Modelling diffraction during ray tracing using the concept of energy flow lines

The ray-tracing with diffraction on facets (RTDF) model is suitable for rapid computation of scattering on faceted dielectric objects such as ice crystals. It combines ray tracing with diffraction on flat facets. The model calculates diffraction using an approximation for the far-field direction of the Poynting vector. In this paper, an estimate based on an approximation by Prosser for the electric and magnetic fields describing diffraction at a slit is used to calculate energy flow lines and their far-field deflection angles. Best-fit formulas describing the dependence of the far-field deflection angle on the size parameter, angle of incidence and the position of the flow line in the plane of the slit are derived and incorporated into the RTDF model. Phase functions for hexagonal columns are presented and compared with an analytic technique, the separation of variables method, and geometric optics with projected area diffraction.