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The development of aerosol radiation scattering models for the purposes of remote sensing is related to the essential account of the polarization properties (the most complete) of the scattered radiation. The smoothness of the spatial spectrum of the light field distribution vector function caused by mathematical singularities of the boundary conditions for the vectorial radiative transfer equation (vectorial radiative transfer equation) boundary problem allows us to restrict the light-field general spherical functions expansion coefficients in a Taylor series with respect to a discrete zenith-number (the order) of the general spherical function to two terms. This gives relatively simple expressions for the matrix general spherical function expansion coefficients of the vectorial radiative transfer equation solution - the vectorial small angle modification of the spherical harmonics method (vectorially modified spherical harmonics). The subsequent determination of the solution smooth non-small angle part using the boundary problem for the vectorial radiative transfer equation with the vectorially modified spherical harmonics as the source function gives the complete solution to the vectorial radiative transfer equation and prevents some calculation problems caused by ill conditions of the matrices.