Inversion of dynamic light scattering combining Tikhonov regularization with multi-grid technique

Wang Ya-jing; Shen Jin; Zheng Gang; Liu Wei; Sun Xian-ming

doi:10.3788/OPE.20122005.0963

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Inversion of dynamic light scattering combining Tikhonov regularization with multi-grid technique

Article | 更新时间：2020-08-12

- Inversion of dynamic light scattering combining Tikhonov regularization with multi-grid technique
- Optics and Precision Engineering Vol. 20, Issue 5, Pages: 963-971(2012)
- 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：
- DOI：10.3788/OPE.20122005.0963
  CLC： O436.2;TP301
- Received：14 November 2011，
  
  Revised：06 January 2012，
  
  Published Online：10 May 2012，
  
  Published：10 May 2012
- 稿件说明：
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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.

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Keywords

references

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