Luminous efficacy

Last updated
Luminous efficacy
Common symbols
K
SI unit lm⋅W−1
In SI base units cd⋅s3⋅kg−1⋅m−2
Dimension

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. [1] [2] [3] 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, [4] and the latter luminous efficacy of a light source [5] or overall luminous efficacy. [6] [7]

Contents

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

Explanation

The response of a typical human eye to light, as standardized by the CIE in 1924. The horizontal axis is wavelength in nanometers. CIE 1931 Luminosity.png
The response of a typical human eye to light, as standardized by the CIE in 1924. The horizontal axis is wavelength in nanometers.

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. [4] Light with wavelengths outside the visible spectrum reduces luminous efficacy, 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.

Photopic luminous efficacy of radiation has a maximum possible value of 683.002 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 monochromatic light at a wavelength of 507 nm.

Mathematical definition

Luminous efficacy (of radiation), denoted K, is defined as [4]

where

Examples

Photopic vision

TypeLuminous efficacy
of radiation (lm/W)		Luminous
efficiency [note 1]
Tungsten light bulb, typical, 2800 K15 [9] 2%
Class M star (Antares, Betelgeuse), 3300 K 304%
Black body, 4000 K, ideal54.7 [note 2] 8%
Class G star (Sun, Capella), 5800 K93 [9] 13.6%
Black-body, 7000 K, ideal95 [note 2] 14%
Black-body, 5800 K, truncated to 400–700 nm (ideal "white" source) [note 3] 251 [9] [note 4] [10] 37%
Black-body, 5800 K, truncated to ≥ 2% photopic sensitivity range [note 5] 292 [10] 43%
Black-body, 2800 K, truncated to ≥ 2% photopic sensitivity range [note 5] 299 [10] 44%
Black-body, 2800 K, truncated to ≥ 5% photopic sensitivity range [note 6] 343 [10] 50%
Black-body, 5800 K, truncated to ≥ 5% photopic sensitivity range [note 6] 348 [10] 51%
Monochromatic source at 540 THz683 (exact)99.9997%
Ideal monochromatic source: 555 nm (in air)683.002 [11] 100%

Scotopic vision

TypeLuminous efficacy

of radiation (lm/W)

Luminous

efficiency [note 1]

Ideal monochromatic 507 nm source1699 [12] or 1700 [13] 100%
Blackbody efficacy 1000-16000K.svg
Spectral radiance of a black body. Energy outside the visible wavelength range (~380-750 nm, shown by grey dotted lines) reduces the luminous efficiency. Wiens law vis limits.svg
Spectral radiance of a black body. Energy outside the visible wavelength range (~380–750 nm, shown by grey dotted lines) reduces the luminous efficiency.

Lighting efficiency

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.

CategoryTypeOverall luminous
efficacy (lm/W)		Overall luminous
efficiency [note 1]
Combustion Gas mantle 1–2 [14] 0.15–0.3%
Incandescent 15, 40, 100 W tungsten incandescent (230 V)8.0, 10.4, 13.8 [15] [16] [17] [18] 1.2, 1.5, 2.0%
5, 40, 100 W tungsten incandescent (120 V)5.0, 12.6, 17.5 [19] 0.7, 1.8, 2.6%
Halogen incandescent 100, 200, 500 W tungsten halogen (230 V)16.7, 17.6, 19.8 [20] [18] 2.4, 2.6, 2.9%
2.6 W tungsten halogen (5.2 V)19.2 [21] 2.8%
Halogen-IR (120 V)17.7–24.5 [22] 2.6–3.5%
Tungsten quartz halogen (12–24 V)243.5%
Photographic and projection lamps35 [23] 5.1%
Light-emitting diode LED screw base lamp (120 V)102 [24] [25] [26] 14.9%
5–16 W LED screw base lamp (230 V)75–212 [27] [28] [29] 11–31%
21.5 W LED retrofit for T8 fluorescent tube (230 V)172 [30] 25%
Theoretical limit for a white LED with phosphorescence color mixing260–300 [31] 38.1–43.9%
Arc lamp Carbon arc lamp 2–7 [32] 0.29–1.0%
Xenon arc lamp 30–90 [33] [34] [35] 4.4–13.5%
Mercury-xenon arc lamp50–55 [33] 7.3–8%
Ultra-high-pressure (UHP) mercury-vapor arc lamp, free mounted58–78 [36] 8.5–11.4%
Ultra-high-pressure (UHP) mercury-vapor arc lamp, with reflector for projectors 30–50 [37] 4.4–7.3%
Fluorescent 32 W T12 tube with magnetic ballast60 [38] 9%
9–32 W compact fluorescent (with ballast)46–75 [18] [39] [40] 8–11.45% [41]
T8 tube with electronic ballast80–100 [38] 12–15%
PL-S 11 W U-tube, excluding ballast loss82 [42] 12%
T5 tube70–104.2 [43] [44] 10–15.63%
70–150 W inductively-coupled electrodeless lighting system71–84 [45] 10–12%
Gas discharge 1400 W sulfur lamp 100 [46] 15%
Metal-halide lamp 65–115 [47] 9.5–17%
High-pressure sodium lamp 85–150 [18] 12–22%
Low-pressure sodium lamp 100–200 [18] [48] [49] [50] 15–29%
Plasma display panel 2–10 [51] 0.3–1.5%
Cathodoluminescence Electron-stimulated luminescence 30–110 [52] [53] 15%
Ideal sourcesTruncated 5800 K black-body [note 4] 251 [9] 37%
Green light at 555 nm (maximum possible luminous efficacy by definition)683.002 [11] [54] 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." [23] At temperatures where the tungsten filament of an ordinary light bulb remains solid (below 3683 kelvin), most of its emission is in the infrared. [23]

