Luminous efficacy

Luminous efficacy is a figure of merit for light sources. It is the ratio of luminous flux (in lumens) to power (usually measured in watts). As most commonly used, it is the ratio of luminous flux emitted from a light source to the electric power consumed by the source, and thus describes how well the source provides visible light from a given amount of electricity. This is also referred to as luminous efficacy of a source.

The term luminous efficacy can also refer to luminous efficacy of radiation (LER), which is the ratio of emitted luminous flux to radiant flux. Luminous efficacy of radiation is a characteristic of a given spectrum that describes how sensitive the human eye is to the mix of wavelengths involved. Which sense of the term is intended must usually be inferred from the context, and is sometimes unclear. The luminous efficacy of a source is the LER of its emission spectrum times the conversion efficiency from electrical energy to electromagnetic radiation.

Efficacy and efficiency

In some other 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 or luminous coefficient 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.

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 LER, 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. The luminous coefficient is

${\frac {\int _{0}^{\infty }y_{\lambda }J_{\lambda }d\lambda }{\int _{0}^{\infty }J_{\lambda }d\lambda }},$

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 $\int _{0}^{\infty }y_{\lambda }J_{\lambda }d\lambda$ is an inner product between $y_{\lambda }$ and $J_{\lambda }$ and that $\int _{0}^{\infty }J_{\lambda }d\lambda$ is the one-norm of $J_{\lambda }$.

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
Class M star (Antares, Betelgeuse), 3000 K	30	4%
ideal black-body radiator at 4000 K	47.5	7.0%
Class G star (Sun, Capella), 5800 K	80	12%
natural sunlight	93	14%
ideal black-body radiator at 7000 K	95	14%
5800 K clone, truncated to 400–700 nm (ideal "white" source)	251	37%
ideal monochromatic 555 nm source	683	100%

Lighting efficiency

Artificial light sources are usually evaluated in terms 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
Combustion	candle	0.3	0.04%
	gas mantle	1–2	0.15–0.3%
Incandescent	100 W tungsten incandescent (220 V)	13.8	2.0%
	200 W tungsten incandescent (220 V)	15.2	2.2%
	100 W tungsten glass halogen (220 V)	16.7	2.4%
	200 W tungsten glass halogen (220 V)	17.6	2.6%
	500 W tungsten glass halogen (220 V)	19.8	2.9%
	5 W tungsten incandescent (120 V)	5	0.7%
	40 W tungsten incandescent (120 V)	12.6	1.9%
	100 W tungsten incandescent (120 V)	17.5	2.6%
	2.6 W tungsten glass halogen (5.2 V)	19.2	2.8%
	tungsten quartz halogen (12–24 V)	24	3.5%
	photographic and projection lamps	35	5.1%
Light-emitting diode	white LED	10–150	1.5–22%
Arc lamp	xenon arc lamp	30–50	4.4–7.3%
	mercury-xenon arc lamp	50–55	7.3–8.0%
Fluorescent	9–26 W compact fluorescent	46–72	8–11%
	T12 tube with magnetic ballast	60	9%
	T5 tube	70–100	10–15%
	T8 tube with electronic ballast	80–100	12–15%
Gas discharge	1400 W sulfur lamp	100	15%
	170 W electrodeless lamp	100–120	15–18%
	metal halide lamp	65–115	9.5–17%
	high pressure sodium lamp	85–150	12–22%
	low pressure sodium lamp	100–200	15–29%
Ideal white light	Mimics sun from 400–700 nm	251	37%
Theoretical maximum	Green light at 555 nm	683.002	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.” At temperatures where the tungsten filament of an ordinary light bulb remains solid (below 3683 kelvins), most of its emission is in the infrared.

SI photometry units

SI photometry quantities

Quantity		Unit		Dimension	Notes
Name	Symbol	Name	Symbol
Luminous energy	Qv	lumen second	lm⋅s	T⋅J	The lumen second is sometimes called the talbot.
Luminous flux, luminous power	Φv	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	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

• Luminous coefficient
• Photometry
• Light pollution
• Wall-plug efficiency - a related principle, but slightly different

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