In
radiometry
Radiometry is a set of techniques for measurement, measuring electromagnetic radiation, including visible light. Radiometric techniques in optics characterize the distribution of the radiation's power (physics), power in space, as opposed to phot ...
, radiance is the
radiant flux
In radiometry, radiant flux or radiant power is the radiant energy emitted, reflected, transmitted, or received per unit time, and spectral flux or spectral power is the radiant flux per unit frequency or wavelength, depending on whether the Spec ...
emitted, reflected, transmitted or received by a given surface, per unit
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 poi ...
per unit projected area. Radiance is used to characterize diffuse emission and
reflection Reflection or reflexion may refer to:
Science and technology
* Reflection (physics), a common wave phenomenon
** Specular reflection, reflection from a smooth surface
*** Mirror image, a reflection in a mirror or in water
** Signal reflection, in s ...
of
electromagnetic radiation
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...
, and to quantify emission of
neutrino
A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...
s and other particles. The
SI unit of radiance is the
watt
The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James Wa ...
per
steradian per
square metre
The square metre ( international spelling as used by the International Bureau of Weights and Measures) or square meter (American spelling) is the unit of area in the International System of Units (SI) with symbol m2. It is the area of a square w ...
(). It is a ''directional'' quantity: the radiance of a surface depends on the direction from which it is being observed.
The related quantity
spectral radiance is the radiance of a surface per unit
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
or
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
, depending on whether the
spectrum
A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...
is taken as a function of frequency or of wavelength.
Historically, radiance was called "intensity" and spectral radiance was called "specific intensity". Many fields still use this nomenclature. It is especially dominant in
heat transfer
Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, ...
,
astrophysics
Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the h ...
and
astronomy
Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
. "Intensity" has many other meanings in
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, with the most common being
power per unit area.
Description
![photometry_radiometry_units](https://upload.wikimedia.org/wikipedia/commons/c/c6/Photometry_radiometry_units.svg)
Radiance is useful because it indicates how much of the power emitted, reflected, transmitted or received by a surface will be received by an optical system looking at that surface from a specified angle of view. In this case, the solid angle of interest is the solid angle subtended by the optical system's
entrance pupil
In an optical system, the entrance pupil is the optical image of the physical aperture stop, as 'seen' through the front (the object side) of the lens system. The corresponding image of the aperture as seen through the back of the lens system is ...
. Since the
eye
Eyes are organs of the visual system. They provide living organisms with vision, the ability to receive and process visual detail, as well as enabling several photo response functions that are independent of vision. Eyes detect light and conv ...
is an optical system, radiance and its cousin
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 from, or is reflected from a particular area, and falls withi ...
are good indicators of how bright an object will appear. For this reason, radiance and luminance are both sometimes called "brightness". This usage is now discouraged (see the article
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 perception is not linear to luminance, ...
for a discussion). The nonstandard usage of "brightness" for "radiance" persists in some fields, notably
laser physics.
The radiance divided by the index of refraction squared is
invariant
Invariant and invariance may refer to:
Computer science
* Invariant (computer science), an expression whose value doesn't change during program execution
** Loop invariant, a property of a program loop that is true before (and after) each iteratio ...
in
geometric optics. This means that for an ideal optical system in air, the radiance at the output is the same as the input radiance. This is sometimes called ''conservation of radiance''. For real, passive, optical systems, the output radiance is ''at most'' equal to the input, unless the index of refraction changes. As an example, if you form a demagnified image with a lens, the optical power is concentrated into a smaller area, so the
irradiance In radiometry, irradiance is the radiant flux ''received'' by a ''surface'' per unit area. The SI unit of irradiance is the watt per square metre (W⋅m−2). The CGS unit erg per square centimetre per second (erg⋅cm−2⋅s−1) is often used ...
is higher at the image. The light at the image plane, however, fills a larger solid angle so the radiance comes out to be the same assuming there is no loss at the lens.
Spectral radiance expresses radiance as a function of frequency or wavelength. Radiance is the integral of the spectral radiance over all frequencies or wavelengths. For radiation emitted by the surface of an ideal
black body at a given temperature, spectral radiance is governed by
Planck's law
In physics, Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature , when there is no net flow of matter or energy between the body and its environment.
At ...
, while the integral of its radiance, over the hemisphere into which its surface radiates, is given by the
Stefan–Boltzmann law. Its surface is
Lambertian, so that its radiance is uniform with respect to angle of view, and is simply the Stefan–Boltzmann integral divided by π. This factor is obtained from the solid angle 2π steradians of a hemisphere decreased by
integration over the cosine of the zenith angle.
Mathematical definitions
Radiance
Radiance of a ''surface'', denoted ''L''
e,Ω ("e" for "energetic", to avoid confusion with photometric quantities, and "Ω" to indicate this is a directional quantity), is defined as
:
where
*∂ is the
partial derivative
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Part ...
symbol;
*Φ
e is the
radiant flux
In radiometry, radiant flux or radiant power is the radiant energy emitted, reflected, transmitted, or received per unit time, and spectral flux or spectral power is the radiant flux per unit frequency or wavelength, depending on whether the Spec ...
emitted, reflected, transmitted or received;
*Ω is the
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 poi ...
;
*''A'' cos ''θ'' is the ''projected'' area.
In general ''L''
e,Ω is a function of viewing direction, depending on ''θ'' through cos ''θ'' and
azimuth angle
An azimuth (; from ar, اَلسُّمُوت, as-sumūt, the directions) is an angular measurement in a spherical coordinate system. More specifically, it is the horizontal angle from a cardinal direction, most commonly north.
Mathematically, ...
through . For the special case of a
Lambertian surface
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 ...
, is proportional to cos ''θ'', and ''L''
e,Ω is isotropic (independent of viewing direction).
When calculating the radiance emitted by a source, ''A'' refers to an area on the surface of the source, and Ω to the solid angle into which the light is emitted. When calculating radiance received by a detector, ''A'' refers to an area on the surface of the detector and Ω to the solid angle subtended by the source as viewed from that detector. When radiance is conserved, as discussed above, the radiance emitted by a source is the same as that received by a detector observing it.
Spectral radiance
Spectral radiance in frequency of a ''surface'', denoted ''L''
e,Ω,ν, is defined as
:
where ''ν'' is the frequency.
Spectral radiance in wavelength of a ''surface'', denoted ''L''
e,Ω,λ, is defined as
:
where ''λ'' is the wavelength.
Conservation of basic radiance
Radiance of a surface is related to
étendue
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 include a ...
by
:
where
*''n'' is the
refractive index
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 ...
in which that surface is immersed;
*''G'' is the étendue of the light beam.
As the light travels through an ideal optical system, both the étendue and the radiant flux are conserved. Therefore, ''basic radiance'' defined by
[William Ross McCluney, ''Introduction to Radiometry and Photometry'', Artech House, Boston, MA, 1994 ]
:
is also conserved. In real systems, the étendue may increase (for example due to scattering) or the radiant flux may decrease (for example due to absorption) and, therefore, basic radiance may decrease. However, étendue may not decrease and radiant flux may not increase and, therefore, basic radiance may not increase.
SI radiometry units
See also
*
Étendue
*
Light field
*
Sakuma–Hattori equation The Sakuma–Hattori equation is a mathematical model for predicting the amount of thermal radiation, radiometric flux or radiometric power emitted from a perfect blackbody or received by a thermal radiation detector.
History
The Sakuma–Hattori ...
*
Wien displacement law
Wien's displacement law states that the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature. The shift of that peak is a direct consequence of the Planck ...
References
{{reflist
External links
International Lighting in Controlled Environments Workshop
Physical quantities
Radiometry