Luminous efficacy#Lighting efficiency
{{short description|Measure of how well a light source produces visible light}}
{{Infobox physical quantity
| name = Luminous efficacy
| image =
| caption =
| unit = lm⋅W{{superscript|−1}}
| symbols = K
| baseunits = cd⋅s{{superscript|3}}⋅kg{{superscript|−1}}⋅m{{superscript|−2}}
| dimension =
| extensive =
| conserved =
| derivations =
}}
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.{{cite book |author=Allen Stimson |title=Photometry and Radiometry for Engineers |publisher=Wiley and Son |location=New York |year=1974|bibcode=1974wi...book.....S }}{{cite book |title=Optical Radiation Measurements, Vol 1 |publisher=Academic Press |location=New York |author1=Franc Grum |author2=Richard Becherer |year=1979}}{{cite book |title=Radiometry and the Detection of Optical Radiation |publisher=Wiley and Son |location=New York |author=Robert Boyd |year=1983}}
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,International Electrotechnical Commission (IEC): International Electrotechnical Vocabulary, [http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=845-21-090 ref. 845-21-090, Luminous efficacy of radiation (for a specified photometric condition)] and the latter luminous efficacy of a light sourceInternational Electrotechnical Commission (IEC): International Electrotechnical Vocabulary, [http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=845-21-089 ref. 845-21-089, Luminous efficacy (of a light source)] or overall luminous efficacy.{{cite book |title=Photovoltaic systems engineering |url=https://archive.org/details/photovoltaicsyst00mess_644 |url-access=limited |edition=2 |author1=Roger A. Messenger |author2=Jerry Ventre |publisher=CRC Press |year=2004 |isbn=978-0-8493-1793-4 |page=[https://archive.org/details/photovoltaicsyst00mess_644/page/n145 123]}}{{cite book |title=Color imaging: fundamentals and applications |url=https://archive.org/details/colorimagingfund00rein |url-access=limited |author1=Erik Reinhard |author2=Erum Arif Khan |author3=Ahmet Oğuz Akyüz |author4=Garrett Johnson |publisher=A K Peters, Ltd |year=2008 |isbn=978-1-56881-344-8 |page=[https://archive.org/details/colorimagingfund00rein/page/n353 338]}}
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=
File:CIE 1931 Luminosity.png under daytime or bright conditions, as standardized by the CIE in 1924. The horizontal axis is wavelength in nanometers.{{Cite report |url=https://www.iso.org/standard/41641.html |title=ISO 23539:2005 Photometry — The CIE system of physical photometry |last=ISO |date=2005 |access-date=2022-01-05}}]]
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 illumination{{efn|group=note|There are special cases of illumination involving wavelengths of light that are outside the human visible range. One example is Ultraviolet light which is not itself visible, but can excite some pigments to fluoresce, where the pigments re-emit the light into the visible range. Such special cases are not a contributing part of luminous efficacy calculations.}}. 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 {{nowrap|683.002 lm/W}}, for the case of monochromatic light at a wavelength of {{nowrap|555 nm}} {{Colorsample|#78ff00|border=#55b900}}.{{efn|group=note|Standard vision typically perceives {{nowrap|555 nm}} as a hue of yellowish-green {{Colorsample|#78ff00|border=#55b900}}, which can be emulated on an sRGB display with CSS color value rgb(120,255,0)
or hex #78ff00
.}} Scotopic luminous efficacy of radiation reaches a maximum of {{nowrap|1700 lm/W}} for monochromatic light at a wavelength of {{nowrap|507 nm}}.{{efn|group=note|Under standard photopic vision {{nowrap|507 nm}} is perceived as a blue-green hue similar to viridian {{Colorsample|#00a880|border=#005a43}}, however scotopic rod-only vision does not create a color sensation in the standard human vision system.}}
=Mathematical definition=
Luminous efficacy (of radiation), denoted K, is defined as
:
where
- Φv is the luminous flux;
- Φe is the radiant flux;
- Φe,λ is the spectral radiant flux;
- {{nowrap|1=K(λ) = KmV(λ)}} is the spectral luminous efficacy.
