Scattering phase matrix for hexagonal ice crystals computed from ray optics

The scattering phase matrices for finite hexagonal cylinders oriented randomly in space were computed by superposing the scattered intensities of Fraunhofer diffracted rays and geometrical optics rays. However, the effect of interference is considered when the optical path lengths for two rays, split by some obstacle and scattered in the same direction, are equal to each other. Single models (c/a = 2.5 and 0.4) for a hexagonal column and a plate, resembling the corresponding crystals in atmospheric clouds, are used in the computations. Our results showed different values for the phase matrix elements, P33 and P44, from those obtained previously by Cai and Liou. The backscattering linear depolarization ratios and the asymmetry factor for hexagonal plates oriented horizontally were then computed. The backscattering linear depolarization ratios exceeded 1.0 at certain orientations. Within the limitation of the use of single-crystal models for a hexagonal column and a plate, the results appear to agree well with most field and laboratory observations.