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Astrometry ; Space Sciences ; Archaeoastronomy and Astronomy in Culture
Uncontrolled Keywords:
radiative transfer ; diffuse reflection problem ; Ambartsumian’s nonlinear functional equation ; redistribution over frequencies and directions ; multidimensional eigenfunctions and eigenvalues problem
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Abstract:
The method introduced in the author’s two previous works is used to solve the problem of diffuse reflection from a semi-infinite plane-parallel scattering-absorbing medium in the general case of redistribution of radiation by frequencies and directions in an elementary act of scattering. A system of functional equations was obtained to determine the unknown eigenfunctions and eigenvalues. The initial problem of the six explanatory variables is explicitly expressed in terms of these eigenfunctions that depend only on three independent variables (dimensionless frequency, zenith angle, and azimuth).