radiant exitance
{{short description|Radiant flux per unit area}}
In radiometry, radiant exitance or radiant emittance is the radiant flux emitted by a surface per unit area, whereas spectral exitance or spectral emittance is the radiant exitance of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. This is the emitted component of radiosity. The SI unit of radiant exitance is the watt per square metre ({{nobreak|W/m2}}), while that of spectral exitance in frequency is the watt per square metre per hertz (W·m−2·Hz−1) and that of spectral exitance in wavelength is the watt per square metre per metre (W·m−3)—commonly the watt per square metre per nanometre ({{nobreak|W·m−2·nm−1}}). The CGS unit erg per square centimeter per second ({{nobreak|erg·cm−2·s−1}}) is often used in astronomy. Radiant exitance is often called "intensity" in branches of physics other than radiometry, but in radiometry this usage leads to confusion with radiant intensity.
Mathematical definitions
=Radiant exitance=
Radiant exitance of a surface, denoted {{math|Me}} ("e" for "energetic", to avoid confusion with photometric quantities), is defined as{{cite web|url=https://www.iso.org/standard/82088.html|title=Thermal insulation — Heat transfer by radiation — Vocabulary|work=ISO_9288:2022|publisher=International Organization for Standardization|year=2022|accessdate=2023-06-17}}
where
{{math|∂}} is the partial derivative symbol,
{{math|Φe}} is the radiant flux emitted, and
{{mvar|A}} is the surface area.
The radiant flux received by a surface is called irradiance.
The radiant exitance of a black surface, according to the Stefan–Boltzmann law, is equal to:
where {{mvar|σ}} is the Stefan–Boltzmann constant, and {{mvar|T}} is the temperature of that surface.
For a real surface, the radiant exitance is equal to:
where {{mvar|ε}} is the emissivity of that surface.
=Spectral exitance=
Spectral exitance in frequency of a surface, denoted Me,ν, is defined as
:
where {{mvar|ν}} is the frequency.
Spectral exitance in wavelength of a surface, denoted Me,λ, is defined as
where {{mvar|λ}} is the wavelength.
The spectral exitance of a black surface around a given frequency or wavelength, according to Lambert's cosine law and Planck's law, is equal to:
:
\begin{align}
M_{\mathrm{e},\nu}^\circ & = \pi L_{\mathrm{e},\Omega,\nu}^\circ = \frac{2\pi h\nu^3}{c^2} \frac{1}{e^\frac{h\nu}{kT} - 1}, \\[8pt]
M_{\mathrm{e},\lambda}^\circ & = \pi L_{\mathrm{e},\Omega,\lambda}^\circ = \frac{2\pi hc^2}{\lambda^5} \frac{1}{e^\frac{hc}{\lambda kT} - 1},
\end{align}
where
{{mvar|h}} is the Planck constant,
{{mvar|ν}} is the frequency,
{{mvar|λ}} is the wavelength,
{{mvar|k}} is the Boltzmann constant,
{{mvar|c}} is the speed of light in the medium,
{{mvar|T}} is the temperature of that surface.
For a real surface, the spectral exitance is equal to:
\begin{align}
M_{\mathrm{e},\nu} & = \varepsilon M_{\mathrm{e},\nu}^\circ = \frac{2\pi h\varepsilon \nu^3}{c^2} \frac{1}{e^\frac{h\nu}{kT} - 1}, \\[8pt]
M_{\mathrm{e},\lambda} & = \varepsilon M_{\mathrm{e},\lambda}^\circ = \frac{2\pi h\varepsilon c^2}{\lambda^5} \frac{1}{e^\frac{hc}{\lambda kT} - 1}.
\end{align}
SI radiometry units
{{SI radiometry units}}
