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Книга Light Scattering Review 5 под редакцией Александра Кохановского, в которой одна из глав написана Будаком В.П, Клюйковым Д.А. и Коркиным С.В.
Статья JQSRT Benchmark results in vector atmospheric radiative transfer
Примеры реализации алгоритмов решения векторного уравнения переноса излучения с устранением особенностей решения вмсесте с анизотропной частью. C Будак В.П., Коркин С.В.
The spatial polarization distribution over the dome of the sky for abnormal irradiance of the atmosphere. JQSRT. Budak V.P., Korkin S.V.

Journal of Quantitative Spectroscopy & Radiative Transfer, 2008


The paper deals with the polarized radiative transfer within a slab irradiated by a collimated infinitely wide beam of arbitrary polarized light. The efficiency of the proposed analytical solution lies in the assumption that the complete vectorial radiative transfer solution is the superposition of the most anisotropic and smooth parts, computed separately. The vectorial small-angle modification of the spherical harmonics method is used to evaluate the anisotropic part, and the vectorial discrete ordinates method is used to obtain the smooth one. The azimuthal expansion is used in order to describe the light field spatial distribution for the case of abnormal irradiance and to obtain some known neutral points in the sky especially useful for polarized remote sensing of the atmosphere.
On the solution of a vectorial radiative transfer equation in an arbitrary three-dimensional turbid medium with anisotropic scattering. JQSRT. Budak V.P., Korkin S.V.

Journal of Quantitative Spectroscopy & Radiative Transfer, 2007


The authors developed a numerical method of the boundary-value problem solution in the vectorial radiative transfer theory applicable to the turbid media with an arbitrary three-dimensional geometry. The method is based on the solution representation as the sum of an anisotropic part that contains all the singularities of the exact solution and a smooth regular part. The regular part of the solution could be found numerically by the finite element method that enables to extend the approach to the arbitrary medium geometry. The anisotropic part of the solution is determined analytically by the special form of the small-angle approximation. The method development is performed by the examples of the boundary-value problems for the plane unidirectional and point isotropic sources in a turbid medium slab.
Моделирование пространственного распределения степени поляризации рассеянного атмосферой излучения на основании полного аналитического решения векторного уравнения переноса. Будак В.П., Коркин С.В.

Оптика атмосферы и океана, 2008
Mathematical model of the polarized light reflection by the turbid medium slab with an anisotropic scattering. Budak V.P., Korkin S.V. SPIE


The registration of the reflected radiation polarization at the remote sensing allows gaining all the information available to optical methods about the observed object. Mathematically it gives a boundary-value problem of the vectorial radiative transfer equation (VRTE). The natural media of the radiative transfer have strongly anisotropic light scattering. Because of their singularities the solution of the boundary-value problem of VRTE for such media is a mathematically illconditioned problem. The classical method (S.Chandrasekhar) of the elimination of this problem is based on the subtraction of the nonscattered component from the solution. However under the conditions of strong anisotropy a diffusion part is not distinguished enough from the nonscattered part that gives heavy oscillations in the numerical solution. In this paper it is offered to subtract from the required solution of VRTE its solution in a small angle approximation (SAA), which besides nonscattered component contains all the anisotropic part. The rest of the solution is a smooth function, which can be easily found by any numerical method. As SAA it is offered to take a small angle modification of a spherical harmonics method (MSH), presenting the generalization of Goudsmit-Saunderson's solution for the case of VRTE.
Обзор работы 5-го Международного симпозиума по дистанционному зондированию Азиатско-Тихоокеанского региона. Будак В.П., Коркин С.В.

Оптика атмосферы и океана, 2007.
The Computation of the Polarization Characteristics of the Scattered Solar Radiation in the Ocean. Budak V.P., Korkin S.V.

XVIII Ocean Optics Conference, 2006


We offer the generalization of the vectorial small angle modification of the spherical harmonics method (VMSH) for an arbitrary angle and polarization state of irradiance of a slab. Non diagonal elements of an aerosol scattering matrix were taken into account. The smooth addition part for the VMSH was given. Thus we obtained a complete and accelerated solution of the vectorial radiative transfer equa-tion. The suggested method was compared with Monte Carlo simulation, the single scattering approxi-mation and some scalar methods for the total intensity for different media including those ones with strongly anisotropy scattering typical of the ocean, that the main application field of the described method.

The vectorial radiative transfer equation problem in the small angle modification of the spherical harmonics method with the determination of the solution smooth part. Budak V.P., Korkin S.V. SPIE, 2006


The paper deals with the vectorial radiative transfer equation (VRTE) problem for a homogeneous strongly anisotropic scattering slab illuminated by a plain unidirectional source of light with an arbitrary angle of irradiance and polarization state. The problem is a theoretical base for the polarized satellite remote sensing (POLDER, PARASOL and others). The VRTE boundary problem decomposition allows reducing to the nonreflecting bottom with subsequent including its polarization properties. We give the complete analysis for the solution smooth non-small angle part for the vectorial small angle modification of the spherical harmonics method (VMSH) built upon the smoothness of the spatial spectrum of the light field distribution vector-function caused by mathematical singularities of the top-boundary condition for the VRTE boundary problem and the anisotropy of many natural scattering media (clouds, ocean). The VMSH itself is described as well.

The aerosol influence upon the polarization state of the atmosphere solar radiation. Budak V.P., Korkin S.V.
International Journal of Remote Sensing, 2008