7. Boundary conditions

Once the direction of propagation has been set, the radiative transfer equation is a hyperbolic partial differential equation. It is of degree one with respect to each of the spatial variables ( x , y , z in Cartesian coordinates) or, in terms of curvilinear abscissa, with respect to the s variable.

To integrate the RTE, we therefore need to know the value of the intensity emanating from the boundary where each optical path starts. Restricting ourselves to the case of opaque and diffuse walls (see the notes below remark 21), these are conditions of the form: