spectral-total directional emissivity

[] ϵ(θ,φ,T), (at a point on the surface of a thermal radiator and in a given direction)
The ratio of the radiance of the thermal radiator at temperature T, at the point and in the given direction, to that of a blackbody (bb) at the same temperature T.

\epsilon \left ( x,y,\theta ,\phi ,T \right )= L\left ( x,y,\theta ,\phi ,T \right )/L_{bb}\left ( T \right )

x, y = the coordinates of the point and θ, φ defines the direction

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