# Radiant Exitance

Author: the photonics expert Dr. Rüdiger Paschotta

Definition: radiant flux emitted by a surface per unit area

Alternative term: radiant emittance

Category: light detection and characterization

Units: W/m^{2}, W/cm^{2}

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

DOI: 10.61835/wse Cite the article: BibTex plain textHTML 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 m^{2}, the radiant excitance is 1 μW / 1 mm^{2} = 1 W/m^{2}.

In the SI system, the units of the radiant exitance are W/m^{2} (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 / (m^{2} Hz) or W / (m^{2} 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:

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

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