Tikhonov正则化与多重网格技术相结合的动态光散射反演

王雅静; 申晋; 郑刚; 刘伟; 孙贤明

doi:10.3788/OPE.20122005.0963

您当前的位置：

首页 >

文章列表页 >

Tikhonov正则化与多重网格技术相结合的动态光散射反演

现代应用光学 | 更新时间：2020-08-12

- Tikhonov正则化与多重网格技术相结合的动态光散射反演
- Inversion of dynamic light scattering combining Tikhonov regularization with multi-grid technique
- 光学精密工程 2012年20卷第5期页码：963-971
- 作者机构：
  
  1. 山东理工大学电气与电子工程学院,山东淄博 255091
  2. 上海理工大学光学与电子信息工程学院,上海 200093
- 作者简介：
- 基金信息：
  
  山东省自然科学基金资助项目(No.ZR2010FM005,No.ZR2009AQ013)();上海市重点学科建设资助项目(No.S0502)();山东理工大学博士点学科
- DOI：10.3788/OPE.20122005.0963
  中图分类号： O436.2;TP301
- 收稿日期：2011-11-14，
  
  修回日期：2012-01-06，
  
  网络出版日期：2012-05-10，
  
  纸质出版日期：2012-05-10
- 稿件说明：
移动端阅览
王雅静, 申晋, 郑刚, 刘伟, 孙贤明. Tikhonov正则化与多重网格技术相结合的动态光散射反演[J]. 光学精密工程, 2012,20(5): 963-971

Wang Ya-jing, Shen Jin, Zheng Gang, Liu Wei, Sun Xian-ming. Inversion of dynamic light scattering combining Tikhonov regularization with multi-grid technique[J]. Editorial Office of Optics and Precision Engineering, 2012,20(5): 963-971
王雅静, 申晋, 郑刚, 刘伟, 孙贤明. Tikhonov正则化与多重网格技术相结合的动态光散射反演[J]. 光学精密工程, 2012,20(5): 963-971 DOI： 10.3788/OPE.20122005.0963.

Wang Ya-jing, Shen Jin, Zheng Gang, Liu Wei, Sun Xian-ming. Inversion of dynamic light scattering combining Tikhonov regularization with multi-grid technique[J]. Editorial Office of Optics and Precision Engineering, 2012,20(5): 963-971 DOI： 10.3788/OPE.20122005.0963.

摘要

针对单尺度反演方法中存在的精度偏低问题

结合Tikhonov正则化与瀑布型多重网格技术

提出了一种多尺度Tikhonov正则化(ML-TIK)动态光散射反演方法。该方法利用多重网格技术将原反演问题分解到多尺度的网格空间

按着网格从粗到细的顺序

采用单尺度Tikhonov正则化(TIK)对每个子反演问题进行求解

获取颗粒的粒度分布。分别采用TIK和ML-TIK法对噪声水平为0、0.005、0.01的200~650 nm模拟双峰分布颗粒数据进行了反演

结果表明:ML-TIK法的反演结果与理论分布吻合

平滑性更好;相对于TIK法

ML-TIK法最多可减少粒径峰值误差8.19％

粒径反演误差0.448 2;而TIK法在噪声水平为0.005、0.01时

反演结果双峰特征不明显。因此

ML-TIK方法的反演精度更高、抗干扰能力更强。最后

用60 nm与200 nm实测数据的反演结果验证了该结论。

Abstract

For the low accuracy of single-level inversion methods to dynamic light scattering

a novel Multi-level Tikhonov regularization inversion (ML-TIK) method combining the Tikhonov regularization method with cascadic multi-grid technique was developed. Firstly

this method divided the original problem into several sub-inversion problems with different grid spaces by a multi-grid technique. Then

from the coarsest scale to the finest scale

each sub-inversion problem was inverted by single-level Tikhonov regularization (TIK) method. Finally

the Particle Size Distribution (PSD) was successively obtained by solving several sub-inversion problems. This method effectively reduces the ill-condition of the original equations. At noise levels 0

0.005 and 0.01

the simulation data of 200~650 nm bimodal distribution particles were respectively inverted by the TIK and ML-TIK. The results indicate that the inversion PSD of ML-TIK is more consistent with that of the theoretical one and it has better smoothness. Comparing to TIK

the ML-TIK can reduce the peak value error by 8.19% and relative error by 0.448 2. However

when the noise level is 0.005 and 0.01

the PSD of TIK has not obvious bimodal features. Therefore

the ML-TIK has improved the inversion accuracy and noise immunity. Inversion results of 60 and 200 nm experimental data verify above conclusions.

