Hemispherical spectral emissive power and total intensity

3 Hemispherical spectral emissive power and total intensity 

The spectral intensity Lx(X,f3,p,T) characterises in a detailed way the dependence of the energy emitted on the wavelength and direction. An important task of both theoretical and experimental investigations is to determine this distribution function for as many materials as possible. This is a difficult task to carry out, and it is normally satisfactory to just determine the radiation quantities that either combine the emissions into all directions of the hemisphere or the radiation over all wavelengths. The quantities, the hemispherical spectral emissive power Mx and the total intensity L, characterise the distribution of the radiative flux over the wavelengths or the directions in the hemisphere. 

The hemispherical spectral emissive power MX, T) is obtained by integrating (5.4) over all the solid angles in the hemisphere. This yields 

The integration in (5.6) over all the solid angles of the hemisphere corresponds to a double integration over the angular coordinates / and p. With du according to (5.3) we obtain 

In most cases, the spectral intensity Lx only depends on the polar angle j3 and not on the circumferential angle ip. We then obtain the more simple relationship 

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