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Luminance is a photometric measure of the luminous intensity per unit area of
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 ter ...
travelling in a given direction. 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 In geometry, a solid angle (symbol: ) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point. The po ...
. Brightness is the term for the ''subjective'' impression of the ''objective'' luminance measurement standard (see for the importance of this contrast). The
SI unit The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...
for luminance is
candela per square metre The candela per square metre (symbol: cd/m2) is the unit of luminance in the International System of Units (SI). The unit is based on the candela, the SI unit of luminous intensity, and the square metre, the SI unit of area. The nit (symbol: nt) ...
(cd/m2). A non-SI term for the same unit is the nit. The unit in the Centimetre–gram–second system of units (CGS) (which predated the SI system) is the stilb, which is equal to one candela per square centimetre or 10 kcd/m2.

# Description

Luminance is often used to characterize emission or reflection from flat,
diffuse Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical ...
surfaces. Luminance levels indicate how much luminous power could be detected by the
human eye The human eye is a sensory organ, part of the sensory nervous system, that reacts to visible light and allows humans to use visual information for various purposes including seeing things, keeping balance, and maintaining circadian rhythm. T ...
looking at a particular surface from a particular angle of view. Luminance is thus an indicator of how
bright Bright may refer to: Common meanings *Bright, an adjective meaning giving off or reflecting illumination; see Brightness *Bright, an adjective meaning someone with intelligence People * Bright (surname) * Bright (given name) *Bright, the stage na ...
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 . The sun has a luminance of about at noon. Luminance is invariant in
geometric optics Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ca ...
. 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 In photometry, illuminance is the total luminous flux incident on a surface, per unit area. It is a measure of how much the incident light illuminates the surface, wavelength-weighted by the luminosity function to correlate with human brightne ...
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

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.

# 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 In geometry, a solid angle (symbol: ) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point. The po ...
. 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.

# Mathematical definition

The luminance of a specified point of a light source, in a specified direction, is defined by the
derivative In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. ...
$L_\mathrm = \frac$ where * v is the luminance ( cd/ m2), * d2v is the luminous flux ( lm) leaving the area d in any direction contained inside the solid angle dΣ, * d is an infinitesimal area ( m2) of the source containing the specified point, * dΣ is an infinitesimal
solid angle In geometry, a solid angle (symbol: ) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point. The po ...
( sr) containing the specified direction, * Σ is the angle between the normal nΣ to the surface d and the specified direction. 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 $L_\mathrm = \frac$ where * d is the infinitesimal area of ''S'' seen from the source inside the solid angle dΣ, * dS is the infinitesimal solid angle subtended by d as seen from d, * S is the angle between the normal nS to d and the direction of the light. More generally, the luminance along a light ray can be defined as $L_\mathrm = n^2\frac$ where * d is the
etendue Etendue or étendue (; ) is a property of light in an optical system, which characterizes how "spread out" the light is in area and angle. It corresponds to the beam parameter product (BPP) in Gaussian beam optics. Other names for etendue includ ...
of an infinitesimally narrow beam containing the specified ray, * dv is the luminous flux carried by this beam, * is the
index of refraction In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
of the medium.

# Relation to illuminance

The luminance of a reflecting surface is related to the
illuminance In photometry, illuminance is the total luminous flux incident on a surface, per unit area. It is a measure of how much the incident light illuminates the surface, wavelength-weighted by the luminosity function to correlate with human brightne ...
it receives: $\int_ L_\text \mathrm\Omega_\Sigma \cos \theta_\Sigma = M_\text = E_\text R,$ where the integral covers all the directions of emission , * v is the surface's
luminous exitance In photometry, illuminance is the total luminous flux incident on a surface, per unit area. It is a measure of how much the incident light illuminates the surface, wavelength-weighted by the luminosity function to correlate with human brightness ...
, * v is the received illuminance, * 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 $L_\text = \frac.$

# Units

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

* Relative luminance * Orders of magnitude (luminance) *
Diffuse reflection Diffuse reflection is the reflection of light or other waves or particles from a surface such that a ray incident on the surface is scattered at many angles rather than at just one angle as in the case of specular reflection. An ''ideal'' ...
*
Etendue Etendue or étendue (; ) is a property of light in an optical system, which characterizes how "spread out" the light is in area and angle. It corresponds to the beam parameter product (BPP) in Gaussian beam optics. Other names for etendue includ ...
* *
Lambertian reflectance Lambertian reflectance is the property that defines an ideal "matte" or diffusely reflecting surface. The apparent brightness of a Lambertian surface to an observer is the same regardless of the observer's angle of view. More technically, the su ...
* Lightness (color) * Luma, the representation of luminance in a video monitor * Lumen (unit) *
, radiometric quantity analogous to luminance * Brightness, the subjective impression of luminance *
Glare (vision) Glare is difficulty of seeing in the presence of bright light such as direct or reflected sunlight or artificial light such as car headlamps at night. Because of this, some cars include mirrors with automatic anti-glare functions and in buildin ...

{{SI light units