Optical wave propagation in discrete random media with large particles: a treatment of the phase function

A treatment of the phase function in the radiative transfer equation is discussed for describing optical wave propagation in discrete random media with large particles. Unlike the conventional small-angle approximation, the phase function is normalized so that half of the scattered power is removed from a small angle in the forward direction for large particles with the refractive index not close to unity. With this normalization, an improved small-angle solution of the radiative transfer equation is given for the phase function adopted here. The validity of the proposed theory is confirmed by comparisons with both numerical solutions and experimental data on the attenuation of millimeter and optical waves in rain.