View source for Luminance

{{Short description|Photometric measure}}
{{Distinguish|Luma (video)|Luminescence|Illuminance}}
{{Other uses}}
{{More citations needed|date=April 2023}}
[[File:TealightLuminanceImage.jpg|thumb|A [[tea light]]-type candle, imaged with a luminance camera; [[false color]]s indicate luminance levels per the bar on the right (cd/m<sup>2</sup>)]]
'''Luminance''' is a [[Photometry (optics)|photometric]] measure of the [[luminous intensity]] per [[units of measurement|unit area]] of [[light]] travelling in a given direction.<ref>{{cite encyclopedia | title=luminance, 17-21-050 | encyclopedia=CIE S 017:2020 ILV: International Lighting Vocabulary, 2nd edition. | publisher=CIE - International Commission on Illumination | accessdate=20 April 2023 | year=2020 | url=https://cie.co.at/eilvterm/17-21-050}}</ref> 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]].

The procedure for conversion from spectral [[radiance]] to luminance is standardized by the [[International Commission on Illumination|CIE]] and [[International Organization for Standardization|ISO]].<ref>{{cite book | url=https://www.iso.org/standard/83178.html | title=ISO/CIE 23539:2023 CIE TC 2-93 Photometry — The CIE system of physical photometry | publisher=ISO/CIE | date=2023 | language=en | doi=10.25039/IS0.CIE.23539.2023}}</ref>

[[Brightness]] is the [[terminology|term]] for the ''subjective'' impression of the ''objective'' luminance measurement standard (see {{section link|Objectivity (science)#Objectivity in measurement}} for the importance of this contrast).

The [[SI base unit|SI unit]] for luminance is [[candela per square metre]] (cd/m<sup>2</sup>). A non-SI term for the same unit is the [[nit (unit)|nit]]. The unit in the [[Centimetre–gram–second system of units|Centimetre–gram–second system of units (CGS)]] (which predated the SI system) is the [[stilb (luminance)|stilb]], which is equal to one candela per square centimetre or 10&nbsp;kcd/m<sup>2</sup>.

==Description==
Luminance is often used to characterize emission or reflection from flat, [[diffuse reflection|diffuse]] surfaces. Luminance levels indicate how much [[luminous flux|luminous power]] could be detected by the [[human eye]] looking at a particular surface from a particular [[angle of view]]. Luminance is thus an indicator of how [[brightness|bright]] the surface will appear. In this case, the solid angle of interest is the solid angle subtended by the eye's [[pupil]].

Luminance is used in the video industry to characterize the brightness of displays. A typical computer display emits between {{val|50|and|300|u=cd/m<sup>2</sup>}}. The sun has a luminance of about {{val|1.6|e=9|u=cd/m<sup>2</sup>}} at noon.<ref>{{cite web |url=http://www.schorsch.com/kbase/glossary/luminance.html |title=Luminance |work=Lighting Design Glossary |access-date=Apr 13, 2009}}</ref>

Luminance is [[Invariant (physics)|invariant]] in [[geometric optics]].<ref>{{cite book |title=Handbook of Optical Systems |volume=5, Metrology of Optical Components and Systems |first1=Bernd |last1=Dörband |first2=Herbert |last2=Gross |first3=Henriette |last3=Müller |page=326 |publisher=[[Wiley (publisher)|Wiley]] |year=2012 |isbn=978-3-527-40381-3 |editor-first=Herbert |editor-last=Gross}}</ref> This means that for an ideal optical system, the luminance at the output is the same as the input luminance.

For real, passive optical systems, the output luminance is {{em|at most}} equal to the input. As an example, if one uses a lens to form an image that is smaller than the source object, the luminous power is concentrated into a smaller area, meaning that the [[illuminance]] is higher at the image. The light at the image plane, however, fills a larger solid angle so the luminance comes out to be the same assuming there is no loss at the lens. The image can never be "brighter" than the source.

