Quasi-isoplanatic radiation transfer through randomly moving particles

An iterative solution of an improved forward-scattering approximation for the radiative-transfer equation is derived. The narrow-angle approximation is useful for optical and acoustic beam propagation in the ocean and the atmosphere, where particle sizes are much larger than the wavelength. The improved narrow-angle approximation is useful for a cluster of anisotropic scatterers, and when the cluster is subjected to winds or currents. The solution of the derived equation is sought in terms of uniformly convergent iteration series via the two-scale embedding technique. The lowest iterative of the technique provides an approximate solution that differs from the commonly used successive substitution technique because it takes into account some of the multiple scattering terms. An example of wave propagation through randomly moving particles, useful for remote sensing, is considered