Basic relation between received spectral power and sky brightness

The spectral power (infinitesimal power per unit frequency bandwidth) received from a solid angle of the sky on a surface of area is

$\displaystyle \ensuremath{dw}(\ensuremath{\theta_{},\phi_{}},\ensuremath{\nu}) ...
...phi_{}},\ensuremath{\nu})\,\cos \theta \,\ensuremath{d\Omega}\,\ensuremath{dA},$ (72)

where

$dw$ [ $\mathrm{W\,Hz^{-1}}$] spectral power,
$\theta$ [rad] angle between $d\Omega$ and Zenith,
$\phi$ [rad] angle between $d\Omega$ and East,
$\nu$ [Hz] frequency of observation,
$B_{}$ [ $\mathrm{W\,m^{-2}\,Hz^{-1}\,sr^{-1}}$] sky brightness at position ( $\theta_{},\phi_{}$) and frequency $\nu$,
$d\Omega$ [sr] infinitesimal solid angle of sky $(= \sin \theta\,d\theta\,d\phi)$,
$dA$ [ $\mathrm{m^{2}}$] infinitesimal surface area.