An investigation of the ability of modified radiative transfer equations to accommodate laws of geometrical optics

The radiative transfer equation (RTE) and its approximations are widely used for describing light propagation in biological tissues. However, the RTE is valid for media with constant refractive indices, an assumption that does not hold in many practical situations. Recently three RTEs for media with spatially varying refractive index (RTEvri) have been proposed to eliminate that limitation. In this paper we test the RTE and the new RTEvris, applying them to solve two problems of geometrical optics with well-known solutions. We show that only one of those equations gives solutions consistent with the laws of geometrical optics due to its ability to model the effect of spatially varying refractive index and non-negligible ray divergence. This process allows us to determine which RTEvri provides the best description of light propagation in turbid media with spatially varying refractive index and a link between the radiative transfer theory and geometrical optics.