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Advances in Mathematical Physics
Volume 2017, Article ID 7862462, 7 pages
Research Article

Analysis of Waterman’s Method in the Case of Layered Scatterers

1St. Petersburg State University of Aerospace Instrumentation, Bol. Morskaya 67, St. Petersburg 190000, Russia
2St. Petersburg University, Universitetsky Pr. 28, St. Petersburg 198504, Russia
3Pulkovo observatory, Pulkovskoe Sh. 65/1, St. Petersburg 196140, Russia

Correspondence should be addressed to Vladimir Il’in; ur.ubps@nili.b.v

Received 6 September 2016; Accepted 21 December 2016; Published 16 January 2017

Academic Editor: Antonio Scarfone

Copyright © 2017 Victor Farafonov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The method suggested by Waterman has been widely used in the last years to solve various light scattering problems. We analyze the mathematical foundations of this method when it is applied to layered nonspherical (axisymmetric) particles in the electrostatic case. We formulate the conditions under which Waterman’s method is applicable, that is, when it gives an infinite system of linear algebraic equations relative to the unknown coefficients of the field expansions which is solvable (i.e., the inverse matrix exists) and solutions of the truncated systems used in calculations converge to the solution of the infinite system. The conditions obtained are shown to agree with results of numerical computations. Keeping in mind the strong similarity of the electrostatic and light scattering cases and the agreement of our conclusions with the numerical calculations available for homogeneous and layered scatterers, we suggest that our results are valid for light scattering as well.