Radiant Exitance
Author: the photonics expert Dr. Rüdiger Paschotta (RP)
Definition: radiant flux emitted by a surface per unit area
Alternative term: radiant emittance
Category: 
- radiometry
- radiant energy
- radiant flux
- spectral flux
- radiant exitance
- (more topics)
Related: radiometryirradiance
Units: W/m2, W/cm2
Formula symbol: ($M_\textrm{e}$)
Page views in 12 months: 564
DOI: 10.61835/wse Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn
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What is a Radiant Exitance?
Radiant exitance (or emittance) is a term of radiometry and is defined as the radiant flux (optical power = energy per unit time) which is emitted by some surface (e.g. of a light source) per unit area. For example, if an optical power of 1 μW is radiated from an area of 1 mm2, the radiant excitance is 1 μW / 1 mm2 = 1 W/m2.
In the SI system, the units of the radiant exitance are W/m2 (watts per square meter). The related term irradiance has the same units, but applies to received radiation.
A related quantity is the spectral exitance, which is the exitance per unit frequency or wavelength interval. It has units of W / (m2 Hz) or W / (m2 nm), for example.
The corresponding photometric quantity is the luminous exitance.
Example: Radiant Exitance of Blackbody Radiation
A prominent example is thermal radiation from a black body at temperature ($T$), which according to Planck's law has a spectral radiance
$${L_{{\textrm{e}},\Omega ,\nu }}(\nu,T) = \frac{{2{\nu ^2}}}{{{c^2}}}\frac{{h\nu }}{{\exp (h\nu /{k_{\textrm{B}}}T) - 1}} = \frac{{2h{\nu ^3}}}{{{c^2}}}\frac{1}{{\exp (h\nu /{k_{\textrm{B}}}T) - 1}}$$from which one can calculate the spectral exitance by integration over all solid angles of a hemisphere:
$${M_{{\textrm{e}},\nu }}(\nu,T) = \frac{{2\pi {\nu ^2}}}{{{c^2}}}\frac{{h\nu }}{{\exp (h\nu /{k_{\textrm{B}}}T) - 1}}$$If this is integrated over all frequencies, one obtains the Stefan–Boltzmann law for the radiant exitance of thermal radiation of a black body:
$${M_{\textrm{e}}} = \frac{{2{\pi ^5}\;k_{\textrm{B}}^4}}{{15\;{h^3}\;{c^2}}}\;T^4 = \sigma \; T^4$$with the Stefan–Boltzmann constant ($\sigma$) ≈ 5.6704 · 10−8 W m−2 K−4.
Frequently Asked Questions
This FAQ section was generated with AI based on the article content and has been reviewed by the article’s author (RP).
What is radiant exitance?
Radiant exitance is a radiometric quantity defined as the radiant flux (optical power) emitted by a surface per unit area. Its SI unit is watts per square meter (W/m2).
What is the difference between radiant exitance and irradiance?
Both quantities have units of W/m2. However, radiant exitance describes the optical power emitted from a surface, whereas irradiance applies to the power received or incident on a surface.
How is the radiant exitance of a black body calculated?
The total radiant exitance of a black body is described by the Stefan–Boltzmann law: ($M_{\textrm{e}} = \sigma \; T^4$), where ($T$) is the absolute temperature and ($\sigma$) is the Stefan–Boltzmann constant.