MIE Scattering Theory for Particle Sizing Interferometry with the Dual Beam Laser Velocimeter.

摘要

An analytical solution for the light scattered by a sphere located in the cross over region of two laser beams is developed to allow computation of the visibility parameter for in situ particle sizing. The solution provides for evaluation of the visibility particle sizing concept for application to high temperature coal-fired magnetohydrodynamic electrical power generation. The solution is very general since it is applicable to laser beams with any desired wavelength, propagation directions and polarization orientations and to light collecting apertures of any size and location. Therefore, the solution provides for comparative selection of optical configurations for optimal implementation of the visibility particle sizing technique in the severe environment of coal-fired magnetohydrodynamics. The visibility solution is developed from a detailed solution of the Mie theory scattering problem obtained by using the vector multipole field method. Group theory is used to develop a generalized expression of the Mie solution for coordinate systems rotated with respect to the coordinates of the laser beam as conventionally chosen for the Mie problem. Explicit expressions for expansion coefficients of the generalized Mie solution expression are given which allow the coefficients to be obtained from recursion relations for associated Legendre functions, thus avoiding evaluation of Jacobi polynomials or hypergeometric series. In addition, a numerical integration algorithm for the computer calculation of visibility parameter is developed for the particle sizing interferometer (PSI) with a circular light collecting aperture. (ERA citation 08:023773)