==Health effects==
{{Further|Laser safety}}
Retinal damage can occur when the eye is exposed to high luminance. Damage can occur because of local heating of the retina. Photochemical effects can also cause damage, especially at short wavelengths.<ref name="iec-2060825-1">IEC 60825-1:2014 {{cite book |url=https://webstore.iec.ch/publication/3587 |title=Safety of laser products - Part 1: Equipment classification and requirements |publisher=[[International Electrotechnical Commission]] |edition=3rd |language=EN, FR, ES |pages=220 |date=2014-05-15 }} - [[List of IEC technical committees|TC 76]] - Optical radiation safety and laser equipment</ref>

The IEC 60825 series gives guidance on safety relating to exposure of the eye to lasers, which are high luminance sources. The IEC 62471 series gives guidance for evaluating the photobiological safety of lamps and lamp systems including luminaires. Specifically it specifies the exposure limits, reference measurement technique and classification scheme for the evaluation and control of photobiological hazards from all electrically powered incoherent broadband sources of optical radiation, including LEDs but excluding lasers, in the wavelength range from {{val|200|u=nm}} through {{val|3000|u=nm}}. This standard was prepared as Standard CIE S 009:2002 by the International Commission on Illumination.

==Luminance meter==
A '''luminance meter''' is a device used in [[Photometry (optics)|photometry]] that can measure the luminance in a particular direction and with a particular [[solid angle]]. The simplest devices measure the luminance in a single direction while imaging luminance meters measure luminance in a way similar to the way a [[digital camera]] records color images.<ref>{{cite web | url=http://eilv.cie.co.at/term/718 | title=e-ILV : Luminance meter | publisher=CIE | access-date=20 February 2013 | archive-date=16 September 2017 | archive-url=https://web.archive.org/web/20170916183341/http://eilv.cie.co.at/term/718 | url-status=dead }}</ref>

== Formulation ==
[[Image:Etendue.svg|right|thumb|Parameters for defining the luminance]]

The luminance of a specified point of a light source, in a specified direction, is defined by the [[mixed partial derivative]]
<math display="block">L_\mathrm{v} = \frac{\mathrm{d}^2\Phi_\mathrm{v}}{\mathrm{d}\Sigma\,\mathrm{d}\Omega_\Sigma \cos \theta_\Sigma}</math>
where
* {{math|''L''<sub>v</sub>}} is the luminance ([[candela|cd]]/[[square metre|m<sup>2</sup>]]);
* {{math|d<sup>2</sup>Φ<sub>v</sub>}} is the [[luminous flux]] ([[Lumen (unit)|lm]]) leaving the area {{math|dΣ}} in any direction contained inside the solid angle {{math|dΩ<sub>Σ</sub>}};
* {{math|dΣ}} is an [[infinitesimal]] area (m<sup>2</sup>) of the source containing the specified point;
* {{math|dΩ<sub>Σ</sub>}} is an infinitesimal [[solid angle]] ([[Steradian|sr]]) containing the specified direction; and
* {{math|''θ''<sub>Σ</sub>}} is the [[angle]] between the [[Normal (geometry)|normal]] {{math|'''n'''<sub>Σ</sub>}} to the surface {{math|dΣ}} and the specified direction.<ref>{{cite book | last = Chaves | first = Julio | title = Introduction to Nonimaging Optics, Second Edition | url = https://books.google.com/books?id=e11ECgAAQBAJ | publisher = [[CRC Press]] | year = 2015 | page = 679 | isbn = 978-1482206739 | url-status = live | archive-url = https://web.archive.org/web/20160218223513/https://books.google.com/books?id=e11ECgAAQBAJ | archive-date = 2016-02-18 }}</ref>