SI photometry units

SI photometry quantities
QuantityUnitDimension
[nb 1] 		Notes
NameSymbol [nb 2] NameSymbol
Luminous energy Qv [nb 3] lumen second lm⋅sT⋅JThe lumen second is sometimes called the talbot.
Luminous flux, luminous powerΦ v [nb 3] lumen (= candela steradian)lm (= cd⋅sr)JLuminous energy per unit time
Luminous intensity Iv candela (= lumen per steradian) cd (= lm/sr)JLuminous flux per unit solid angle
Luminance Lv candela per square metre cd/m2 (= lm/(sr⋅m2))L−2⋅JLuminous 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⋅JLuminous flux incident on a surface
Luminous exitance, luminous emittanceMvlumen per square metrelm/m2L−2⋅JLuminous flux emitted from a surface
Luminous exposure Hv lux second lx⋅sL−2⋅T⋅JTime-integrated illuminance
Luminous energy densityωvlumen second per cubic metrelm⋅s/m3L−3⋅T⋅J
Luminous efficacy (of radiation)Klumen per watt lm/W M−1⋅L−2⋅T3⋅JRatio of luminous flux to radiant flux
Luminous efficacy (of a source)η [nb 3] lumen per watt lm/W M−1⋅L−2⋅T3⋅JRatio of luminous flux to power consumption
Luminous efficiency, luminous coefficientV1Luminous efficacy normalized by the maximum possible efficacy
See also:
  1. ↑ The symbols in this column denote dimensions; "L", "T" and "J" are for length, time and luminous intensity respectively, not the symbols for the units litre, tesla and joule.
  2. ↑ Standards organizations recommend that photometric quantities be denoted with a subscript "v" (for "visual") to avoid confusion with radiometric or photon quantities. For example: USA Standard Letter Symbols for Illuminating Engineering USAS Z7.1-1967, Y10.18-1967
  3. 1 2 3 Alternative symbols sometimes seen: W for luminous energy, P or F for luminous flux, and ρ for luminous efficacy of a source.

See also

Notes

  1. 1 2 3 Defined such that the maximum possible luminous efficacy corresponds to a luminous efficiency of 100%.
  2. 1 2 Black body visible spectrum
  3. ↑ Most efficient source that mimics the solar spectrum within range of human visual sensitivity.
  4. 1 2 Integral of truncated Planck function times photopic luminosity function times 683.002 lm/W.
  5. 1 2 Omits the part of the spectrum where the eye's sensitivity is very poor.
  6. 1 2 Omits the part of the spectrum where the eye's sensitivity is low (≤ 5% of the peak).

Related Research Articles

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The candela is the unit of luminous intensity in the International System of Units (SI). It measures luminous power per unit solid angle emitted by a light source in a particular direction. Luminous intensity is analogous to radiant intensity, but instead of simply adding up the contributions of every wavelength of light in the source's spectrum, the contribution of each wavelength is weighted by the luminous efficiency function, the model of the sensitivity of the human eye to different wavelengths, standardized by the CIE and ISO. A common wax candle emits light with a luminous intensity of roughly one candela. If emission in some directions is blocked by an opaque barrier, the emission would still be approximately one candela in the directions that are not obscured.

<span class="mw-page-title-main">Luminance</span> Photometric measure

Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted from, or is reflected from a particular area, and falls within a given solid angle.

<span class="mw-page-title-main">Radiometry</span> Techniques for measuring electromagnetic radiation

Radiometry is a set of techniques for measuring electromagnetic radiation, including visible light. Radiometric techniques in optics characterize the distribution of the radiation's power in space, as opposed to photometric techniques, which characterize the light's interaction with the human eye. The fundamental difference between radiometry and photometry is that radiometry gives the entire optical radiation spectrum, while photometry is limited to the visible spectrum. Radiometry is distinct from quantum techniques such as photon counting.

