Luminance

# Luminance

Discussion

Encyclopedia
Luminance is a photometric
Photometry (optics)
Photometry is the science of the measurement of light, in terms of its perceived brightness to the human eye. It is distinct from radiometry, which is the science of measurement of radiant energy in terms of absolute power; rather, in photometry, the radiant power at each wavelength is weighted by...

measure of the luminous intensity
Luminous intensity
In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model of the sensitivity of the human eye...

per unit area of light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

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
Solid angle
The solid angle, Ω, is the two-dimensional angle in three-dimensional space that an object subtends at a point. It is a measure of how large that object appears to an observer looking from that point...

. The SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

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
Diffuse reflection
Diffuse reflection is the reflection of light from a surface such that an incident ray is reflected at many angles rather than at just one angle as in the case of specular reflection...

surfaces. The luminance indicates how much luminous power
Luminous flux
In photometry, luminous flux or luminous power is the measure of the perceived power of light. It differs from radiant flux, the measure of the total power of light emitted, in that luminous flux is adjusted to reflect the varying sensitivity of the human eye to different wavelengths of...

will be detected by an eye
Human eye
The human eye is an organ which reacts to light for several purposes. As a conscious sense organ, the eye allows vision. Rod and cone cells in the retina allow conscious light perception and vision including color differentiation and the perception of depth...

looking at the surface from a particular angle of view. Luminance is thus an indicator of how bright
Brightness
Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light. In other words, brightness is the perception elicited by the luminance of a visual target...

the surface will appear. In this case, the solid angle of interest is the solid angle subtended by the eye's pupil
Pupil
The pupil is a hole located in the center of the iris of the eye that allows light to enter the retina. It appears black because most of the light entering the pupil is absorbed by the tissues inside the eye. In humans the pupil is round, but other species, such as some cats, have slit pupils. In...

. 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
Invariant (physics)
In mathematics and theoretical physics, an invariant is a property of a system which remains unchanged under some transformation.-Examples:In the current era, the immobility of polaris under the diurnal motion of the celestial sphere is a classical illustration of physical invariance.Another...

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
Illuminance
In photometry, illuminance is the total luminous flux incident on a surface, per unit area. It is a measure of the intensity of the incident light, wavelength-weighted by the luminosity function to correlate with human brightness perception. Similarly, luminous emittance is the luminous flux per...

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
Derivative
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...

where is the luminance (cd
Candela
The candela is the SI base unit of luminous intensity; that is, power emitted by a light source in a particular direction, weighted by the luminosity function . A common candle emits light with a luminous intensity of roughly one candela...

/m2
Square metre
The square metre or square meter is the SI derived unit of area, with symbol m2 . It is defined as the area of a square whose sides measure exactly one metre...

), is the luminous flux
Luminous flux
In photometry, luminous flux or luminous power is the measure of the perceived power of light. It differs from radiant flux, the measure of the total power of light emitted, in that luminous flux is adjusted to reflect the varying sensitivity of the human eye to different wavelengths of...

or luminous power (lm
Lumen (unit)
The lumen is the SI derived unit of luminous flux, a measure of the total "amount" of visible light emitted by a source. Luminous flux differs from power in that luminous flux measurements reflect the varying sensitivity of the human eye to different wavelengths of light, while radiant flux...

), is the angle
Angle
In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...

between the surface normal
Surface normal
A surface normal, or simply normal, to a flat surface is a vector that is perpendicular to that surface. A normal to a non-flat surface at a point P on the surface is a vector perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a...

and the specified direction, is the area
Area
Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...

of the surface (m2
Square metre
The square metre or square meter is the SI derived unit of area, with symbol m2 . It is defined as the area of a square whose sides measure exactly one metre...

), and is the solid angle
Solid angle
The solid angle, Ω, is the two-dimensional angle in three-dimensional space that an object subtends at a point. It is a measure of how large that object appears to an observer looking from that point...

(sr
The steradian is the SI unit of solid angle. It is used to describe two-dimensional angular spans in three-dimensional space, analogous to the way in which the radian describes angles in a plane...

).
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
Stilb (unit)
The stilb is the CGS unit of luminance for objects that are not self-luminous. It is equal to one candela per square centimeter or 104 nits . The name was coined by the French physicist André Blondel around 1920. It comes from the Greek word stilbein meaning "to glitter".It was in common use in...

(the CGS unit of luminance)
• π apostilb
Apostilb
The apostilb is an old unit of luminance, which was withdrawn from use in 1978. The SI unit of luminance is the candela per square metre . In 1942 it was proposed to rename the apostilb the blondel, after the French physicist André Blondel...

s
• π×10-4 lambert
Lambert (unit)
The lambert is a non-SI unit of luminance named for Johann Heinrich Lambert , a Swiss mathematician, physicist and astronomer. A related unit of luminance, the foot-lambert, is used in the lighting, cinema and flight simulation industries...

s
• 0.292 foot-lamberts

• Diffuse reflection
Diffuse reflection
Diffuse reflection is the reflection of light from a surface such that an incident ray is reflected at many angles rather than at just one angle as in the case of specular reflection...

• Etendue
Etendue
Etendue or étendue is a property of pencils of rays in an optical system, which characterizes how "spread out" light is in area and angle. It may also be seen as a volume in phase space....

• Exposure value
• Illuminance
Illuminance
In photometry, illuminance is the total luminous flux incident on a surface, per unit area. It is a measure of the intensity of the incident light, wavelength-weighted by the luminosity function to correlate with human brightness perception. Similarly, luminous emittance is the luminous flux per...

• Lambertian reflectance
Lambertian reflectance
If a surface exhibits Lambertian reflectance, light falling on it is scattered such that the apparent brightness of the surface to an observer is the same regardless of the observer's angle of view. More technically, the surface luminance is isotropic...

• Lightness
Lightness (color)
Lightness is a property of a color, or a dimension of a color space, that is defined in a way to reflect the subjective brightness perception of a color for humans along a lightness–darkness axis. A color's lightness also corresponds to its amplitude.Various color models have an explicit term for...

, property of a color
• Luma
Luma (video)
In video, luma, sometimes called luminance, represents the brightness in an image . Luma is typically paired with chrominance. Luma represents the achromatic image without any color, while the chroma components represent the color information...

, the representation of luminance in a video monitor
• Lumen (unit)
Lumen (unit)
The lumen is the SI derived unit of luminous flux, a measure of the total "amount" of visible light emitted by a source. Luminous flux differs from power in that luminous flux measurements reflect the varying sensitivity of the human eye to different wavelengths of light, while radiant flux...