Invariance properties of exact solutions of the radiative transfer equation. (December 2021) - Martelli, Fabrizio; Tommasi, Federico; Fini, Lorenzo; Cortese, Lorenzo; Sassaroli, Angelo; Cavalieri, Stefano
Highlights: Invariance properties hold for all RTE solutions under uniform Lambertian illumination. Lambertian illumination offers a unique reference standard for forward computational codes. Uniform and isotropic radiance is the physical insight at the ground of the invariance property. A Lambertian surface exists in a non-absorbing medium subjected to uniform isotropic radiance. Abstract: In this work, special invariance properties of a class of exact solutions of the radiative transfer equation (RTE) pertaining to a uniform Lambertian illumination of any non-absorbing homogeneous and inhomogeneous volume are presented and discussed. This class of solutions of the RTE traces a reference ground under which light propagation can be studied in a special simplified regime. Despite the difficulties to obtain general solutions of the radiative transfer equation, the condition of Lambertian illumination determines a unique regime of photon transport where quite easy and simple invariant solutions can be obtained in all generality for homogeneous and inhomogeneous geometries. These solutions are invariant both with respect to the geometry (size and shape of the volume) and with respect to the scattering properties, i.e. scattering coefficient, scattering function and homogeneity of the considered domain. Another evident advantage of these solutions is that they are exact solutions known with arbitrary precision and can thus be used as reference standard for photon migration studies.