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Luminous efficacy

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Luminous efficacy
Common symbols
K
SI unitlm⋅W−1
InSI base unitscd⋅s3⋅kg−1⋅m−2
Dimension

Luminous efficacyis a measure of how well a light source produces visible light. It is the ratio ofluminous fluxtopower,measured inlumensperwattin theInternational System of Units(SI). Depending on context, the power can be either theradiant fluxof 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 calledluminous efficacy of radiation,[4]and the latterluminous efficacy of a light source[5]oroverall luminous efficacy.[6][7]

Not all wavelengths of light are equally visible, or equally effective at stimulating human vision, due to thespectral sensitivityof thehuman eye;radiation in theinfraredandultravioletparts 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

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Luminous efficacy can be normalized by the maximum possible luminous efficacy to adimensionlessquantity calledluminous efficiency.The distinction betweenefficacyandefficiencyis 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

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By definition, light outside the visible spectrum cannot be seen by thestandard human vision system,and therefore does not contribute to, and indeed can subtract from, luminous efficacy.

Explanation

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The typicalresponse of human vision to lightunder daytime or bright conditions, as standardized by theCIEin 1924. The horizontal axis is wavelength in nanometers.[8]

Luminous efficacy of radiation measures the fraction of electromagnetic power which is useful for lighting. It is obtained by dividing theluminous fluxby theradiant flux.[4]Light wavelengths outside thevisible spectrumreduce luminous efficacy, because they contribute 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.

Wavelengthsof light outside of thevisible spectrumare not useful for general illumination[note 1].Furthermore, human vision responds more to some wavelengths of light than others. This response of the eye is represented by theluminous efficiency function.This is a standardized function representingphotopic vision,which models the response of the eye'scone cells,that are active under typical daylight conditions. A separate curve can be defined for dark/night conditions, modeling the response ofrod cellswithoutcones, known asscotopic vision.(Mesopic visiondescribes the transition zone in dim conditions, between photopic and scotopic, where both cones and rods are active.)

Photopic luminous efficacy of radiation has a maximum possible value of683.002 lm/W,for the case of monochromatic light at a wavelength of555 nm .[note 2]Scotopic luminous efficacy of radiation reaches a maximum of1700 lm/Wfor monochromatic light at a wavelength of507 nm.[note 3]

Mathematical definition

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Luminous efficacy (of radiation),denotedK,is defined as[4]

where

Examples

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Photopic vision

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Type Luminous efficacy
of radiation (lm/W) 		Luminous
efficiency[note 4]
Tungsten light bulb, typical, 2800 K 15[9] 2%
Class M star (Antares,Betelgeuse),3300K 30 4%
Black body,4000 K, ideal 54.7[note 5] 8%
Class G star (Sun,Capella), 5800K 93[9] 13.6%
Black-body, 7000 K, ideal 95[note 5] 14%
Black-body, 5800 K, truncated to 400–700 nm (ideal "white" source)[note 6] 251[9][note 7][10] 37%
Black-body, 5800 K, truncated to ≥ 2% photopic sensitivity range[note 8] 292[10] 43%
Black-body, 2800 K, truncated to ≥ 2% photopic sensitivity range[note 8] 299[10] 44%
Black-body, 2800 K, truncated to ≥ 5% photopic sensitivity range[note 9] 343[10] 50%
Black-body, 5800 K, truncated to ≥ 5% photopic sensitivity range[note 9] 348[10] 51%
Monochromatic source at540 THz 683 (exact) 99.9997%
Ideal monochromatic source:555 nm(in air) 683.002[11] 100%

Scotopic vision

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Type Luminous efficacy

of radiation (lm/W)

Luminous

efficiency[note 4]

Ideal monochromatic 507 nm source 1699[12]or 1700[13] 100%
Spectral radianceof ablack body.Energy outside thevisible wavelengthrange (~380–750nm, shown by grey dotted lines) reduces the luminous efficiency.

