Transport of the mutual coherence functions and the intensity of a backscattered pulse in a random medium

Starting with a Helmholtz wave equation, the transport equations for the coherent and incoherent parts of the two-frequency two-position mutual coherence function in the transform domain can be derived. These equations have their respective analogs in the conventional radiative transfer theory. By solving the equations for the coherent part and the incoherent part, the incoherent scattered intensity is expressed as an infinite series, each term of which can be interpreted as an 'nth order' scattered contribution. A procedure is given to compute the effective wavenumber and the total cross section, starting from a proper form of the mean Green's function. The intensity of a backscattered pulse is next investigated. A series expression is obtained. In order to be able to localize the position of pulse returns, 'higher order' scattering terms must not be important when compared with the 'single' scattered pulse. Numerical examples, applicable to the microwave scattering, show that the backscattered intensity is reduced when it is compared with the Booker-Gordon formula, even when the mean-square dielectric fluctuation is very small. This reduction is attributed to the multiple scattering effects, especially the multiple large-angle scatterings.