<span class="mw-page-title-main">Luminous efficiency function</span> Description of the average spectral sensitivity of human visual perception of brightness

A luminous efficiency function or luminosity function represents the average spectral sensitivity of human visual perception of light. It is based on subjective judgements of which of a pair of different-colored lights is brighter, to describe relative sensitivity to light of different wavelengths. It is not an absolute reference to any particular individual, but is a standard observer representation of visual sensitivity of theoretical human eye. It is valuable as a baseline for experimental purposes, and in colorimetry. Different luminous efficiency functions apply under different lighting conditions, varying from photopic in brightly lit conditions through mesopic to scotopic under low lighting conditions. When not specified, the luminous efficiency function generally refers to the photopic luminous efficiency function.

In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model of the sensitivity of the human eye. The SI unit of luminous intensity is the candela (cd), an SI base unit.

<span class="mw-page-title-main">Photometry (optics)</span> Science of the measurement of visible light

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<span class="mw-page-title-main">Luminous flux</span> Perceived luminous power

In photometry, luminous flux or luminous power is the measure of the perceived power of light. It differs from radiant flux, the measure of the total power of electromagnetic radiation, in that luminous flux is adjusted to reflect the varying sensitivity of the human eye to different wavelengths of light.

<span class="mw-page-title-main">Illuminance</span> Luminous flux incident on a surface per area

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The lumen is the unit of luminous flux, a measure of the perceived power of visible light emitted by a source, in the International System of Units (SI). Luminous flux differs from power in that radiant flux includes all electromagnetic waves emitted, while luminous flux is weighted according to a model of the human eye's sensitivity to various wavelengths; this weighting is standardized by the CIE and ISO. One lux is one lumen per square metre.

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<span class="mw-page-title-main">Photopic vision</span> Visual perception under well-lit conditions

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In photometry, luminous energy is the perceived energy of light. This is sometimes called the quantity of light. Luminous energy is not the same as radiant energy, the corresponding objective physical quantity. This is because the human eye can only see light in the visible spectrum and has different sensitivities to light of different wavelengths within the spectrum. When adapted for bright conditions, the eye is most sensitive to light at a wavelength of 555 nm. Light with a given amount of radiant energy will have more luminous energy if the wavelength is 555 nm than if the wavelength is longer or shorter. Light whose wavelength is well outside the visible spectrum has a luminous energy of zero, regardless of the amount of radiant energy present.

<span class="mw-page-title-main">Radiant flux</span> Measure of radiant energy over time

In radiometry, radiant flux or radiant power is the radiant energy emitted, reflected, transmitted, or received per unit time, and spectral flux or spectral power is the radiant flux per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. The SI unit of radiant flux is the watt (W), one joule per second, while that of spectral flux in frequency is the watt per hertz and that of spectral flux in wavelength is the watt per metre —commonly the watt per nanometre.

Mesopic vision, sometimes also called twilight vision, is a combination of photopic and scotopic vision under low-light conditions. Mesopic levels range approximately from 0.01 to 3.0 cd/m2 in luminance. Most nighttime outdoor and street lighting conditions are in the mesopic range.

<span class="mw-page-title-main">Energy conversion efficiency</span> Ratio between the useful output and the input of a machine

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Light-emitting diodes (LEDs) produce light by the recombination of electrons and electron holes in a semiconductor, a process called "electroluminescence". The wavelength of the light produced depends on the energy band gap of the semiconductors used. Since these materials have a high index of refraction, design features of the devices such as special optical coatings and die shape are required to efficiently emit light. A LED is a long-lived light source, but certain mechanisms can cause slow loss of efficiency of the device or sudden failure. The wavelength of the light emitted is a function of the band gap of the semiconductor material used; materials such as gallium arsenide, and others, with various trace doping elements, are used to produce different colors of light. Another type of LED uses a quantum dot which can have its properties and wavelength adjusted by its size. Light-emitting diodes are widely used in indicator and display functions, and white LEDs are displacing other technologies for general illumination purposes.

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  4. 1 2 3 International Electrotechnical Commission (IEC): International Electrotechnical Vocabulary, ref. 845-21-090, Luminous efficacy of radiation (for a specified photometric condition)
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  54. ↑ Choudhury, Asim Kumar Roy (2014). "Characteristics of light sources: luminous efficacy of lamps". Principles of Colour and Appearance Measurement: Object appearance, colour perception and instrumental measurement. Vol. 1. Woodhead Publishing. p. 41. doi:10.1533/9780857099242.1. ISBN   978-0-85709-229-8. If the lamp emits all radiation at 555 nm (where Vλ = 1), the luminous efficacy will be of about 680 lm W−1, the theoretical maximum value. The lamp efficacy will be 26 and 73 lm W−1, when the whole light is emitted at 450 and 650 nm respectively. The luminous coefficient is luminous efficiency expressed as a value between zero and one, with one corresponding to an efficacy of 683 lm W−1.
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