Lighting efficiency

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Main article:Wall-plug efficiency

Artificial light sources are usually evaluated in terms of luminous efficacy of the source, also sometimes calledwall-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 calledluminous efficiency of a source,overall luminous efficiencyorlighting 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 asheator 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

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The following table lists luminous efficacy of a source and efficiency for various light sources. Note that all lamps requiringelectrical/electronic ballastare unless noted (see also voltage) listed withoutlossesfor that, reducing total efficiency.

Category Type Overall luminous
efficacy (lm/W) 		Overall luminous
efficiency[note 4]
Combustion Gas mantle 1–2[14] 0.15–0.3%
Incandescent 15, 40, 100W tungsten incandescent (230 V) 8.0, 10.4, 13.8[15][16][17][18] 1.2, 1.5, 2.0%
5, 40, 100W tungsten incandescent (120 V) 5.0, 12.6, 17.5[19] 0.7, 1.8, 2.6%
Halogen incandescent 100, 200, 500W tungsten halogen (230 V) 16.7, 17.6, 19.8[20][18] 2.4, 2.6, 2.9%
2.6W tungsten halogen (5.2 V) 19.2[21] 2.8%
Halogen-IR (120 V) 17.7–24.5[22] 2.6–3.5%
Tungsten quartz halogen (12–24 V) 24 3.5%
Photographic and projection lamps 35[23] 5.1%
Light-emitting diode LEDscrew baselamp (120 V) 102[24][25][26] 14.9%
5–16W LED screw base lamp (230 V) 75–217[27][28][29][30] 11–32%
21.5W LED retrofit for T8 fluorescent tube (230V) 172[31] 25%
Theoretical limit for a white LED with phosphorescence color mi xing 260–300[32] 38.1–43.9%
Arc lamp Carbon arc lamp 2–7[33] 0.29–1.0%
Xenon arc lamp 30–90[34][35][36] 4.4–13.5%
Mercury-xenonarc lamp 50–55[34] 7.3–8%
Ultra-high-pressure(UHP)mercury-vaporarc lamp, free mounted 58–78[37] 8.5–11.4%
Ultra-high-pressure (UHP) mercury-vapor arc lamp, with reflector forprojectors 30–50[38] 4.4–7.3%
Fluorescent 32W T12 tube with magnetic ballast 60[39] 9%
9–32Wcompact fluorescent(with ballast) 46–75[18][40][41] 8–11.45%[42]
T8 tube with electronic ballast 80–100[39] 12–15%
PL-S 11W U-tube, excluding ballast loss 82[43] 12%
T5 tube 70–104.2[44][45] 10–15.63%
70–150W inductively-coupled electrodeless lighting system 71–84[46] 10–12%
Gas discharge 1400Wsulfur lamp 100[47] 15%
Metal-halide lamp 65–115[48] 9.5–17%
High-pressure sodium lamp 85–150[18] 12–22%
Low-pressure sodium lamp 100–200[18][49][50][51] 15–29%
Plasma display panel 2–10[52] 0.3–1.5%
Cathodoluminescence Electron-stimulated luminescence 30–110[53][54] 15%
Ideal sources Truncated 5800 K black-body[note 7] 251[9] 37%
Green light at555 nm(maximum possible luminous efficacy by definition) 683.002[11][55] 100%

Sources that depend on thermal emission from a solid filament, such asincandescent 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. Thesurface of the sunis not quite that hot. "[23]At temperatures where thetungstenfilament of an ordinary light bulb remains solid (below 3683 kelvin), most of its emission is in theinfrared.[23]

