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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: article belongs to category light detection and characterization light detection and characterization

Units: W/m², W/cm²

Formula symbol: <$M_\textrm{e}$>

DOI: 10.61835/wse Cite the article: BibTex plain text HTML Link to this page! LinkedIn

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 m², 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

$${L_{{\rm{e}},\Omega ,\nu }}(\nu ,T) = \frac{{2{\nu ^2}}}{{{c^2}}}\frac{{h\nu }}{{\exp (h\nu /{k_{\rm{B}}}T) - 1}} = \frac{{2h{\nu ^3}}}{{{c^2}}}\frac{1}{{\exp (h\nu /{k_{\rm{B}}}T) - 1}}$$

from which one can calculate the spectral exitance by integration over all solid angles of a hemisphere:

$${M_{{\rm{e}},\nu }}(\nu ,T) = \frac{{2\pi {\nu ^2}}}{{{c^2}}}\frac{{h\nu }}{{\exp (h\nu /{k_{\rm{B}}}T) - 1}}$$

If this is integrated over all frequencies, one obtains the Stefan–Boltzmann law for the radiant exitance of thermal radiation of a black body:

$${M_{\rm{e}}} = \frac{{2{\pi ^5}\;k_{\rm{B}}^4}}{{15\;{h^3}\;{c^2}}}\;{T^4} = \sigma \;{T^4}$$

with the Stefan–Boltzmann constant <$\sigma$> ≈ 5.6704 · 10⁻⁸ W m⁻² K⁻⁴.

More to Learn

Radiometry

Irradiance

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