Mie光散射理论的数值计算方法

Numerical calculation of Mie theory

  • 摘要: Mie散射级数的计算速度和精度对颗粒测量结果有着重要的影响。针对不同颗粒直径和相对折射率,一般采用前向递推,后向递推,连分式法等计算Mie散射级数。在这3种方法的基础上提出一种改进算法,即首先通过连分式法计算Mie散射级数的初始值,然后后向递推其余各值。该算法在Matlab中实现时,数据以数组的数据类型存储和调用,程序采用递归算法。通过比较计算结果发现,该算法耗时短且结果不易溢出,具有快速、稳定、不受颗粒直径和折射率范围影响等优点。

     

    Abstract: The Mie scattering theory is used to measure the particle size by light scattering. The calculation speed and precision of Mie scattering series are very important to the measurement results. Mie scattering series are calculated usually by forward recursion, backward recursion and link recursion for the different particle sizes and relative refractive indexes. The improved method based on the above mentioned three methods is reported, in which the initial value of Mie scattering series is calculated by continuous fractions and the others are calculated by backward recursion. The data are saved in the array data type and the program uses the recurrent method while the algorithm is realized in Matlab. The comparison of the results indicates that the calculation time is very short and the results are hard to overflow. Numerical calculation shows that the algorithm is efficient, reliable and robust in extremely wide range of particle size and refractive index.

     

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