基于奇异值分解的动态光散射反演算法  

An Inversion Algorithm of Dynamic Light Scattering Based on Singular Value Decomposition

作　　者：于向飞[1] 杨晖[1,2,3] 杨海马[1] 郑刚[1,2] 李军[1] 胡恒庆[1] Mark BIGGS 

机构地区：[1]上海理工大学光学与电子信息工程学院,上海200093 [2]上海理工大学上海市现代光学重点实验室,上海200093 [3]阿德雷德大学化工学院

出　　处：《光子学报》2013年第11期1324-1328,共5页Acta Photonica Sinica

基　　金：国家自然科学基金(No.61007002)资助

摘　　要：针对动态光散射颗粒测量法在反演多分散系粒径分布时,算法需要先验信息或者解的约束条件的问题,提出了一种基于奇异值分解的动态光散射反演算法.首先利用多分散颗粒系光强自相关函数构造Hankel矩阵;其次对矩阵进行奇异值分解;再次根据奇异值的大小分布,确定噪音级别,重建矩阵的秩;最后对新的矩阵进行特征值分解,得到颗粒的粒径分布.采样两种和三种不同粒径的颗粒系进行了实验,结果显示:在没有任何先验信息和对解的约束条件下,该方法对两种粒径的颗粒系测量取得了较好的效果.但对于三种粒径的颗粒系测量效果并不理想,虽然能分辨出不同的三种粒径,但测量结果偏差较大,特别是小颗粒的粒径.通过分析认为主要原因是小颗粒的散射光容易被大颗粒阻挡.To solve the problem that the traditional inversion of dispersion particle size distribution with the method of dynamic light scattering requires prior knowledge or constraints for the solution, a new inversion algorithm of dynamic light scattering based on singular value decomposition was proposed. Firstly, the Hankel matrix H with the intensity autocorrelation data was constructed. Secondly, the singular value decomposition of H was calculated. Thirdly, the rank of the reconstruction matrix with the singular value of H was determined. Finally, the characteristic value decomposition with the new matrix was calculated, and then the particle size distribution was obtained. The experiment was carried out using two and three different sized particles dispersion respectively. The results show that, in the measuring with two different size particles, the new method can achieve good results without any prior knowledge or constraints for the solution; it is not so good in the measuring with three different size particles and can distinguish three different size particles, but the results have large deviation, especially for the smaller particles. Through the analysis of the experiment, the main reason was found that the small particles scattered light is easily blocked by large particles.

关 键 词：动态光散射 奇异值分解 多分散 反演 

分 类 号：TN247[电子电信—物理电子学] O436.1[机械工程—光学工程]