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T-matrix method (EBCM)The T-matrix or transition matrix is well known in the quantum theory of scattering [56] where one also uses the Heisenberg S-matrix connected with the T-matrix by the relation![]() The analysis of the scattering characteristics of polydisperse ensembles of particles with random orientation needs two additional integrations - over size and orientation of scatterers and hence larger computational resources. Therefore, very important is the derivation of equations for the analytic orientational averaging of all physically interesting optical characteristics: the integral cross-sections and Mueller matrix [54,98,281,345,350,348], the extinction matrix of the transfer equation [344,348] and small-angle scattering flux [57,388]. Using the apparatus of the quantum theory of angular momentum we demonstrated that the equations for the orientational averaging of the T-matrix and its bilinear forms (and hence the physically observer quantities) do not depend on the particle nature and scattering waves [98,281]. In the works of M.I. Mishchenko [344] and L.E. Paramonov [59,60] (see also the references in [60]) this approach was generalized for disperse systems with ordered orientation of particles. The numerical algorithms built on the equations of the analytical orientational averaging were found to be the most efficient ones for the analysis of light scattering characteristics of ensembles of non-spherical particles with random orientation (see the works of Mishchenko's group at the NASA Goddard Institute for Space Studies [345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362] and also the papers [47,48,49,60,63,64,78,102,103] in Russian). The important advantage of the T-matrix method is its natural adaptation to the problems of the multi-scattering wave theory [331,468,469,511,471,480,481,482,485,486,487], radiative transfer equations [60,472,473], scattering by cluster of particles [195,353,354,355,362], particles of irregular shape [193] and Chebyshev T ![]() |