Radiance is the derivative of radiative flux at the angle and projected surface section S\cos\theta

equation

The spectral radiance L_{\Omega,
u} is the energy per area of the photons of frequency
u emitted at a solid angle d\Omega.

If the spectral radiance is integrated in the frequency, the total radiance is obtained:

equation

The integration of the radiance L on the solid angle d\Omega gives us the radiative flux \Phi

equation

The radiative flux is the radiative energy that by time is irradiated:

equation

The radiative intensity is the radiative flux per element of solid angle:

equation

The photon transport equation is

equation

where \mu_t is the absorption coefficient and scattering, c the velocity of light, P(\hat{n}',\hat{n}) is the phase function that gives the probability that a photon traveling in the direction \hat{n} is deflected in the direction \hat{n}'.

For the case in which they are considered uniformly distributed thermal photons their number per cell will be according to the distribution of Bose-Einstein

\displaystyle\frac{1}{e^{\hbar\omega/kT} -1}

where \hbar is the Planck constant divided by 2\pi, \omega is the angular velocity, k the Boltzmann constant, and T the temperature.

If the flow is isotropic it will be necessary that the $ m components will be equal and therefore:

equation