基于核矩阵扩展的动态光散射截断奇异值分解反演  

Truncated Singular Value Decomposition Inversion Based on Extended Nuclear Matrix in Dynamic Light Scattering

作　　者：黄钰 申晋[1] 徐敏[1] 孙成 刘伟[1] 孙贤明[1] 王雅静[1] HUANG Yu;SHEN Jin;XU Min;SUN Cheng;LIU Wei;SUN Xian-ming;WANG Ya-jing(School of Electrical and Electronic Engineering, Shandong University of Technology, Zibo, Shandong 255049, Chin)

机构地区：[1]山东理工大学电气与电子工程学院,山东淄博255049

出　　处：《光子学报》2018年第7期197-206,共10页Acta Photonica Sinica

基　　金：山东省自然科学基金(Nos.ZR2018MF032;ZR2016EL16;ZR2017LF026;ZR2017MF009)资助~~

摘　　要：针对截断奇异值分解方法进行动态光散射反演存在的颗粒粒度信息丢失问题,本文在分析自相关函数不同衰减时段粒度信息分布差异的基础上,提出利用每一角度核矩阵与对应角度下粒度信息在自相关函数不同延迟时刻的分布构建扩展矩阵的扩展截断奇异值分解方法.该方法通过用自相关函数中每一延迟时刻的粒度信息,调节同一时刻原核矩阵数据对信噪比的贡献,进而保留了更多的有效奇异值,减少了由于奇异值截断引起的信息丢失,在保证抗噪性的基础上,提高了自相关函数的信息利用率.在1×10-3噪声水平下,对一组单峰宽分布(260nm)和三组双峰颗粒分布(250/750nm)、(270/800nm)以及(306/974nm)的模拟动态光散射数据,进行了单角度、3角度和6角度反演.结果表明,与截断奇异值分解方法相比,采用扩展截断奇异值分解方法反演得到的峰值粒度误差和分布误差均明显减小.对306/974nm颗粒体系的6角度实测数据的反演表明,采用扩展截断奇异值分解法得到的颗粒峰值粒度误差由非扩展方法的0.032/0.016降至0.029/0.006,且得到的峰值比更接近真实值.In order to solve the problem of particle size information loss in dynamic light scattering inversion by truncated singular value decomposition method,on the base of analyzing the difference of particle size information distribution in autocorrelation function at different delay time,extended truncated singular value decomposition method was proposed which uses nuclear matrix and particle size information distribution in autocorrelation function at different delay time in the same angle to build the extended nuclear matrix.The method adjusts the contribution of the original nucleus matrix datas to the SNR at the same time using the particle size information at each delay time in the autocorrelation function,thereby preserves more effective singular values and reduces information loss due to singular value truncation. On the basis of ensuring noise reduction,the information utilization for the autocorrelation function is improved.At noise level 1×10-3,the datas a set of single peak width distribution（260 nm）and three sets of bimodal particle distributions（250/750 nm）,（270/800 nm）and（306/974 nm）simulated in dynamic light scattering in single angle,3 angles and 6 angles was inverted.The results show that,compared with truncated singular value decomposition method,the peak size errors and distribution errors obtained by extended truncated singular value decomposition method are obviously reduced.The inversion of the measured datas for 306/974 nm particle system in 6-angles shows that the peak particle size error obtained by the extended truncated singular value decomposition method is reduced from 0.032/0.016 by the truncated singular value decomposition method to 0.029/0.006,and peak ratio is closer to actual value.

关 键 词：动态光散射 粒度分布 反演 颗粒测量 奇异值分解 

分 类 号：TN911.74[电子电信—通信与信息系统]