Brightness temperature or radiance temperature is a measure of the intensity of electromagnetic energy coming from a source.
In particular, it is the temperature at which a
black body would have to be in order to duplicate the observed
intensity of a
grey body object at a frequency
.
This concept is used in
radio astronomy
Radio astronomy is a subfield of astronomy that studies Astronomical object, celestial objects using radio waves. It started in 1933, when Karl Jansky at Bell Telephone Laboratories reported radiation coming from the Milky Way. Subsequent observat ...
,
planetary science
Planetary science (or more rarely, planetology) is the scientific study of planets (including Earth), celestial bodies (such as moons, asteroids, comets) and planetary systems (in particular those of the Solar System) and the processes of ...
,
materials science
Materials science is an interdisciplinary field of researching and discovering materials. Materials engineering is an engineering field of finding uses for materials in other fields and industries.
The intellectual origins of materials sci ...
and
climatology
Climatology (from Greek , ''klima'', "slope"; and , '' -logia'') or climate science is the scientific study of Earth's climate, typically defined as weather conditions averaged over a period of at least 30 years. Climate concerns the atmospher ...
.
The brightness temperature provides "a more physically recognizable way to describe intensity".
When the electromagnetic radiation observed is
thermal radiation emitted by an object simply by virtue of its temperature, then the actual temperature of the object will always be equal to or higher than the brightness temperature.
Since the
emissivity is limited by 1, the brightness temperature is a lower bound of the object’s actual temperature.
For radiation emitted by a non-thermal source such as a pulsar, synchrotron, maser, or a laser, the brightness temperature may be far higher than the actual temperature of the source.
In this case, the brightness temperature is simply a measure of the intensity of the radiation as it would be measured at the origin of that radiation.
In some applications, the brightness temperature of a surface is determined by an optical measurement, for example using a
pyrometer, with the intention of determining the real temperature. As detailed below, the real temperature of a surface can in some cases be calculated by dividing the brightness temperature by the
emissivity of the surface. Since the emissivity is a value between 0 and 1, the real temperature will be greater than or equal to the brightness temperature. At high frequencies (short wavelengths) and low temperatures, the conversion must proceed through
Planck's law.
The brightness temperature is not a temperature as ordinarily understood. It characterizes radiation, and depending on the mechanism of radiation can differ considerably from the physical temperature of a radiating body (though it is theoretically possible to construct a device which will heat up by a source of radiation with some brightness temperature to the actual temperature equal to brightness temperature).
Nonthermal sources can have very high brightness temperatures. In
pulsars the brightness temperature can reach 10
30 K.
For the radiation of a
helium–neon laser with a power of 1 mW, a frequency spread Δf = 1 GHz, an output aperture of 1 mm, and a beam dispersion half-angle of 0.56 mrad, the brightness temperature would be .
For a black body,
Planck's law gives:
[Rybicki, George B., Lightman, Alan P., (2004) ''Radiative Processes in Astrophysics'', ]
where
(the
Intensity or Brightness) is the amount of
energy
Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...
emitted per unit
surface area
The surface area (symbol ''A'') of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the d ...
per unit time per unit
solid angle and in the frequency range between
and
;
is the
temperature
Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...
of the black body;
is the
Planck constant
The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...
;
is
frequency
Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
;
is the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...
; and
is the
Boltzmann constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative thermal energy of particles in a ideal gas, gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin (K) and the ...
.
For a grey body the
spectral radiance is a portion of the black body radiance, determined by the
emissivity .
That makes the reciprocal of the brightness temperature: