Scattering on Bispheres

Abstract

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.