A generalized Mie theory solution and its application to particle sizing interferometry

A detailed solution of the Mie theory scattering problem is obtained by using the vector multipole field method. Group theory is then used to develop a generalized expression of the solution for coordinate systems rotated with respect to the conventionally chosen system of the Mie problem. Explicit expressions for expansion coefficients of this expression are given which allow the coefficients to be obtained from recursion relations for associated Legendre functions. The evaluation of Jacobi polynomials or hypergeometric series is thereby avoided.

An analytical series solution for the power scattered into a conical solid angle centered on any chosen direction from the scattering particle is obtained by an application of the generalized Mie solution. Application of this technique to a sphere scattering light from two crossed laser beams gives analytical series which allow computation of the visibility parameter for particle sizing. This solution is very general since the beams can have any desired polarization orientations and propagation directions and the aperture can have any size and location. Specialization to several configurations is considered.

A numerical integration algorithm for the computer calculation of interferometric visibility is developed for the particle sizing interferometer (PSI) with circular light collecting aperture. This algorithm uses orthogonal matrix transformations of the conventional Mie equations and allows unrestricted choice of aperture location. Some results obtained with a code based on this algorithm are compared with results originally obtained by other researchers using the diffraction and refraction theories. Symmetries are shown to exist which may be exploited to achieve significant reductions in computer time, and it is shown that symmetry results can provide some indication of the aperture locations which are useful for spherical particle sizing with the visibility method.