多弥散体散射光强的一种简化计算分析

A SIMPLIFIED ANALYSIS AND COMPUTATION OF THE SCATTERING INTENSITY OF A POLYDISPERSOIN

本文提出了以计算多弥散体散射光强分布的一种递推公式,目的在于减少对Mic 系数 a_1、b_1和π_1、τ_1的计算工作量.计算了几种散射截面,其结果与有关文献的数据符合很好.计算中发现,Mic 无穷级数的收敛性与微粒的相对折射率的关系不明显,但与无因次直径α有关.并得出相对散射光强 I/I_0-散射角θ、无因次直径α及相对折射率 m 的三组曲线,其中,把根据 Fraunhofer 衍射理论计算的曲线与根据 Mic 散射理论计算的曲线作了比较,可以看出,当用 Fraunhofer 衍射理论代替 Mic 散射理论处理散射问题时,是可以找到参数(θ、α、m)的适用范围的,并且能确定其误差的大小.

In this paper new recurrence relations are proposed to calculate the distribution of scattering intensity of a polydispersoin with the aim of reducing the number of terms to be included in the Mic coefficients a_l,b_l and π_l,τ_l.The scattering cross sections have been calculated and the results obtained are in good agreement with known literature data.It is found that the convergence of the Mie infinitive series is linked not with the relative refractive index m but with the dimension less diameter α.Three diagrams are plotted to show the relation between relative scattering intensity Ⅰ/Ⅰ_0 and scattering angle θ,and al- so the relations between I/I_0 and dimensionless diameter α and relative refractive index m.In cach of them,the curves calculated from Mie scattering theory and the curves calcu- lated from Fraunhofer diffracting theory are compared.It can be seen that when Fraunhof- cr diffraction theory is used instead of Mie scattering theory to deal with such a problem, appropriate ranges of the parameters(θ,α,m)and also the magnitude of the error can be determined.