Analytical expressions for characteristics of light scattering by arbitrarily shaped particles in the WKB approximation.

Light scattering in the Wentzel-Kramers-Brillouin (WKB) approximation is considered from the point of view of stereology. The extinction and absorption cross sections for an ensemble of chaotically oriented particles of arbitrary shape are expressed analytically through the chord length distribution. The analytical approximation for the scattering phase function is proposed. The derived analytical expressions are compared to the calculations with the discrete-dipole-approximation method.

Light scattering by optically soft large particles of arbitrary shape.

Light scattering by chaotically oriented optically soft large particles of arbitrary shape is considered within the framework of the Rayleigh-Gans approximation. It has been shown that outside the forward direction, the scattering pattern has the dependence of Δk⁻4(1+cos²Î¸), where is an average particle surface area, Δk is the difference between scattered and initial wave vectors, θ is the scattering angle, and this pattern is independent of particle shape. A simple approximating formula is suggested, which correctly describes the scattering pattern in the entire range of scattering angles. This formula is compared to the particular case of size-distributed spherical particles and is shown to have high accuracy. Also, it is shown that the inherent optical properties, as total, transport, and backward scattering coefficients, are determined by the specific particle surface area and the effective particle size.

Fraunhofer diffraction by a random screen.

The stochastic approach is applied to the problem of Fraunhofer diffraction by a random screen. The diffraction pattern is expressed through the random chord distribution. Two cases are considered: the sparse ensemble, where the interference between different obstacles can be neglected, and the densely packed ensemble, where this interference is to be taken into account. The solution is found for the general case and the analytical formulas are obtained for the Switzer model of a random screen, i.e., for the case of Markov statistics.

Approximation of the Fraunhofer diffraction peak, produced by particles of arbitrary shape.

A simple analytical formula is developed to describe light diffraction by chaotically oriented particles of arbitrary shape. The formula expresses the angular pattern through three well-defined microphysical characteristics of an ensemble: the average cross-sectional area, the average area squared, and the average length of the contour bordering the particle projection.

Fraunhofer diffraction by arbitrary-shaped obstacles.

We consider Fraunhofer diffraction by an ensemble of large arbitrary-shaped screens that are randomly oriented in the plane of a wavefront and have edges of arbitrary shape. It is shown that far outside the main diffraction peak the differential scattering cross section behaves asymptotically as theta(-3), where theta is the diffraction angle. Moreover, the differential scattering cross section depends only on the length of the contours bordering the screens and does not depend on the shape of the obstacles. As both strictly forward and total diffraction cross sections are specified by obstacle area only, the differential cross section of size-distributed obstacles is expected to be nearly independent of obstacle shape over the entire region of the diffraction angles.

Possibilities of warm cloud microstructure profiling with multiple-field-of-view Raman lidar.

The possibilities of cloud characteristics retrieval with multiple-field-of-view Raman lidar are considered. It has been shown that the Raman lidar return is sensitive to two cloud characteristics; the scattering coefficient and the effective droplet size. This sensitivity is studied and the optimal receiver fields-of-view (FOVs) for cloud sounding are recommended. The optimal FOV values are estimated to be approximately R/H (R, the collecting optics radius, H, the cloud altitude) to measure the scattering coefficient profiles, and approximately 0.01z/H for the droplet size measurements (z, the cloud thickness). The algorithm based on the iterative scheme and singular value decomposition as a regularization procedure is presented and verified using computer simulation. The recommendations for profile retrieval with variable altitude resolution are given.

Retrieving seawater-backscattering profiles from coupling Raman and elastic lidar data.

We propose a technique for retrieving seawater-backscattering profiles that is based on the joint use of elastic and Raman lidar returns. We suggest using two lidar channels: the Raman channel and the elastic channel with a light frequency equal to a half-sum of initial and Raman-shifted frequencies of the Raman channel. These specific wavelengths provide the same attenuation laws for elastic and Raman signals if absorption and scattering spectra can be approximated by a power law. In particular, seawater supplies such a possibility in the region of 400-500 nm if extremely bioproductive waters are not considered and the chlorophyll absorption peak at 440 nm does not come out of the background of dissolved organic matter absorption. With these specific initial wavelengths, the elastic and Raman lidar returns differ only in the backscattering coefficients. Because the Raman-backscattering coefficient is constant along the profile, the (elastic-to-Raman) ratio of these lidar returns directly produces the profile of the elastic-backscattering coefficient. This technique stays valid even under multiple-scattering conditions, which is of great importance for seawater sounding.

Analytical modeling of Raman lidar return, including multiple scattering.

An analytical approach to modeling Raman lidar return with multiple scattering in presented. This approach is based on a small-angle quasi-single-scattering approximation developed earlier for elastic lidar sounding. An approximation of isotropic backscattering for the Raman-scattering case is proposed and tested. The computed results are presented and compared with known data. The approximation was found to be quite simple and provided a high accuracy of Raman lidar return calculations.