中国激光, 2015, 42 (9): 0908003, 网络出版: 2015-09-06
正则矩阵对双峰分布动态光散射数据反演的影响
Influence of Regularization Matrix on Inversion of Bimodal Dynamic Light Scattering Data
散射 动态光散射 Tikhonov正则化 双峰分布颗粒 颗粒粒径反演 scattering dynamic light scattering Tikhonov regularization bimodal distribution particles particle size inversion
摘要
双峰分布数据的反演是动态光散射中的难点,在双峰分布数据反演中经常采用Tikhonov正则化方法,但不同正则矩阵对反演结果的影响还不明确。分别采用单位矩阵L1、一阶差分矩阵L2、二阶差分矩阵L3,在6种噪声水平下,对两种双峰分布颗粒进行了反演研究,模拟数据表明:随着噪声水平的增加,双峰分辨力下降,光强比越接近、颗粒越大,算法抗干扰能力越强;在同等噪声情况下,矩阵L3的双峰分辨力最好、反演误差最小,L1双峰分辨力最差、反演误差最大;L3能够分辨出的峰值粒径比最低,L1最大。同等噪声水平下,峰值粒径比越大,双峰分辨力越强。因此在处理有噪声数据时,为保证反演结果的准确性,应优先选择L3。最后通过实验数据的反演结果验证了模拟数据的结论。
Abstract
The inversion of bimodal dynamic light scattering data is very difficult. Tikhonov regularization method is the often used inversion algorithm, however, the influence of different regularization matrices on the inversion is not clear yet. Two bimodal particle size distributions with 6 levels of noise are inverted by using identity matrix L1, first order difference matrix L2 and second order differential matrix L3. Simulation data shows that the bimodal resolution decrease with the increase of noise level. The anti-interference ability of the algorithm is stronger when the components of bimodal distribution are closer. Under the same noise level, the bimodal resolution of matrix L3 is of the best, while the error of inversion is minimum; correspondingly the bimodal resolution of matrix L1 is of the worst, while the error of inversion is maximum. The matrix L3 can distinguish the smallest peak value size ratio, while matrix L1 can only distinguish the biggest peak value size ratio. Under the same noise level, peak value size ratio is bigger and the bimodal resolution is stronger. Therefore, matrix L3 should be used in order to get the correct inversion result by inverting the noisy scattering data. Finally, the inversion of experimental particles confirms this conclusion.
刘伟, 王雅静, 陈文钢, 马立修, 申晋. 正则矩阵对双峰分布动态光散射数据反演的影响[J]. 中国激光, 2015, 42(9): 0908003. Liu Wei, Wang Yajing, Chen Wengang, Ma Lixiu, Shen Jin. Influence of Regularization Matrix on Inversion of Bimodal Dynamic Light Scattering Data[J]. Chinese Journal of Lasers, 2015, 42(9): 0908003.