=Examples=
==[[Photopic vision]]==
class="wikitable sortable" |
Type
! Luminous efficacy ! Luminous |
---|
Tungsten light bulb, typical, 2800 K
| 2% |
Class M star (Antares, Betelgeuse), 3300{{nbsp}}K
| 30 | 4% |
Black body, 4000 K, ideal
| 54.7{{efn|group=note|name="blackbody"|Black body visible spectrum}} | 8% |
Class G star (Sun, Capella), 5800{{nbsp}}K
| 13.6% |
Black-body, 7000 K, ideal
| 95{{efn|group=note|name="blackbody"}} | 14% |
Black-body, 5800 K, truncated to 400–700 nm (ideal "white" source){{efn|group=note|Most efficient source that mimics the solar spectrum within range of human visual sensitivity.}}
| 251{{efn|group=note|name=ideal_white|Integral of truncated Planck function times photopic luminosity function times 683.002 lm/W.}} | 37% |
Black-body, 5800 K, truncated to ≥ 2% photopic sensitivity range{{efn|group=note|name=max-eff-truncated|Omits the part of the spectrum where the eye's sensitivity is very poor.}}
| 43% |
Black-body, 2800 K, truncated to ≥ 2% photopic sensitivity range{{efn|group=note|name=max-eff-truncated}}
| 44% |
Black-body, 2800 K, truncated to ≥ 5% photopic sensitivity range{{efn|group=note|name=max-eff-truncated-1|Omits the part of the spectrum where the eye's sensitivity is low (≤ 5% of the peak).}}
| 50% |
Black-body, 5800 K, truncated to ≥ 5% photopic sensitivity range{{efn|group=note|name=max-eff-truncated-1}}
| 51% |
Monochromatic source at {{val|540|u=THz}}
| 683 (exact) | 99.9997% |
Ideal monochromatic source: {{val|555|u=nm}} (in air)
{{cite web |url = https://www.bipm.org/utils/common/pdf/SI-statement.pdf |title = BIPM statement: Information for users about the proposed revision of the SI |access-date = 5 May 2018 |archive-url = https://web.archive.org/web/20180121160000/https://www.bipm.org/utils/common/pdf/SI-statement.pdf |archive-date = 21 January 2018 |url-status = live |df = dmy-all }} | 100% |
== [[Scotopic vision]] ==
class="wikitable"
!Type !Luminous efficacy of radiation (lm/W) !Luminous efficiency{{efn|group=note|name=max}} |
Ideal monochromatic 507 nm source
|1699{{cite book|author1=Kohei Narisada|title=Light Pollution Handbook|author2=Duco Schreuder|publisher=Springer|year=2004|isbn=1-4020-2665-X}} or 1700{{cite book|author=Casimer DeCusatis|title=Handbook of Applied Photometry|publisher=Springer|year=1998|isbn=1-56396-416-3}} |100% |
File:Blackbody_efficacy_1000-16000K.svg
File:Wiens_law_vis_limits.svg of a black body. Energy outside the visible wavelength range (~380–750{{nbsp}}nm, shown by grey dotted lines) reduces the luminous efficiency.]]
== Lighting efficiency ==
{{main|Wall-plug 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.
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.
SI photometry units
{{SI light units}}
See also
- Photometry
- Light pollution
- Wall-plug efficiency
- Coefficient of utilization
- List of light sources
- SI defining constants, including Kcd (used in the definition of candela)
Notes
{{noteslist|group=note}}
References
{{reflist|30em|refs=
{{cite journal|doi=10.1063/1.4721897
| url=https://tmurphy.physics.ucsd.edu/papers/JAP_111_104909.pdf
| title=Maximum spectral luminous efficacy of white light|journal=Journal of Applied Physics
| volume=111 | issue=10 | year=2012
| last1=Murphy | first1=Thomas W.
| author-link=Tom Murphy (physicist)
| pages=104909–104909–6| arxiv = 1309.7039
| bibcode = 2012JAP...111j4909M
| s2cid=6543030}}
}}
External links
- Hyperphysics has these [http://hyperphysics.phy-astr.gsu.edu/hbase/vision/bright.html#c2 graphs of efficacy] that do not quite comply with the standard definition
- [http://www.cus.net/electricity/subcats/eleclighting.html Energy Efficient Light Bulbs]
- [http://www.otherpower.com/otherpower_lighting.html Other Power]
{{Artificial light sources}}