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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 does at providing visible light while using little electricity.1 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.1

Contents

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.2 The luminous coefficient is

\frac{ \int^\infin_0 y_\lambda J_\lambda d\lambda } { \int^\infin_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.

Note that \int^\infin_0 y_\lambda J_\lambda d\lambda is an inner product between yλ and Jλ and that \int^\infin_0 J_\lambda d\lambda is the one-norm of Jλ.

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 efficiency3
 
Class M star (Antares, Betelgeuse), 3000 K 30 4%
ideal black-body radiator at 4000 K 47.5 4 7.0%
Class G star (Sun, Capella), 5800 K 80 12%
natural sunlight 93 14%
ideal black-body radiator at 7000 K 95 4 14%
ideal monochromatic 555 nm source 683 5 100%

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 efficiency3
Combustion candle 0.3 6 0.04%
gas mantle 2 7 0.3%
Incandescent 5 W tungsten incandescent (120 V) 5 0.7%
40 W tungsten incandescent (120 V) 12.6 8 1.9%
100 W tungsten incandescent (220 V) 13.8 9 2.0%
100 W tungsten glass halogen (220 V) 16.7 10 2.4%
100 W tungsten incandescent (120 V) 17.5 8 2.6%
2.6 W tungsten glass halogen (5.2 V) 19.2 11 2.8%
quartz halogen (12–24 V) 24 3.5%
photographic and projection lamps 35 12 5.1%
Fluorescent 9–26 W compact fluorescent 60–72 1314 9–11%
T12 tube with magnetic ballast 60 15 9%
T5 tube 70–100 16 10–15%
T8 tube with electronic ballast 80–100 15 12–15%
Light-emitting diode white LED 10–100 171819 1.5–15%
Arc lamp xenon arc lamp 30–50 2021 4.4–7.3%
mercury-xenon arc lamp 50–55 20 7.3–8.0%
Gas discharge 1400 W sulfur lamp 100 15%
metal halide lamp 65–115 22 9.5–17%
high pressure sodium lamp 150 23 22%
low pressure sodium lamp 183–200 2324 27–29%
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 [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.”12 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 units
v • d • e
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
SI • Photometry

See also

References

  1. ^ a b Ohno, Yoshi (2004), "Color Rendering and Luminous Efficacy of White LED Spectra", Proc. of SPIE (Fourth International Conference on Solid State Lighting), 5530, SPIE, Bellingham, WA, doi:10.1117/12.565757, http://physics.nist.gov/Divisions/Div844/facilities/photo/Publications/OhnoSPIE2004.pdf 
  2. ^ Van Nostrand's Scientific Encyclopedia, 3rd Edition. Princeton, New Jersey, Toronto, London, New York: D. Van Nostrand Company, Inc.. January 1958. 
  3. ^ a b Defined such that the maximum value possible is 100%.
  4. ^ a b Black body visible spectrum
  5. ^ See luminosity function.
  6. ^ 1 candela*4π steradians/40 W
  7. ^ Waymouth, John F., "Optical light source device", US patent # 5079473, published September 8, 1989, issued January 7, 1992. col. 2, line 34.
  8. ^ a b Keefe, T.J. (2007). "The Nature of Light". Retrieved on 2007-11-05.
  9. ^ Bulbs: Gluehbirne.ch: Philips Standard Lamps (German)
  10. ^ "Osram halogen" (PDF) (in German). www.osram.de. Retrieved on 2008-01-28.dead link
  11. ^ "Osram Miniwatt-Halogen". www.ts-audio.biz. Retrieved on 2008-01-28.dead link
  12. ^ a b Klipstein, Donald L. (1996). "The Great Internet Light Bulb Book, Part I". Retrieved on 2006-04-16.
  13. ^ "Low Mercury CFLs". Energy Federation Incorporated. Retrieved on 2008-12-23.
  14. ^ "Conventional CFLs". Energy Federation Incorporated. Retrieved on 2008-12-23.
  15. ^ a b Federal Energy Management Program (December 2000). "How to buy an energy-efficient fluorescent tube lamp". U.S. Department of Energy.
  16. ^ Department of the Environment, Water, Heritage and the Arts, Australia. "Energy Labelling—Lamps". Retrieved on 2008-08-14.
  17. ^ Klipstein, Donald L.. "The Brightest and Most Efficient LEDs and where to get them". Don Klipstein's Web Site. Retrieved on 2008-01-15.
  18. ^ "Cree launches the new XLamp 7090 XR-E Series Power LED, the first 160-lumen LED!".
  19. ^ "Luxeon K2 with TFFC; Technical Datasheet DS60" (PDF). PhilipsLumileds. Retrieved on 2008-04-23.
  20. ^ a b "Technical Information on Lamps" (pdf). Optical Building Blocks. Retrieved on 2007-10-14. Note that the figure of 150 lm/W given for xenon lamps appears to be a typo. The page contains other useful information.
  21. ^ OSRAM Sylvania Lamp and Ballast Catalog. 2007. 
  22. ^ "The Metal Halide Advantage". Venture Lighting (2007). Retrieved on 2008-08-10.
  23. ^ a b "LED or Neon? A scientific comparison".
  24. ^ "Why is lightning coloured? (gas excitations)".

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