光学 精密工程, 2012, 20 (5): 963, 网络出版: 2012-08-08
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
动态光散射 多重网格 Tikhonov正则化 反演 粒度分布 dynamic light scattering multi-grid Tikhonov regularization inversion particle size distribution
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.
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. 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]. Optics and Precision Engineering, 2012, 20(5): 963.