A general view of the backscattering Mueller matrix for the quasi-horizontally oriented hexagonal ice crystals of cirrus clouds has been obtained in the case of tilted and scanning lidars. It is shown that the main properties of this matrix are caused by contributions from two qualitatively different components referred to the specular and corner-reflection terms. The numerical calculation of the matrix is worked out in the physical optics approximation. These matrices calculated for two wavelengths and two tilt angles (initial and present) of CALIPSO lidar are presented as a data bank. The depolarization and color ratios for these data have been obtained and discussed.

Light backscattering by randomly oriented hexagonal ice crystals of cirrus clouds is considered within the framework of the physical-optics approximation. The fine angular structure of all elements of the Mueller matrix in the vicinity of the exact backward direction is first calculated and discussed. In particular, an approximate equation for the differential scattering cross section is obtained. Its simple spectral dependence is discussed. Also, a hollow of the linear depolarization ratio around the exact backward direction inherent to the long hexagonal columns is revealed.

The backscattering reciprocity theorem is considered for large particles as compared with the incident wavelength particles of arbitrary shape. It is shown that, in the specific case of faceted particles, this theorem is provided by the appearance of pairs of conjugate backscattered beams. A parameter characterizing a deviation of any approximation from the reciprocity theorem is proposed, and it is used for estimation of reliability for the physical-optics approximation.

Matrices of light scattering on a truncated plate-like droxtal oriented preferably in a horizontal plane have been calculated in the geometrical optics approximation. New halos are shown to appear...