The MIE scattering series and convergence acceleration

Abstract

In this thesis we present an algorithm for the precise determination of the Mie extinction efficiency parameter. The mathematical representation of the Mie parameters is in the form of an infinite series, and any technique that could be found to accelerate the convergence of the Mie series would have great commercial and military application. Results are presented that show the comparison of the rate of convergence obtained by directly summing the individual terms of the extinction efficiency parameter and the rate obtained using an existing series acceleration technique. It was found that the acceleration method we employed, known as the Levin method of series transformation, proved unsuccessful in accelerating the convergence of the Mie series. However, other acceleration techniques exist and should be explored. In this thesis we present an algorithm for the precise determination of the Mie extinction efficiency parameter. The mathematical representation of the Mie parameters is in the form of an infinite series, and any technique that could be found to accelerate the convergence of the Mie series would have great commercial and military application. Results are presented rate of convergence obtained by directly summing the individual terms of the extinction efficiency parameter and the rate obtained using an existing series acceleration technique. It was found that the acceleration method we employed, known as the Levin method of series transformation, proved unsuccessful in accelerating the convergence of the Mie series. However, other acceleration techniques exist and should be explored