Optics and Precision Engineering, Volume. 20, Issue 5, 963(2012)

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

Wang Ya-jing1、*, Shen Jin1, Zheng Gang2, Liu Wei1, and Sun Xian-ming1
Author Affiliations
  • 1[in Chinese]
  • 2[in Chinese]
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    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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    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

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    Paper Information

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    Received: Nov. 14, 2011

    Accepted: --

    Published Online: Aug. 8, 2012

    The Author Email: Wang Ya-jing (wangyjing0725@126.com)

    DOI:10.3788/ope.20122005.0963

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