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, 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.^[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,^[4] and the latter luminous efficacy of a light source^[5] or overall luminous efficacy.^[6][7]

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

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

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

Explanation

The typical response of human vision to light under daytime or bright conditions, as standardized by the CIE in 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 the luminous flux by the radiant flux.^[4] Light wavelengths outside the visible spectrum reduce 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.

Wavelengths of light outside of the visible spectrum are 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 the luminous efficiency function. This is a standardized function representing photopic vision, which models the response of the eye's cone cells, that are active under typical daylight conditions. A separate curve can be defined for dark/night conditions, modeling the response of rod cells without cones, known as scotopic vision. (Mesopic vision describes 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 of 683.002 lm/W, for the case of monochromatic light at a wavelength of 555 nm  .^{[note 2]} Scotopic luminous efficacy of radiation reaches a maximum of 1700 lm/W for monochromatic light at a wavelength of 507 nm.^{[note 3]}

Mathematical definition

Luminous efficacy (of radiation), denoted K, is defined as^[4]

${\displaystyle K={\frac {\Phi _{\mathrm {v} }}{\Phi _{\mathrm {e} }}}={\frac {\int _{0}^{\infty }K(\lambda )\Phi _{\mathrm {e} ,\lambda }\,\mathrm {d} \lambda }{\int _{0}^{\infty }\Phi _{\mathrm {e} ,\lambda }\,\mathrm {d} \lambda }},}$

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[note 4]
Tungsten light bulb, typical, 2800 K	15[9]	2%
Class M star (Antares, Betelgeuse), 3300 K	30	4%
Black body, 4000 K, ideal	54.7[note 5]	8%
Class G star (Sun, Capella), 5800 K	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]	37%
Black-body, 5800 K, truncated to ≥ 2% photopic sensitivity range[note 8]	292[9]	43%
Black-body, 2800 K, truncated to ≥ 2% photopic sensitivity range[note 8]	299[9]	44%
Black-body, 2800 K, truncated to ≥ 5% photopic sensitivity range[note 9]	343[9]	50%
Black-body, 5800 K, truncated to ≥ 5% photopic sensitivity range[note 9]	348[9]	51%
Monochromatic source at 540 THz	683 (exact)	99.9997%
Ideal monochromatic source: 555 nm (in air)	683.002[10]	100%

Scotopic vision

Type	Luminous efficacy of radiation (lm/W)	Luminous efficiency[note 4]
Ideal monochromatic 507 nm source	1699[11] or 1700[12]	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[note 4]
Combustion	Gas mantle	1–2[13]	0.15–0.3%
Incandescent	15, 40, 100 W tungsten incandescent (230 V)	8.0, 10.4, 13.8[14][15][16][17]	1.2, 1.5, 2.0%
	5, 40, 100 W tungsten incandescent (120 V)	5.0, 12.6, 17.5[18]	0.7, 1.8, 2.6%
Halogen incandescent	100, 200, 500 W tungsten halogen (230 V)	16.7, 17.6, 19.8[19][17]	2.4, 2.6, 2.9%
	2.6 W tungsten halogen (5.2 V)	19.2[20]	2.8%
	Halogen-IR (120 V)	17.7–24.5[21]	2.6–3.5%
	Tungsten quartz halogen (12–24 V)	24	3.5%
	Photographic and projection lamps	35[22]	5.1%
Light-emitting diode	LED screw base lamp (120 V)	102[23][24][25]	14.9%
	5–16 W LED screw base lamp (230 V)	75–217[26][27][28][29]	11–32%
	21.5 W LED retrofit for T8 fluorescent tube (230 V)	172[30]	25%
	Theoretical limit for a white LED with phosphorescence color mixing	260–300[31]	38.1–43.9%
Arc lamp	Carbon arc lamp	2–7[32]	0.29–1.0%
	Xenon arc lamp	30–90[33][34][35]	4.4–13.5%
	Mercury-xenon arc lamp	50–55[33]	7.3–8%
	Ultra-high-pressure (UHP) mercury-vapor arc lamp, free mounted	58–78[36]	8.5–11.4%
	Ultra-high-pressure (UHP) mercury-vapor arc lamp, with reflector for projectors	30–50[37]	4.4–7.3%
Fluorescent	32 W T12 tube with magnetic ballast	60[38]	9%
	9–32 W compact fluorescent (with ballast)	46–75[17][39][40]	8–11.45%[41]
	T8 tube with electronic ballast	80–100[38]	12–15%
	PL-S 11 W U-tube, excluding ballast loss	82[42]	12%
	T5 tube	70–104.2[43][44]	10–15.63%
	70–150 W inductively-coupled electrodeless lighting system	71–84[45]	10–12%
Gas discharge	1400 W sulfur lamp	100[46]	15%
	Metal-halide lamp	65–115[47]	9.5–17%
	High-pressure sodium lamp	85–150[17]	12–22%
	Low-pressure sodium lamp	100–200[17][48][49][50]	15–29%
	Plasma display panel	2–10[51]	0.3–1.5%
Cathodoluminescence	Electron-stimulated luminescence	30–110[52][53]	15%
Ideal sources	Truncated 5800 K black-body[note 7]	251[9]	37%
	Green light at 555 nm (maximum possible luminous efficacy by definition)	683.002[10][54]	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."^[22] At temperatures where the tungsten filament of an ordinary light bulb remains solid (below 3683 kelvin), most of its emission is in the infrared.^[22]

SI photometry units

SI photometry quantities

• v
• t
• e

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: SI Photometry Radiometry

1. 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.
2. 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
3. Alternative symbols sometimes seen: W for luminous energy, P or F for luminous flux, and ρ for luminous efficacy of a source.

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)

Notes

1. There are special cases of illumination involving wavelengths of light that are outside the human visible range. One example is Ultraviolet light which 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 perceives 555 nm as a hue of yellowish-green  , which can be emulated on an sRGB display with CSS color value rgb(120,255,0) or hex #78ff00.
3. Under standard photopic vision 507 nm is perceived as a blue-green hue similar to viridian  , however scotopic rod-only vision does not create a color sensation in the standard human vision system.
4. Defined such that the maximum possible luminous efficacy corresponds to a luminous efficiency of 100%.
5. Black body visible spectrum
6. Most efficient source that mimics the solar spectrum within range of human visual sensitivity.
7. Integral of truncated Planck function times photopic luminosity function times 683.002 lm/W.
8. Omits the part of the spectrum where the eye's sensitivity is very poor.
9. Omits the part of the spectrum where the eye's sensitivity is low (≤ 5% of the peak).