2008-12-23.</ref><ref>"Conventional CFLs". Energy Federation Incorporated. Archived from the original on October 14, 2008. Retrieved 2008-12-23.</ref>	</ref>
	T8 tube with electronic ballast	80–100<ref name=FEMP />	12–15%
	PL-S 11 W U-tube, excluding ballast loss	82<ref name="U-tubes">Phillips. "Phillips Master". Retrieved 2010-12-21.</ref>	12%
	T5 tube	70–104.2<ref name="energyrating">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.{{cite web}}: CS1 maint: multiple names: authors list (link)</ref><ref name="Plusrite">"BulbAmerica.com". Bulbamerica.com. Archived from the original on December 1, 2012. Retrieved 2010-02-20.</ref>	10–15.63%
	70–150 W inductively-coupled electrodeless lighting system	71–84<ref name="ICETRON®">SYLVANIA. "Sylvania Icetron Quicktronic Design Guide" (PDF). Retrieved 2015-06-10.</ref>	10–12%
Gas discharge	1400 W sulfur lamp	100<ref>"1000-watt sulfur lamp now ready". IAEEL newsletter. No. 1. IAEEL. 1996. Archived from the original on 2003-08-18.</ref>	15%
	Metal-halide lamp	65–115<ref>"The Metal Halide Advantage". Venture Lighting. 2007. Archived from the original on 2012-02-15. Retrieved 2008-08-10.</ref>	9.5–17%
	High-pressure sodium lamp	85–150<ref name="philc" />	12–22%
	Low-pressure sodium lamp	100–200<ref name="philc" /><ref name="sodium">"LED or Neon? A scientific comparison".</ref><ref name="lightning">"Why is lightning coloured? (gas excitations)". webexhibits.org.</ref><ref>Hooker, J.D. (1997). "The low-pressure sodium lamp". IEEE Conference Record - Abstracts. 1997 IEEE International Conference on Plasma Science. p. 289. doi:10.1109/PLASMA.1997.605090. ISBN 0-7803-3990-8. S2CID 102792535.</ref>	15–29%
	Plasma display panel	2–10<ref>"Future Looks Bright for Plasma TVs" (PDF). Panasonic. 2007. Retrieved 2013-02-10.</ref>	0.3–1.5%
Cathodoluminescence	Electron-stimulated luminescence	30–110<ref>"TV-Tube Technology Builds an Efficient Light Bulb". OSA. 2019. Retrieved 2020-09-12.</ref><ref>Sheshin, Evgenii P.; Kolodyazhnyj, Artem Yu.; Chadaev, Nikolai N.; Getman, Alexandr O.; Danilkin, Mikhail I.; Ozol, Dmitry I. (2019). "Prototype of cathodoluminescent lamp for general lighting using carbon fiber field emission cathode". Journal of Vacuum Science & Technology B. AVS. 37 (3): 031213. Bibcode:2019JVSTB..37c1213S. doi:10.1116/1.5070108. S2CID 155496503. Retrieved 2020-09-12.</ref>	15%
Ideal sources	Truncated 5800 K black-body<ref name="ideal_white" group="note"></ref>	251<ref name="ideal-white" />	37%
	Green light at 555 nm (maximum possible luminous efficacy by definition)	683.002<ref name=SI-statement/><ref>Choudhury, Asim Kumar Roy (2014). "Characteristics of light sources: luminous efficacy of lamps". Principles of Colour and Appearance Measurement: Object appearance, colour perception and instrumental measurement. Vol. 1. Woodhead Publishing. p. 41. doi:10.1533/9780857099242.1. ISBN 978-0-85709-229-8. If the lamp emits all radiation at 555 nm (where Vλ = 1), the luminous efficacy will be of about 680 lm W−1, the theoretical maximum value. The lamp efficacy will be 26 and 73 lm W−1, when the whole light is emitted at 450 and 650 nm respectively. The luminous coefficient is luminous efficiency expressed as a value between zero and one, with one corresponding to an efficacy of 683 lm W−1.</ref>	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."<ref name="bulbguide" /> At temperatures where the tungsten filament of an ordinary light bulb remains solid (below 3683 kelvin), most of its emission is in the infrared.<ref name="bulbguide" />

SI photometry units

SI photometry quantities

Quantity		Unit		Dimension <ref group="nb" name="note-dimension-symbol">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.</ref>	Notes
Name	Symbol<ref group="nb" name="note-suffix-v">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</ref>	Name	Symbol
Luminous energy	Qv<ref group="nb" name="note-alternative-symbol-photometric">Alternative symbols sometimes seen: W for luminous energy, P or F for luminous flux, and ρ for luminous efficacy of a source.</ref>	lumen second	lm⋅s	T⋅J	The lumen second is sometimes called the talbot.
Luminous flux, luminous power	Φv<ref group="nb" name="note-alternative-symbol-photometric"></ref>	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<ref group="nb" name="note-alternative-symbol-photometric"></ref>	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

See also

• Photometry
• Light pollution
• Wall-plug efficiency
• Coefficient of utilization
• List of light sources
• SI defining constants, including K_cd (used in the definition of candela)

External links

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