Mie散射中递推方法的比较

Comparison of the Recursion Formula in Calculation of Mie Scattering

比较了Mie理论计算中的3个递推公式,既正向递推公式、倒递推公式和赵递推公式,分析了3个公式计算归一化消光截面、散射截面和后向散射截面的收敛性能,发现正向递推公式的3种散射截面当x较大时都会出现发散现象,而倒递推公式和赵递推公式都收敛,另外也分析了截断项数的容错性,分析表明赵递推公式对截断项数有最好的鲁棒性。通过上述分析,表明赵递推公式有着最广泛的适用范围与最准确的精度。

A comparison of three recursion formulae in the calculation of Mie scattering is made herein,namely the forward recursive formula,the backward recursive formula and Zhao recursive formula.The convergence performance of the three formulae for calculating the normalized extinction cross section,normalized scattering cross section and normalized backscatter cross section is analyzed.It is found that the three scattering cross sections of the forward recursion formula diverge when x is larger,and the results of the backward reverse recursion formula and Zhao recursion formula both converge.In addition,the fault tolerance of the truncated items is also analyzed.The analysis shows that Zhao recursive formula has the best robustness to the truncated items.Through the above analysis,it is shown that Zhao recursive formula has the widest applicable range and the most accurate precision.