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. 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 light source or overall luminous efficacy.

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.

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 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 illuminationTemplate:Efn. 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 Template:Nowrap, for the case of monochromatic light at a wavelength of Template:Nowrap Template:Colorsample.Template:Efn Scotopic luminous efficacy of radiation reaches a maximum of Template:Nowrap for monochromatic light at a wavelength of Template:Nowrap.Template:Efn

Mathematical definition

Luminous efficacy (of radiation), denoted K, is defined as

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

where

• Φ_v is the luminous flux;
• Φ_e is the radiant flux;
• Φ_e,λ is the spectral radiant flux;
• Template:Nowrap is the spectral luminous efficacy.

Examples

Photopic vision

Type	Luminous efficacy of radiation (lm/W)	Luminous efficiencyTemplate:Efn
Tungsten light bulb, typical, 2800 K	15	2%
Class M star (Antares, Betelgeuse), [[color temperature|3300Template:NbspK]]	30	4%
Black body, 4000 K, ideal	54.7Template:Efn	8%
Class G star (Sun, Capella), 5800Template:NbspK	93	13.6%
Black-body, 7000 K, ideal	95Template:Efn	14%
Black-body, 5800 K, truncated to 400–700 nm (ideal "white" source)Template:Efn	251Template:Efn	37%
Black-body, 5800 K, truncated to ≥ 2% photopic sensitivity rangeTemplate:Efn	292	43%
Black-body, 2800 K, truncated to ≥ 2% photopic sensitivity rangeTemplate:Efn	299	44%
Black-body, 2800 K, truncated to ≥ 5% photopic sensitivity rangeTemplate:Efn	343	50%
Black-body, 5800 K, truncated to ≥ 5% photopic sensitivity rangeTemplate:Efn	348	51%
Monochromatic source at Template:Val	683 (exact)	99.9997%
Ideal monochromatic source: Template:Val (in air)	683.002	100%

Scotopic vision

Type	Luminous efficacy of radiation (lm/W)	Luminous efficiencyTemplate:Efn
Ideal monochromatic 507 nm source	1699 or 1700	100%

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

Lighting efficiency

Template:Main 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 efficiencyTemplate:Efn
Combustion	Gas mantle	1–2	0.15–0.3%
Incandescent	15, 40, 100Template:NbspW tungsten incandescent (230 V)	8.0, 10.4, 13.8	1.2, 1.5, 2.0%
	5, 40, 100Template:NbspW tungsten incandescent (120 V)	5.0, 12.6, 17.5	0.7, 1.8, 2.6%
Halogen incandescent	100, 200, 500Template:NbspW tungsten halogen (230 V)	16.7, 17.6, 19.8	2.4, 2.6, 2.9%
	2.6Template:NbspW tungsten halogen (5.2 V)	19.2	2.8%
	Halogen-IR (120 V)	17.7–24.5	2.6–3.5%
	Tungsten quartz halogen (12–24 V)	24	3.5%
	Photographic and projection lamps	35	5.1%
Light-emitting diode	LED screw base lamp (120 V)	Template:Rnd	Template:Rnd%
	5–16Template:NbspW LED screw base lamp (230 V)	75–217	11–32%
	21.5Template:NbspW LED retrofit for T8 fluorescent tube (230Template:NbspV)	172	25%
	Theoretical limit for a white LED with phosphorescence color mixing	Template:Rnd–Template:Rnd	Template:Rnd–Template:Rnd%
Arc lamp	Carbon arc lamp	2–7	0.29–1.0%
	Xenon arc lamp	30–90	4.4–13.5%
	Mercury-xenon arc lamp	50–55	7.3–8%
	Ultra-high-pressure (UHP) mercury-vapor arc lamp, free mounted	58–78	8.5–11.4%
	Ultra-high-pressure (UHP) mercury-vapor arc lamp, with reflector for projectors	30–50	4.4–7.3%
Fluorescent	32Template:NbspW T12 tube with magnetic ballast	60	9%
	9–32Template:NbspW compact fluorescent (with ballast)	46–75	8–11.45%
	T8 tube with electronic ballast	80–100	12–15%
	PL-S 11Template:NbspW U-tube, excluding ballast loss	82	12%
	T5 tube	70–104.2	10–15.63%
	70–150Template:NbspW inductively-coupled electrodeless lighting system	71–84	10–12%
Gas discharge	1400Template:NbspW sulfur lamp	100	15%
	Metal-halide lamp	65–115	9.5–17%
	High-pressure sodium lamp	85–150	12–22%
	Low-pressure sodium lamp	100–200	15–29%
	Plasma display panel	2–10	0.3–1.5%
Cathodoluminescence	Electron-stimulated luminescence	30–110	15%
Ideal sources	Truncated 5800 K black-bodyTemplate:Efn	251	37%
	Green light at Template:Val (maximum possible luminous efficacy by definition)	683.002	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." At temperatures where the tungsten filament of an ordinary light bulb remains solid (below 3683 kelvin), most of its emission is in the infrared.

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