When a photon beam of radiance \(L_{\lambda}\) and angular distribution \(\mathit{\Omega}\) passes along a single direction of propagation through a medium, which is totally absorbing and/or scattering, i.e., the processes occurring are described by the following equation: \[\begin{array} \\ \frac{{\rm{d}}L_{\Omega,\lambda}(\boldsymbol{x},t)}{{\rm{d}}s} + \underbrace{\alpha_{\lambda}(\boldsymbol{x},t) L_{\mathit{\Omega},\lambda}(\boldsymbol{x},t)}_{\rm{adsorption}} + \underbrace{\sigma_{\lambda}(\boldsymbol{x},t) L_{\mathit{\Omega},\lambda}(\boldsymbol{x},t)}_{\rm{out\mbox{-}scattering}} = \\ \underbrace{j_{\lambda}(\boldsymbol{x},t)}_{\rm{emission}} + \underbrace{\frac{\sigma_{\lambda}(\boldsymbol{x},t)}{4\pi}B_{\lambda}(\mathit{\Omega}' \to \mathit{\Omega}) L_{\mathit{\Omega},\lambda}(\boldsymbol{x},t){\rm{d}}\mathit{\Omega}'}_{\rm{in\mbox{-}scattering}} \end{array}\] where \(\frac{{\rm{d}}L_{\Omega,\lambda}(\boldsymbol{x},t)}{{\rm{d}}s}\) is the directional derivative along the direction \(s\) at a point \(\boldsymbol{x}\) in the reaction space of the incident radiance, \(\alpha_{\lambda}(\boldsymbol{x},t)\) is the space- and time-dependent spectral linear napierian absorption coefficient, \(\sigma_{\lambda}(\boldsymbol{x},t)\) is the space- and time-dependent spectral linear napierian scattering coefficient, \(j_{\lambda}(\boldsymbol{x},t)\) represents the spontaneous and/or induced emission, and \(B_{\lambda}\) is the phase function. All quantities are a function of time. The RTE is written for the direction \(s\).