光学精密工程2012，Vol.20Issue(5)：963-971,9.DOI:10.3788/OPE.20122005.0963
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
摘要
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 regulariza-tion 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 sue-cessively 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
动态先散射/多重网格/Tikhonov正则化/反演/粒度分布Key words
dynamic light scattering/ multi-grid/ Tikhonov regularization/ inversion) particle size dis-tribution分类
数理科学引用本文复制引用
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):963-971,9.基金项目
山东省自然科学基金资助项目(No.ZR2010FM005,No.ZR2009AQ013) （No.ZR2010FM005,No.ZR2009AQ013）
上海市重点学科建设资助项目(No.S0502) （No.S0502）
山东理工大学博士点学科建设资助项目(No.103123) （No.103123）
