Luminance

Not to be confused with Luma (video) or Luminescence.
For other uses, see Luminance (disambiguation).

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.

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 300 cd/m2. The sun has luminance of about 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

L_\mathrm{v} = \frac{\mathrm{d}^2\Phi_\mathrm{v}} {\mathrm{d}\Sigma\,\mathrm{d}\Omega_\Sigma \cos \theta_\Sigma}

where

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

L_\mathrm{v} = \frac{\mathrm{d}^2\Phi_\mathrm{v}} {\mathrm{d}S\,\mathrm{d}\Omega_S \cos \theta_S}

where

More generally, the luminance along a light ray can be defined as

L_\mathrm{v} = n^2\frac{\mathrm{d}\Phi_\mathrm{v}}{\mathrm{d}G}

where

Relation to Illuminance

The luminance of a reflecting surface is related to the illuminance it receives:

\begin{align} \int_{\Omega_\Sigma} L_\mathrm{v} \mathrm{d}\Omega_\Sigma \cos \theta_\Sigma & = M_\mathrm{v} \\ & = E_\mathrm{v} R \end{align}

where the integral covers all the directions of emission ΩΣ, and

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

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:

Health effects

See also: Laser safety

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.

See also

SI photometry quantities
Quantity Unit Dimension Notes
Name Symbol[nb 1] Name Symbol Symbol
Luminous energy Qv [nb 2] lumen second lm⋅s T⋅J [nb 3] Units are sometimes called talbots.
Luminous flux / luminous power Φv [nb 2] lumen (= cd⋅sr) lm J [nb 3] Luminous energy per unit time.
Luminous intensity Iv candela (= lm/sr) cd J [nb 3] Luminous power per unit solid angle.
Luminance Lv candela per square metre cd/m2 L−2⋅J Luminous power per unit solid angle per unit projected source area. Units are sometimes called nits.
Illuminance Ev lux (= lm/m2) lx L−2⋅J Luminous power incident on a surface.
Luminous exitance / luminous emittance Mv lux lx L−2⋅J Luminous power emitted from a surface.
Luminous exposure Hv lux second lx⋅s L−2⋅T⋅J
Luminous energy density ωv lumen second per cubic metre lm⋅s⋅m−3 L−3⋅T⋅J
Luminous efficacy η [nb 2] 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
See also: SI · Photometry · Radiometry
  1. ↑ 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
  2. 1 2 3 Alternative symbols sometimes seen: W for luminous energy, P or F for luminous flux, and ρ or K for luminous efficacy.
  3. 1 2 3 "J" here is the symbol for the dimension of luminous intensity, not the symbol for the unit joules.

References

  1. ↑ "Luminance". Lighting Design Glossary. Retrieved Apr 13, 2009.
  2. ↑ 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.
  3. ↑ Chaves, Julio (2015). Introduction to Nonimaging Optics, Second Edition. CRC Press. p. 679. ISBN 978-1482206739.

External links

This article is issued from Wikipedia - version of the Tuesday, May 03, 2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.