光散射粒度测量中Mie理论两种改进的数值计算方法

Two Improved Numerical Algorithms of Mie Theory in the Particle Sizing by Light Scattering Method

本文提出了两种 Ｍｉｅ 散射程序算法：改进连分式方法和修正倒推法。改进连分式方法对 Ｌｅｎｔｚ 提出的连分式数值计算方法进行了改进，使 Ｍｉｅ 程序的计算范围大大拓宽：颗粒当量直径达到１０５ ，折射率虚部绝对值达到１０５ 。解决了以往一些算法不稳定的现象。修正倒推法在兼顾精度的同时，大大缩短了 Ｍｉｅ 程序的计算时间，是一种很实用的方法。从计算结果可以看出以上两种方法各有所长，适合应用在不同的场合。

Two improved Mie scattering numerical algorithms are presented in this paper, which are Improved Continued Fraction Method(ICFM) and Modified Downward Recurrence Method(MDRM). In ICFM, the Bessel function is calculated by using the way proposed by Lentz to broaden the calculative range very much: size parameter up to 10 5, the imaginary part of the refractive index large to 10 5. ICFM solves the problem of unstable recurrence. MDRM decreases the calculative time considerably and is a very practical method. According to results given in this paper, each method has its own advantage and is available in different cases.