Luminous efficacy

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Luminous efficacy is a property of light sources, which indicates what portion of the emitted electromagnetic radiation is usable for human vision. It is the ratio of emitted luminous flux to radiant flux. Luminous efficacy is related to the overall efficiency of a light source for illumination, but the overall lighting efficiency also depends on how much of the input energy is converted into electromagnetic waves (whether visible or not).

The response of a typical human eye to light. The horizontal axis is wavelength in nm.
The response of a typical human eye to light. The horizontal axis is wavelength in nm.

Contents

[edit] Explanation

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 not specified, photopic conditions are generally assumed.

Luminous efficacy 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 does not contribute to the efficacy at all, because 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 has a maximum possible value of 683 lm/W, for the case of monochromatic light at a wavelength of 555 nm. Scotopic luminous efficacy reaches a maximum of 1700 lm/W for narrowband light of wavelength 507 nm.

[edit] Efficacy and efficiency

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, 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.

[edit] 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.[1] The luminosity coefficient is:

\frac{ \int^{\lambda = \infin}_{\lambda = 0} y_\lambda J_\lambda d\lambda } { \int^{\lambda = \infin}_{\lambda = 0} J_\lambda d\lambda }

where

yλ is the standard luminosity function
Jλ is the spectral power distribution of the radiant intensity

The luminous coefficient is unity for a narrow band of wavelengths at 555 nanometres.

[edit] Examples

Type
 		 Luminous efficacy
(lm/W)		 Luminous efficiency[2]
 
Class M star (Antares, Betelgeuse), 3000 K 30 4%
ideal black-body radiator at 4000 K 47.5 [3] 7.0%
Class G star (Sun, Capella), 5800 K 80 12%
natural sunlight 93 14%
ideal black-body radiator at 7000 K 95 [3] 14%
ideal white light source 242.5 [4] 35.5%
ideal monochromatic 555 nm source 683 [5] 100%

[edit] Lighting efficiency

Artificial light sources are usually evaluated in terms of a related quantity, the 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. 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, or simply the lighting efficiency.

The main difference between the regular and "overall" efficacies, is that the latter account for input energy that is lost as heat, or otherwise exits the source as something other than electromagnetic radiation. True luminous efficacy is a property of the radiation emitted by a source. Overall luminous efficacy is a property of the source as a whole.

[edit] Examples

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

Category
 		 Type
 		 Overall
luminous efficacy (lm/W)		 Overall
luminous efficiency[2]
Combustion candle 0.3 [6] 0.04%
Incandescent 5 W tungsten incandescent 5 0.7%
40 W tungsten incandescent 12.6 [7] 1.9%
100 W tungsten incandescent 17.5 [7] 2.6%
glass halogen 16 2.3%
quartz halogen 24 3.5%
high-temperature incandescent 35 [4] 5.1%
Fluorescent 5–24 W compact fluorescent 45–60 [8] 6.6%–8.8%
34 W fluorescent tube (T12) 50 7%
32 W fluorescent tube (T8) 60 9%
36 W fluorescent tube (T8) up to 93 up to 14%
28 W fluorescent tube (T5) 104 15.2%
Light-emitting diode white LED 26–70 [9][10] 3.8%–10.2%
white LED (prototypes) up to 150 [11][12][13] up to 22%
Arc lamp xenon arc lamp typ. 30–50; up to 150 [14] 4.4%–7.3%; to 22%
mercury-xenon arc lamp 50–55 [14] 7.3%–8.0%
Gas discharge high pressure sodium lamp 150 [15] 22%
low pressure sodium lamp 183 [15] up to 200 [16] 27%
1400 W sulfur lamp 100 15%
Theoretical maximum 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 efficiency [sic] 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."[4] At temperatures where the tungsten filament of an ordinary light bulb remains solid (below 3683 kelvin), most of its emission is in the infrared.

[edit] SI photometry units

[edit]

SI photometry units
Quantity Symbol SI unit Abbr. Notes
Luminous energy Qv lumen second lm·s units are sometimes called talbots
Luminous flux F lumen (= cd·sr) lm also called luminous power
Luminous intensity Iv candela (= lm/sr) cd an SI base unit
Luminance Lv candela per square metre cd/m2 units are sometimes called nits
Illuminance Ev lux (= lm/m2) lx Used for light incident on a surface
Luminous emittance Mv lux (= lm/m2) lx Used for light emitted from a surface
Luminous efficacy   lumen per watt lm/W ratio of luminous flux to radiant flux; maximum possible is 683.002


[edit] See also

[edit] References

  1. ^ (January 1958) Van Nostrand's Scientific Encyclopedia, 3rd Edition. Princeton, New Jersey, Toronto, London, New York: D. Van Nostrand Company, Inc.. 
  2. ^ a b Defined such that the maximum value possible is 100%.
  3. ^ a b Black body visible spectrum
  4. ^ a b c Klipstein, Donald L. (1996). The Great Internet Light Bulb Book, Part I. Retrieved on 2006-04-16.
  5. ^ See luminosity function.
  6. ^ 1 candela*4π steradians/40 W
  7. ^ a b http://physics.ccri.cc.ri.us/keefe/light.htm. Retrieved on 2003-02-13. Referenced page is no longer available.
  8. ^ China energy saving lamp. Retrieved on 2006-04-16.
  9. ^ Klipstein, Donald L.. The Brightest and Most Efficient LEDs and where to get them. Don Klipstein's Web Site. Retrieved on 2006-04-16.
  10. ^ Cree launches the new XLamp 7090 XR-E Series Power LED, the first 160-lumen LED!.
  11. ^ Improving White LED Efficiency Through Scattered Photon Extraction. Rensselaer Polytechnic Institute. Retrieved on 2006-04-19.
  12. ^ Cree Demonstrates 131 Lumens per Watt White LED. Cree, Inc. Press Release (2006-06-20). Retrieved on 2006-12-03.
  13. ^ Nichia Corp. claims white LED delivering 150 lumens/Watt efficiency. Nichia Corp. Press Release (2006-12-22). Retrieved on 2006-12-03.
  14. ^ a b Technical Information on Lamps. Optical Building Blocks. Retrieved on 2006-04-16.
  15. ^ a b LED or Neon? A scientific comparison.
  16. ^ Why is lightning coloured? (gas excitations).

[edit] External links

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