OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 49, Iss. 30 — Oct. 20, 2010
  • pp: 5746–5756

Case study about the accuracy behavior of three different T-matrix methods

Tom Rother and Jochen Wauer  »View Author Affiliations

Applied Optics, Vol. 49, Issue 30, pp. 5746-5756 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (1221 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



In this paper we discuss the influence of two different sets of weighting functions on the accuracy behavior of T-matrix calculations for scalar scattering problems. The first set of weighting functions is related to one of Waterman’s original approaches. The other set results into a least-squares scheme for the transmission problem. It is shown that both sets of weighting functions produce results with a converse accuracy behavior in the near and far fields. Additional information, such as reciprocity and the fulfillment of the boundary condition, are needed to choose the set of weighting functions that is most appropriate for a certain application. The obtained criteria are applied afterward to an iterative T-matrix approach we developed to analyze scattering on regular particle geometries with an impressed but slight surface irregularity. However, its usefulness is demonstrated in this paper by analyzing the far-field scattering behavior of Chebyshev particles of higher orders.

© 2010 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(290.0290) Scattering : Scattering
(290.5825) Scattering : Scattering theory

ToC Category:

Original Manuscript: August 16, 2010
Manuscript Accepted: September 9, 2010
Published: October 13, 2010

Tom Rother and Jochen Wauer, "Case study about the accuracy behavior of three different T-matrix methods," Appl. Opt. 49, 5746-5756 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. A. Wiscombe and A. Mugnai, “Single scattering from nonspherical Chebyshev particles: a compendium of calculations,” NASA Reference Publication 1157 (1986).
  2. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles(Cambridge University Press, 2002).
  3. A. G. Dallas, “On the convergence and numerical stability of the second Waterman scheme for approximation of the acoustic field scattered by a hard object,” Technical Report No. 2000-7(Department of Mathematical Sciences, University of Delaware, 2000).
  4. P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53, 805–812 (1965). [CrossRef]
  5. P. C. Waterman, “New formulation of acoustic scattering,” J. Acoust. Soc. Am. 45, 1417–1429 (1969). [CrossRef]
  6. T. Rother, K. Schmidt, J. Wauer, V. Shcherbakov, and J.-F. Gayet, “Light scattering on Chebyshev particles of higher order,” Appl. Opt. 45, 6030–6037 (2006). [CrossRef] [PubMed]
  7. T. Rother, Electromagnetic Wave Scattering on Nonspherical Particles: Basic Methodology and Simulations (Springer, 2009). [CrossRef]
  8. T. Rother, M. Kahnert, A. Doicu, and J. Wauer, “Surface Green’s function of the Helmholtz equation in spherical coordinates,” Prog. Electromagn. Res. 38, 47–95(2002). [CrossRef]
  9. P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990). [CrossRef]
  10. J. Wauer, K. Schmidt, T. Rother, T. Ernst, and M. Hess, “Two software tools for plane wave scattering on nonspherical particles in the German Aerospace Center’s virtual laboratory,” Appl. Opt. 43, 6371–6379 (2004). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited