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Backscattering Mueller matrix and the depolarization and color ratios for quasi-horizontally oriented hexagonal ice plates have been calculated within the framework of the physical optics approximation. In the case of a tilted lidar, the dependence of the color and depolarization ratios on polarization of the incident light has been analyzed. It is shown that the corner reflection effect inherent to the pristine hexagonal ice crystals results in sharp peaks of both the backscattering cross section and depolarization ratio at the lidar tilts of about 30° off zenith. The experimental results obtained recently by Veselovskii et al. [13] at the lidar tilt of 43° have been interpreted as a partial manifestation of the corner reflection effect. The retrieval of the vertical profile of the ice crystal fraction consisting of quasi-horizontally oriented hexagonal plates has been demonstrated. [ABSTRACT FROM AUTHOR]

Abstract: Scattering matrices for horizontally oriented ice crystals are calculated with a code based on the geometric optics. The main physical regularities inherent to the scattering matrices are discussed. Degree of polarization of the scattered light is shown to be a qualitative criterion of number of photon trajectories that contribute effectively to the scattered light. The inverse scattering problem of retrieving aspect ratios of the horizontally oriented hexagonal ice plates from polarization of the scattered light in the bistatic sounding scheme has been proposed and discussed. [Copyright &y& Elsevier]

The physical optics approximations are derived from the Maxwell equations. The scattered field equations by Kirchhoff, Stratton-Chu, Kottler and Franz are compared and discussed. It is shown that in the case of faceted particles, these equations reduce to a sum of the diffraction integrals, where every diffraction integral is associated with one plane–parallel optical beam leaving a particle facet. In the far zone, these diffraction integrals correspond to the Fraunhofer diffraction patterns. The paper discusses the E-, M- and (E, M)-diffraction theories as applied to ice crystals of cirrus clouds. The comparison to the exact solution obtained by the discontinuous Galerkin time domain method shows that the Kirchhoff diffraction theory is preferable. [ABSTRACT FROM AUTHOR]

The open-source beam-splitting code is described which implements the geometric-optics approximation to light scattering by convex faceted particles. This code is written in C++ as a library which can be easy applied to a particular light scattering problem. The code uses only standard components, that makes it to be a cross-platform solution and provides its compatibility to popular Integrated Development Environments (IDE׳s). The included example of solving the light scattering by a randomly oriented ice crystal is written using Qt 5.1, consequently it is a cross-platform solution, too. Both physical and computational aspects of the beam-splitting algorithm are discussed. Computational speed of the beam-splitting code is obviously higher compared to the conventional ray-tracing codes. A comparison of the phase matrix as computed by our code with the ray-tracing code by A. Macke shows excellent agreement. [ABSTRACT FROM AUTHOR]