For the numerical solution of the radiative transfer equation (RTE) it is required its discretization based on the elimination of the solution anisotropic part and the replacement of the scattering integral by a finite sum. Regardless of the particular method of the RTE sampling the boundary value problem for a slab is transformed into the boundary value problem for the matrix inhomogeneous linear differential equation of the first order. The solution of this problem can be represented both through the solution of the homogeneous equation (propagator), and through the scatterers, possessing the property of invariance that leads to the Ambartsumian invariance principle. It is shown that the equivalence of all these approaches can improve the efficiency of the numerical radiative transfer modeling in the turbid medium slab. Significant acceleration of the RTE solution convergence can be achieved by using the method of synthetic iterations.

Date Published: 25 November 2014
PDF: 10 pages
Proc. SPIE 9292, 20th International Symposium on Atmospheric and Ocean Optics: Atmospheric Physics, 92920Y (25 November 2014); doi: 10.1117/12.2074692

Published in SPIE Proceedings Vol. 9292:
20th International Symposium on Atmospheric and Ocean Optics: Atmospheric Physics
Oleg A. Romanovskii, Editor(s)