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 or is emitted 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.

Luminance is invariant in geometric optics. 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 you form a demagnified image with a lens, 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

Luminance is defined by the derivative

$L_\mathrm{v} = \frac{\mathrm{d}^2 \Phi_\mathrm{v}}{\mathrm{d}A\,\mathrm{d}{\Omega} \cos \theta}$

where

$L_\mathrm{v}$ is the luminance (cd/m²),

$\Phi_\mathrm{v}$ is the luminous flux or luminous power (lm),

$\theta\,$ is the angle between the surface normal and the specified direction,

$A$ is the area of the surface (m²), and

$\Omega\,$ is the solid angle (sr).

The expression is written using Leibniz's notation.

Units

A variety of units have been used for luminance, besides the candela per square metre.

One candela per square metre is equal to:

• 10⁻⁴ stilbs (the CGS unit of luminance)
• π apostilbs
• π×10⁻⁴ lamberts
• 0.292 foot-lamberts

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

• 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
• Luminance meter

SI photometry units

Quantity		Unit		Dimension	Notes
Name	Symbol	Name	Symbol	Symbol
Luminous energy	Qv	lumen second	lm⋅s	T⋅J	units are sometimes called talbots
Luminous flux	Φv	lumen (= cd⋅sr)	lm	J	also called luminous power
Luminous intensity	Iv	candela (= lm/sr)	cd	J	an SI base unit, luminous flux per unit solid angle
Luminance	Lv	candela per square metre	cd/m2	L−2⋅J	units are sometimes called nits
Illuminance	Ev	lux (= lm/m2)	lx	L−2⋅J	used for light incident on a surface
Luminous emittance	Mv	lux (= lm/m2)	lx	L−2⋅J	used for light emitted from a surface
Luminous exposure	Hv	lux second	lx⋅s	L−2⋅T⋅J
Luminous energy density	ωv	lumen second per metre3	lm⋅s⋅m−3	L−3⋅T⋅J
Luminous efficacy	η	lumen per watt	lm/W	M−1⋅L−2⋅T3⋅J	ratio of luminous flux to radiant flux
Luminous efficiency	V			1	also called luminous coefficient
See also: SI · Photometry · Radiometry

External links

• A Kodak guide to Estimating Luminance and Illuminance using a camera's exposure meter. Also available in PDF form and Google Docs online version