Luminous efficacy is the ratio of the total apparent power of a light source to its actual total power. In other words, it is the ratio of luminous flux to radiant flux.

Wavelengths of light outside of the visible spectrum aren't useful for illumination because they can't 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. Luminous efficacy measures the fraction of power which is useful for lighting.

One can distinguish photopic and scotopic luminous efficacy. Scotopic luminous efficacy reaches a maximum of 1700 lm/W for narrowband light of wavelength 507 nm. Photopic luminous efficacy has the maximum possible efficacy of 683 lm/W at a wavelength of 555 nm. The remainder of this article deals with photopic luminous efficacy.

Units

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In SI, luminous efficacy has the unit lumen per watt (lm/W). This is because it equals luminous flux divided by radiant flux. In some other systems of units, luminous flux has the same units as radiant flux. The luminous efficacy is then dimensionless. In this case, it is often instead called the luminous efficiency or luminous coefficient and may be expressed as a percent. For example, it is common to express the luminous efficiency in units where the maximum possible efficacy, 638 lm/W, corresponds to an efficiency of 100%.

Mathematical definition

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The dimensionless luminous coefficient or 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 luminosity coefficient is:

$\backslash frac\{\; \backslash int^\{\backslash lambda\; =\; \backslash infin\}\_\{\backslash lambda\; =\; 0\}\; y\_\backslash lambda\; J\_\backslash lambda\; d\backslash lambda\; \}\; \{\; \backslash int^\{\backslash lambda\; =\; \backslash infin\}\_\{\backslash lambda\; =\; 0\}\; J\_\backslash lambda\; d\backslash lambda\; \}$

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.

Examples

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Type	Luminous efficacy (lm/W)	Luminous efficiencyDefined such that the maximum value possible is 100%.
ideal black-body radiator at 4000 K	47.5 Bild:Blackbodyvisiblerp.png	7.0%
ideal black-body radiator at 7000 K	95	14%
ideal white light source	242.5	35.5%
ideal monochromatic 555 nm source	683 See luminosity function.	100%

Overall luminous efficacy

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A related quantity is the overall luminous efficacy, which is the ratio between the total luminous flux emitted by a device and the total electrical power consumed by it. This is often simply called "luminous efficacy", which can be confusing as it also has units of lm/W. 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.

Examples

The following table lists overall luminous efficacy and efficiency for various light sources:

Category	Type	Overall luminous efficacy (lm/W)	Overall luminous efficiencyDefined such that the maximum value possible is 100%.
Combustion	candle	0.3 1 candela*4π steradians/40 W	0.04%
Incandescent	40 W tungsten incandescent	12.6 Referenced page is no longer available.	1.9%
	100 W tungsten incandescent	17.5	2.6%
	glass halogen	16	2.3%
	quartz halogen	24	3.5%
	high-temperature incandescent	35	5.1%
Fluorescent	13 W twin-tube fluorescent	56.3	8.2%
	compact fluorescent	45-60	6.6%-8.8%
Light-emitting diode	white LED	26-50	3.8%-7.3%
	white LED (prototypes)	up to 131	up to 19%
Arc lamp	xenon arc lamp	30-150	4.4%-22%
	mercury-xenon arc lamp	50-55	7.3%-8.0%
Gas discharge	high pressure sodium lamp	150	22%
	low pressure sodium lamp	183	27%

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 efficiency ^* 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 kelvin), most of its emission is in the infrared.

SI photometry units

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See also

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• Luminous coefficient
• Photometry

References

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External links

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• Hyperphysics has these graphs of efficacy that do not quite comply with the standard definition

Photometry | Physical quantity

発光効率