Radiative wave and cyclical transfer equations for dense nontenuous media

In a dense medium, the discrete scatterers occupy an appreciable fractional volume. In a nontenuous medium, the index of refraction of the scatterers is significantly different from that of the background medium. In a dense nontenuous medium, the classical radiative-transfer theory, which is based on the assumption of independent scattering, is not valid. In this paper, a set of transfer equations has been derived for dense nontenuous media. The derivation is based on field theory under the quasi-crystalline approximation with coherent potential on the first moment of the field and the modified ladder approximation on the second moment of the field. These equations are called radiative wave equations. They include a summation of all the ladder terms and assume a form that is identical to the classical transfer equations. However, the relations of the extinction coefficient, the scattering coefficient, the albedo, and the phase functions to the physical parameters of the medium are modified to include the effects of dense media. Numerical solutions of the dense-media radiative wave equations are illustrated as a function of incident angles, scattered angles, and physical parameters of the medium. The backscattering-enhancement phenomenon is accounted for by a summation of the cyclical scattering terms into a cyclical transfer equation for dense nontenuous media. Numerical solutions of the cyclical transfer equation are also illustrated.