Scattering on Bispheres

  • Tom RotherEmail author


Bisphere configurations are appropriate objects to introduce basic aspects of multiple scattering analysis. This chapter is therefore concerned with the derivation of the multiple scattering T-matrix equation and its iterative solution. The matrix of rotation and the separation matrix are the decisive elements of this method. They are used to accomplish the transformation of the scattered fields generated by each sphere in its local system. A simple approximation is presented that neglects any interaction between the spheres. It takes only the phase difference of the scattered fields into account that results from the different locations of the spheres. It is demonstrated afterwards that this simple approximation and the zero-order iteration of the rigorous T-matrix equation produce identical scattering cross-sections. It is moreover shown that already the first-order iteration produces quite accurate results for many practical applications, but especially if the bispheres are randomly oriented. This chapter ends with a description of the corresponding Python programs. Appendix  D provides a complete listing of these programs.

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  1. 1.
    Eyges, L.: Some nonseparable boundary value problems and the many-body problem. Ann. Phys. 2, 101–128 (1957)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Peterson, B.: Numerical computations of acoustic scattering from two spheres. Swedish Institute of Applied Mathematics, Sweden, Internal Report T.M.F. 73-2 (1973)Google Scholar
  3. 3.
    Kapodistrias, G., Dahl, P.H.: Effects of interaction between two bubble scatterers. JASA 107, 3006–3017 (2000)CrossRefGoogle Scholar
  4. 4.
    Gaunaurd, G.C., Huang, H., Strifors, H.C.: Acoustic scattering by a pair of spheres. JASA 98, 495–507 (1995)CrossRefGoogle Scholar
  5. 5.
    Martin, P.A.: Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles. Cambridge University Press, Cambridge (UK) (2006)CrossRefGoogle Scholar
  6. 6.
    Mishchenko, M.I., Mackowski, D.W., Travis, L.D.: Scattering of light by bispheres with touching and separated components. Appl. Opt. 34, 4589–4599 (1995)ADSCrossRefGoogle Scholar
  7. 7.
    Rother, T.: Green’s Functions in Classical Physics. Springer International Publishing AG, Cham, Switzerland (2017)CrossRefGoogle Scholar
  8. 8.
    Mishchenko, M.I., Mackowski, D.W.: Light scattering by randomly oriented bispheres. Opt. Lett. 19, 1604–1606 (1994)ADSCrossRefGoogle Scholar
  9. 9.
    van de Hulst, H.C.: Light Scattering by Small Particles. Dover, New York (1981)Google Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.German Aerospace CenterNeustrelitzGermany

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