If light travels through a lossless medium, the luminance does not change along a given [[light ray]]. As the ray crosses an arbitrary surface {{mvar|S}}, the luminance is given by
<math display="block">L_\mathrm{v} = \frac{\mathrm{d}^2\Phi_\mathrm{v}}{\mathrm{d}S\,\mathrm{d}\Omega_S \cos \theta_S}</math>
where
* {{math|d''S''}} is the infinitesimal area of {{mvar|S}} seen from the source inside the solid angle {{math|dΩ<sub>Σ</sub>}};
* {{math|dΩ<sub>''S''</sub>}} is the infinitesimal solid angle [[Subtended angle|subtended]] by {{math|dΣ}} as seen from {{math|d''S''}}; and
* {{mvar|θ<sub>S</sub>}} is the angle between the normal {{math|'''n'''<sub>''S''</sub>}} to {{math|d''S''}} and the direction of the light.

More generally, the luminance along a light ray can be defined as
<math display="block">L_\mathrm{v} = n^2\frac{\mathrm{d}\Phi_\mathrm{v}}{\mathrm{d}G}</math>
where
* {{math|d''G''}} is the [[etendue]] of an infinitesimally narrow beam containing the specified ray;
* {{math|dΦ<sub>v</sub>}} is the luminous flux carried by this beam; and
* {{mvar|n}} is the [[index of refraction]] of the medium.

==Relation to illuminance==
[[File:photometry_radiometry_units.svg|thumb|upright=1.5|Comparison of photometric and radiometric quantities]]
The luminance of a reflecting surface is related to the [[illuminance]] it receives:
<math display="block">\int_{\Omega_\Sigma} L_\text{v} \mathrm{d}\Omega_\Sigma \cos \theta_\Sigma = M_\text{v} = E_\text{v} R,</math>
where the integral covers all the directions of emission {{math|Ω<sub>Σ</sub>}},
* {{math|''M''<sub>v</sub>}} is the surface's [[luminous exitance]];
* {{math|''E''<sub>v</sub>}} is the received illuminance; and
* {{mvar|R}} is the [[reflectance]].

In the case of a perfectly [[diffuse reflector]] (also called a [[Lambertian reflector]]), the luminance is isotropic, per [[Lambert's cosine law]]. Then the relationship is simply
<math display="block">L_\text{v} = \frac{E_\text{v} R}{\pi}.</math>

==Units==
A variety of units have been used for luminance, besides the candela per square metre.
<!--
One candela per square metre is equal to:
*10<sup>−4</sup> [[stilb (unit)|stilbs]] (the [[CGS]] unit of luminance)
*π [[apostilb]]s
*π×10<sup>−4</sup> [[lambert (unit)|lambert]]s
*0.292 [[foot-lambert]]s
-->
{{luminance conversions}}

==See also==
*[[Relative luminance]]
*[[Orders of magnitude (luminance)]]
*[[Diffuse reflection]]
*[[Etendue]]
*{{section link|Exposure value#EV as a measure of luminance and illuminance}}
*[[Lambertian reflectance]]
*[[Lightness (color)]]
*[[Luma (video)|Luma]], the representation of luminance in a video monitor
*[[Lumen (unit)]]
*[[Radiance]], radiometric quantity analogous to luminance
*[[Brightness]], the subjective impression of luminance
*[[Glare (vision)]]

===Table of SI light-related units===
{{SI light units}}

==References==
{{Reflist}}

== External links ==
* A Kodak guide to [https://web.archive.org/web/20070805205128/http://www.kodak.com/cluster/global/en/consumer/products/techInfo/am105/am105kic.shtml Estimating Luminance and Illuminance] using a camera's exposure meter. Also available in [https://web.archive.org/web/20070709163424/http://www.kodak.com/cluster/global/en/consumer/products/techInfo/am105/am105kic.pdf PDF form].
* Autodesk Design Academy [https://sustainabilityworkshop.autodesk.com/buildings/measuring-light-levels Measuring Light Levels]

{{Authority control}}

[[Category:Photometry]]
[[Category:Physical quantities]]
<!--Don't add television-related categories. See [[Luma (video)]].-->