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Partic. vol. 41 pp. 30-39 (December 2018)
doi: 10.1016/j.partic.2017.12.015

A regularization algorithm for estimating the multimodal size distribution of nanoparticles from multiangle dynamic light scattering

Lei Lia,b, Kecheng Yanga, Wei Lia, Kai Lia, Long Yua, Min Xiaa,*

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    • A modified self-adaptive algorithm was proposed to retrieve PSDs from MDLS measurement data. • The algorithm chose appropriate regularization methods in iterative recursion. • The algorithm reconstructed the PSDs more precisely. • Numerical and experimental results proved the good anti-noise performance of the algorithm.


The multiangle dynamic light scattering (MDLS) technique provides more robust, reproducible, and accurate particle size distributions (PSDs) than single-angle dynamic light scattering. However, in MDLS, the determination of peak locations is difficult but significant, particularly for multimodal distributions. In this paper, a self-adaptive algorithm, the iterative recursion nonnegative Tikhonov–Phillips–Twomey (IRNNT-PT) algorithm, is proposed for the estimation of the PSD from MDLS measurements. This algorithm optimizes the weighting coefficients, distinguishes features of PSDs and chooses the optimal inversion method from two regularization algorithms self-adaptively. Numerical simulations and experimental results for unimodal and multimodal distributions are presented to demonstrate both the validity and noise immunity of the IRNNT-PT algorithm, and demonstrate that the proposed algorithm can be well applied to reconstruct PSDs from MDLS measurements.

Graphical abstract


Dynamic light scattering; Particle size distribution; Inverse scattering; Mie theory; Scattering measurements