Luminance
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 or reflected from a particular area, and falls within a given solid angle. The SI unit for luminance is candela per square metre (cd/m2). A non-SI term for the same unit is the nit. The CGS unit of luminance is the stilb, which is equal to one candela per square centimetre or 10 kcd/m2.
Contents
1 Explanation
2 Definition
3 Relation to Illuminance
4 Units
5 Health effects
6 Luminance meter
7 See also
8 References
9 External links
Explanation
Luminance is often used to characterize emission or reflection from flat, diffuse surfaces. The luminance indicates how much luminous power will be detected by an eye looking at the surface from a particular angle of view. Luminance is thus an indicator of how 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 50 and 7002300000000000000♠300 cd/m2. The sun has a luminance of about 7009160000000000000♠1.6×109 cd/m2 at noon.[1]
Luminance is invariant in geometric optics.[2] 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 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.
Definition
Parameters for defining the luminance
The luminance of a specified point of a light source, in a specified direction, is defined by the derivative
- Lv=d2ΦvdΣdΩΣcosθΣdisplaystyle L_mathrm v =frac mathrm d ^2Phi _mathrm v mathrm d Sigma ,mathrm d Omega _Sigma cos theta _Sigma
where
Lv is the luminance (cd/m2),- d2Φv is the luminous flux (lm) leaving the area dΣ in any direction contained inside the solid angle dΩΣ,
- dΣ is an infinitesimal area (m2) of the source containing the specified point,
- dΩΣ is an infinitesimal solid angle (sr) containing the specified direction,
θΣ is the angle between the normal nΣ to the surface dΣ and the specified direction.[3]
If light travels through a lossless medium, the luminance does not change along a given light ray. As the ray crosses an arbitrary surface S, the luminance is given by
- Lv=d2ΦvdSdΩScosθSdisplaystyle L_mathrm v =frac mathrm d ^2Phi _mathrm v mathrm d S,mathrm d Omega _Scos theta _S
where
- dS is the infinitesimal area of S seen from the source inside the solid angle dΩΣ,
- dΩS is the infinitesimal solid angle subtended by dΣ as seen from dS,
θS is the angle between the normal nS to dS and the direction of the light.
More generally, the luminance along a light ray can be defined as
- Lv=n2dΦvdGdisplaystyle L_mathrm v =n^2frac mathrm d Phi _mathrm v mathrm d G
where
- dG is the etendue of an infinitesimally narrow beam containing the specified ray,
- dΦv is the luminous flux carried by this beam,
n is the index of refraction of the medium.
Relation to Illuminance
The luminance of a reflecting surface is related to the illuminance it receives:
- ∫ΩΣLvdΩΣcosθΣ=Mv=EvRdisplaystyle beginalignedint _Omega _Sigma L_mathrm v mathrm d Omega _Sigma cos theta _Sigma &=M_mathrm v \&=E_mathrm v Rendaligned
where the integral covers all the directions of emission ΩΣ, and
Mv is the surface's luminous exitance
Ev is the received illuminance, and
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
- Lv=EvR/πdisplaystyle L_mathrm v =E_mathrm v R/pi
Units
A variety of units have been used for luminance, besides the candela per square metre.
One candela per square metre is equal to:
- 10−4stilbs (the CGS unit of luminance)
- π apostilbs
- π×10−4lamberts
- 0.292 foot-lamberts
Health effects
Retinal damage can occur when the eye is exposed to high luminance. Damage can occur due to local heating of the retina. Photochemical effects can also cause damage, especially at short wavelengths.
Luminance meter
A luminance meter is a device used in 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.[4]
See also
- Orders of magnitude (luminance)
- Diffuse reflection
- Etendue
- Exposure value
- Lambertian reflectance
Lightness, property of a color
Luma, the representation of luminance in a video monitor- Lumen (unit)
Radiance, radiometric quantity analogous to luminance
Brightness, the subjective impression of luminance- Glare
| Quantity | Unit | Dimension | Notes | |||||
|---|---|---|---|---|---|---|---|---|
Name | Symbol[nb 1] | Name | Symbol | Symbol[nb 2] | ||||
Luminous energy | Qv[nb 3] | lumen second | lm⋅s | T⋅J | The lumen second is sometimes called the talbot. | |||
Luminous flux, luminous power | Φv[nb 3] | lumen (= candela steradians) | lm (= cd⋅sr) | J | Luminous energy per unit time | |||
Luminous intensity | Iv | candela (= lumen per steradian) | cd (= lm/sr) | J | Luminous flux per unit solid angle | |||
Luminance | Lv | candela per square metre | cd/m2 | L−2⋅J | Luminous 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⋅J | Luminous flux incident on a surface | |||
Luminous exitance, luminous emittance | Mv | lux | lx | L−2⋅J | Luminous flux emitted from a surface | |||
Luminous exposure | Hv | lux second | lx⋅s | L−2⋅T⋅J | Time-integrated illuminance | |||
| Luminous energy density | ωv | lumen second per cubic metre | lm⋅s/m3 | L−3⋅T⋅J | ||||
Luminous efficacy | η[nb 3] | lumen per watt | lm/W | M−1⋅L−2⋅T3⋅J | Ratio of luminous flux to radiant flux or power consumption, depending on context | |||
Luminous efficiency, luminous coefficient | V | 1 | Luminous efficacy normalized by the maximum possible efficacy | |||||
| See also: SI · Photometry · Radiometry | ||||||||
^ Standards organizations recommend that photometric quantities be denoted with a suffix "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
^ 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.
^ abc Alternative symbols sometimes seen: W for luminous energy, P or F for luminous flux, and ρ or K for luminous efficacy.
References
^ "Luminance". Lighting Design Glossary. Retrieved Apr 13, 2009..mw-parser-output cite.citationfont-style:inherit.mw-parser-output .citation qquotes:"""""""'""'".mw-parser-output .citation .cs1-lock-free abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center.mw-parser-output .citation .cs1-lock-subscription abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registrationcolor:#555.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration spanborder-bottom:1px dotted;cursor:help.mw-parser-output .cs1-ws-icon abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center.mw-parser-output code.cs1-codecolor:inherit;background:inherit;border:inherit;padding:inherit.mw-parser-output .cs1-hidden-errordisplay:none;font-size:100%.mw-parser-output .cs1-visible-errorfont-size:100%.mw-parser-output .cs1-maintdisplay:none;color:#33aa33;margin-left:0.3em.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-formatfont-size:95%.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-leftpadding-left:0.2em.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-rightpadding-right:0.2em
^ Dörband, Bernd; Gross, Herbert; Müller, Henriette (2012). Gross, Herbert, ed. Handbook of Optical Systems. 5, Metrology of Optical Components and Systems. Wiley. p. 326. ISBN 978-3-527-40381-3.
^ Chaves, Julio (2015). Introduction to Nonimaging Optics, Second Edition. CRC Press. p. 679. ISBN 978-1482206739. Archived from the original on 2016-02-18.
^ "e-ILV : Luminance meter". CIE. Retrieved 20 February 2013.
External links
- A Kodak guide to Estimating Luminance and Illuminance using a camera's exposure meter. Also available in PDF form.
- Autodesk Design Academy Measuring Light Levels
