Light transfer problem in turbid media with surface reflectivity

Light transfer problems in turbid media with surface reflectivity satisfying Fresnel's law are formulated. The intensity of light is considered as a sum of collimated and diffuse radiances. The problem with a collimated source and boundary conditions with surface reflectivity is solved in terms of the corresponding source-free problem with simple boundary conditions. In order to solve the source-free problem, two-flux models in the differential and integral forms are obtained. For the differential form, weight functions are introduced in order to force the boundary conditions to be met, while in the integral form the boundary conditions are embedded. The integral form has the advantage over the differential form that it permits one to extend the validity of the model and to consider inhomogeneous media. Numerical results are given for albedos and partial fluxes depending upon the refractive index of the medium. The calculations are performed in both semi-infinite and finite media and are compared with the published calculations.