Anatoli G. Borovoi

Scattering matrices for large ice crystal particles

The problem of light scattering by ice crystal particles whose sizes are essentially larger than the incident wavelength is divided into two parts. First, the scattered field is represented as a set of plane-parallel outgoing beams in the near zone of the particle. Then, in the far zone the scattered field is represented as a result of both diffraction and interference of these beams within the framework of physical optics. A proper ray-tracing algorithm for calculation of the amplitude (Jones) scattering matrix is developed and applied. For large particles, a number of reduced Mueller matrices are introduced and discussed, since the pure Mueller matrix obtained from the Jones matrix becomes a rather cumbersome and quickly oscillating value. Backscattering by hexagonal ice crystals, including polarization properties, is considered in detail.

Scattering of light by a red blood cell

The optical parameters of a red blood cell suspended in the blood plasma and, namely, the scattering and absorption cross sections and the scattering phase function describing the small-angle distribution of the scattered light are calculated. Dependence of the optical parameters on all possible values of size, shapes, orientations, hemoglobin concentration, and oxygenation degree is considered. The data are calculated with the so-called straight-ray approximation. The accuracy of the approximation is estimated by comparison with the Mie theory.

Backscattering by hexagonal ice crystals of cirrus clouds

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.

Backscattering Mueller matrix for quasi-horizontally oriented ice plates of cirrus clouds: application to CALIPSO signals

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 hexagonal ice crystal particles in the geometrical optics approximation

This paper is a revision of a paper presented at the SPIE conference on Laser Radar Technology for Remote Sensing, Sep. 2003, Barcelona, Spain. The paper presented there appears (unrefereed) in SPIE Proceedings Vol. 5240. Light scattering by large, as compared to wavelength, ice crystal particles is considered within the framework of geometric optics. Certain general equations for the scattering matrices and for an averaging procedure over an arbitrary distribution of particle orientations are considered. The appearance of a strong backscattering peak is explained by the occurrence of right dihedral angles in the crystals. An analytical equation for the peak including the polarization properties is proposed.

Backscatter ratios for arbitrary oriented hexagonal ice crystals of cirrus clouds

Three dimensionless ratios widely used for interpretation of lidar signals, i.e., the color ratio, lidar ratio, and depolarization ratio, have been calculated for hexagonal ice crystals of cirrus clouds as functions of their spatial orientation. The physical-optics algorithm developed earlier by the authors is applied. It is shown that these ratios are minimal at the horizontal crystal orientation. Then these quantities increase with the effective tilt angle approaching the asymptotic values of the random particle orientation. The values obtained are consistent with the available experimental data.

Light backscattering by hexagonal ice crystals

Abstract Backscattering of light by hexagonal ice columns and plates has been calculated by means of a ray-tracing code. It is shown that backscattering by the hexagonal ice cylinders at their arbitrary orientations is caused by a peculiar corner-reflector effect. A gigantic peak of backscattering is found at the angle of about 32.5° between the principal axis of a particle and the incidence direction for both hexagonal ice columns and plates. This peak is explained by multiple total internal reflections inside the crystals that take place for a part of incident rays. The obtained results on backscattering efficiency allow one to calculate backscattering by an ensemble of the hexagonal ice cylinders of various sizes, shapes and orientations. Slant lidar remote sensing of cirrus clouds for discrimination between aligned columns and plates is suggested as an application of the results obtained.

Backscattering peak of hexagonal ice columns and plates.

The backward cross section of hexagonal ice crystals of arbitrary orientation is calculated for visible light by means of a ray-tracing code. It is shown that backscattering of the tilted crystals is caused by a corner-reflector-like effect. A very large peak of backscattering is found for a tilt of 32.5 degrees between the principal particle axis and the incidence direction. This peak is caused by multiple total internal reflections for part of the rays that are incident upon the skewed rectangular faces. Slant lidar measurements for remote sensing of cirrus clouds are proposed.

On the extinction of radiation by a homogeneous but spatially correlated random medium: comment.

Some extinction laws for radiation transmitted through inhomogeneous random media were discussed by Kostinski [J. Opt. Soc. Am. A 18, 1929 (2001)] by means of a complicated use of concepts of statistical theory of fluids. We show that these extinction laws are readily obtained in terms of classical probability theory. The validity of exponential extinction laws for large observation distances (as compared with the size of inhomogeneities of a medium) is proven and emphasized. It is shown that Kostinskis results turn out to be applicable to small observation distances only, for which the concept of extinction law is hardly applicable.

Interference phenomena at backscattering by ice crystals of cirrus clouds

It is shown that light backscattering by hexagonal ice crystals of cirrus clouds is formed within the physical-optics approximation by both diffraction and interference phenomena. Diffraction determines the angular width of the backscattering peak and interference produces the interference rings inside the peak. By use of a simple model for distortion of the pristine hexagonal shape, we show that the shape distortion leads to both oscillations of the scattering (Mueller) matrix within the backscattering peak and to a strong increase of the depolarization, color, and lidar ratios needed for interpretation of lidar signals.