关键词

Keywords

references

CHU B, LIU T.Characterization of nanoparticles by scat-tering techniques[J].J.Nanoparticle Res.2000,2,(1):29-41.[2] 杨晖,郑刚,王雅静. 用动态光散射现代谱估计法测量纳米颗粒 [J].光学精密工程, 2010,18(9):1996-2001. YANG H, ZHENG G, WANG Y J. Measurement of nano-particles by dynamic light scattering based on spectral estimation[J].Opt. Precision Eng.,2010,18(9):1996-2001. (in Chinese).[3] 杨晖,郑刚,张仁杰. 用动态光散射时间相干度法测量纳米颗粒粒径 [J].光学精密工程, 2011,19(7):1546-1551. YANG H, ZHENG G, ZHANG R J. Measurement of nano-particle sizes by variance of temporal coherence of dynamic light scattering[J]. Opt. Precision Eng., 2011,19(7): 1546-1551. (in Chinese)[4] KOPPEL D E.Analysis of macromolecular polydispersity in intensity correlation spectroscopy:The method of Cumulants [J].Chem Phys,1972,57(11):4814-4820.[5] MCWHIRTER J G, PIKE E R. On the numerical inversion of the Laplace transform and similar Fredholm integral equations of the first kind[J].Phys A:Math Gen, 1978, 11 (9):1729-1745.[6] PROVENCHER S W, CONTIN. A general purpose constrained regularization program for inverting noisy linear algebraic and integral equations[J].Comput Phy Commun, 1982,27(3): 229-242.[7] DAHNEKE B E. Measurement of Suspended partieles by Quasi-Elastie Light Scattering[M]. New York:Wiley Interscience,1983.[8] MORRISON I D, GRABOWSKI E F. Improved techniques for particle size determination by quasi-elastic light scattering[J]. Langmuir, 1985, 1: 496-501.[9] SUN Y F, WALKER J G. Maximum likelihood data inversion for photon correlation spectroscopy[J]. Meas Sci Technol, 2008, 19(11):115-302.[10] ZHU X J, SHEN J, LIU W, et al.. Nonnegative least-squares truncated singular value decomposition to particle size distribution inversion from dynamic light scattering data[J]. Applie Optics,2010, 49(36):6591-6596.[11] 韩秋燕, 申晋, 孙贤明,等. 基于Tikhonov正则参数后验选择策略的PCS颗粒粒度反演方法 [J]. 光子学报, 2009, 38(11):917-2926. HAN Q Y, SHEN J, SUN X M,et al.. A posterior choice strategies of the tikhonov regularization parameter in the inverse algorithm of the photon correlation spectroscopy particle sizing techniques[J]. Acta Photonica Sinica, 2009, 38(11):2917-2926(in Chinese).[12] STUBEN K. A review of algebraic multigrid[J].Journal of Computational and Applied Mathematics, 2001, 128: 281-309.[13] BORNEMANN F, DEUFLHARD P. The cascadic multi-grid method for elliptic problems[J]. Numer Math, 1996, 42(9):917-924.[14] BORNEMANN F, KRAUSE R. Classical and cascadic multigrid methodogicai comparison .Proceedings of the 9th International Conference on Domain Decomposition. New York:John Wiley and Sons,1998[15] BORNEMANN F, DEUFLHARD P. The cascadic multi-grid method . The Eighth International Conference on Domain Decomposition Method for Partial Differential Equations. New York:Wiley and Sons,1997.[16] HANSEN P C. Regularization tools: A matlab package for analysis and solution of discrete ill-posed problems [J]. Numer. Algo, 2007, 46 :189-194.[17] GOLUB G H, HEATH M T, WAHBA G. Generalized cross-validation as a method for choosing a good ridge parameter[J].Technometrics, 1979, 21:215-223.[18] YU A B, STANDISH N. A study of particle size distribution [J]. Power Technol,1990,62(2):101-118.[19] COLEMAN T F, LI Y. An interior trust region approach for nonlinear minimization subject to bounds[J]. SIAM Journal on Optimization,1996,6(2):418-445.[20] 吴杰,李明峰,余腾. 测量数据处理中病态矩阵和正则化方法 [J].大地测量与地球动力学,2010,30 (4):102-105. WU J, LI M , YU T. Ill matrix and regularization method in surveying data processing[J]. Journal of Geodesy and Geodynamics, 2010,30 (4):102-105.(in Chinese)

浏览量

319

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

角度加权对动态光散射信号噪声影响的抑制作用

噪声动态光散射数据Tikhonov与截断奇异值正则化反演

光度数据反演临近空间低速点目标形状尺寸信息

动态光散射颗粒分布软测量

表面粗糙材质的复折射率反演