An algorithm and codes for fast computations of the opposition effects in a semi-infinite discrete random medium

Abstract We present an algorithm and FORTRAN codes to compute the opposition effects in the reflection of light from a semi-infinite discrete random medium at normal incidence to the boundary of the medium. It is assumed that the medium is sparse enough that the waves propagating between the scatterers are spherical. In this case, the reflection matrix is determined only by contributions of the incoherent (diffuse) and coherent components. When calculating the coherent component, the contribution of the doubly scattered radiation to the reflection matrix is rigorously taken into account, while the contributions of the higher orders are calculated approximately. To be more specific, the multiply scattered radiation coming to some point of the medium “from above” is calculated exactly, but the radiation coming “from below”, approximately. Under this supposition, the solution of the system of integral equations is reduced to that of the system of linear algebraic equations. The matrix of this system is calculated with the recurrent relation, which radically speeds up the computations as compared to the direct procedure. This allows the opposition effect characteristics to be computed rapidly enough so that the codes may be used in interpretation of the remotely measured intensity and polarization of light reflected by different media to estimate, at least at a qualitative level, their properties.