spectral-hemispherical emissivity

[] ε(λ,T ) (of an element of surface of an opaque temperature radiator that has an optical smooth surface)
The ratio of its spectral radiant exitance to that of a blackbody at the same temperature:

\epsilon \left ( \lambda ,T \right )=\left ( 1/\pi \right )\int _{2\pi} \epsilon \left ( \lambda ,\theta ,\phi ,T \right ) cos \theta \cdot d\omega

= \equiv M_{\lambda }\left ( \lambda ,T \right )/M{_{\lambda, blackbody}}\left ( \lambda \sqrt{T} \right )

Note: Hemispherical emissivity is frequently called “total” emissivity. “Total” by itself is ambiguous and should be avoided since it may also refer to “spectral-total” (all wavelengths) as well as “directional-total” (all directions). (See Section, spectral-total hemispherical emissivity.)

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