SI photometry units

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SI photometry quantities
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 thetalbot.
Luminous flux,luminous power Φv[nb 3] lumen(= candelasteradian) lm (= cd⋅sr) J Luminous energy per unit time
Luminous intensity Iv candela(= lumen per steradian) cd(= lm/sr) J Luminous flux per unitsolid angle
Luminance Lv candela per square metre cd/m2(= lm/(sr⋅m2)) L−2⋅J Luminous flux per unit solid angle per unitprojectedsource area. The candela per square metre is sometimes called thenit.
Illuminance Ev lux(= lumen per square metre) lx(= lm/m2) L−2⋅J Luminous fluxincidenton a surface
Luminous exitance,luminous emittance Mv lumen per square metre lm/m2 L−2⋅J Luminous fluxemittedfrom 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 perwatt lm/W M−1⋅L−2⋅T3⋅J Ratio of luminous flux toradiant flux
Luminous efficacy(of a source) η[nb 3] lumen perwatt 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:
  1. ^The symbols in this column denotedimensions;"L","T"and"J"are for length, time and luminous intensity respectively, not the symbols for theunitslitre, tesla and joule.
  2. ^Standards organizationsrecommend that photometric quantities be denoted with a subscript "v" (for "visual" ) to avoid confusion with radiometric orphotonquantities. For example:USA Standard Letter Symbols for Illuminating EngineeringUSAS Z7.1-1967, Y10.18-1967
  3. ^abcAlternative symbols sometimes seen:Wfor luminous energy,PorFfor luminous flux, andρfor luminous efficacy of a source.

See also

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Notes

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  1. ^There are special cases of illumination involving wavelengths of light that are outside the human visible range. One example isUltraviolet lightwhich is not itself visible, but can excite some pigments to fluoresce, where the pigments re-emit the light into the visible range. Such special cases are not a contributing part of luminous efficacy calculations.
  2. ^Standard vision typically perceives555 nmas ahueof yellowish-green ,which can be emulated on ansRGBdisplay withCSScolor valuergb(120,255,0)or hex#78ff00.
  3. ^Under standard photopic vision507 nmis perceived as a blue-green hue similar toviridian ,however scotopic rod-only vision does not create a color sensation in the standard human vision system.
  4. ^abcDefined such that the maximum possible luminousefficacycorresponds to a luminousefficiencyof 100%.
  5. ^abBlack body visible spectrum
  6. ^Most efficient source that mimics the solar spectrum within range of human visual sensitivity.
  7. ^abIntegral of truncatedPlanck functiontimes photopicluminosity functiontimes 683.002 lm/W.
  8. ^abOmits the part of the spectrum where the eye's sensitivity is very poor.
  9. ^abOmits the part of the spectrum where the eye's sensitivity is low (≤ 5% of the peak).

References

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  3. ^Robert Boyd (1983).Radiometry and the Detection of Optical Radiation.New York: Wiley and Son.
  4. ^abcInternational Electrotechnical Commission (IEC):International Electrotechnical Vocabulary,ref. 845-21-090, Luminous efficacy of radiation (for a specified photometric condition)
  5. ^International Electrotechnical Commission (IEC):International Electrotechnical Vocabulary,ref. 845-21-089, Luminous efficacy (of a light source)
  6. ^Roger A. Messenger; Jerry Ventre (2004).Photovoltaic systems engineering(2 ed.). CRC Press. p.123.ISBN978-0-8493-1793-4.
  7. ^Erik Reinhard; Erum Arif Khan; Ahmet Oğuz Akyüz; Garrett Johnson (2008).Color imaging: fundamentals and applications.A K Peters, Ltd. p.338.ISBN978-1-56881-344-8.
  8. ^ISO (2005).ISO 23539:2005 Photometry — The CIE system of physical photometry(Report).Retrieved2022-01-05.
  9. ^abcd"Maximum Efficiency of White Light"(PDF).Retrieved2011-07-31.
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  54. ^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.37(3). AVS: 031213.Bibcode:2019JVSTB..37c1213S.doi:10.1116/1.5070108.S2CID155496503.Retrieved2020-09-12.
  55. ^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.ISBN978-0-85709-229-8.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.
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