Particle size distribution recovery in dynamic light scattering by optimized multi-parameter regularization based on the singular value distribution

Abstract

Multi-parameter regularization can improve the over-regularization or under-regularization in the regularized inversion of dynamic light scattering (DLS) data. However, the regularization parameter selected by a fixed adjustment factor is not independent of the other parameters, which results in all the selected parameters being affected by the singular value of the truncation point. This leads to oscillations and false peaks in the recovered particle size distribution (PSD) as the noise in the data increases. In this paper, the singular value distribution characteristics are investigated, and this leads to the proposal of a novel multi-parameter selection method. Using the proportional relationship between two adjacent singular values, a regular parameter function is constructed for the parameter selection. Parameter optimization is performed using fixed point iteration to obtain the regularization parameter sequence corresponding to the singular value distribution. Thus, the effects of small singular values on noise are suppressed. Simulated DLS data for monomodal, closely-spaced bimodal, widely-spaced bimodal and trimodal PSDs were inverted under a range of different noise levels. The results show that, the proposed method greatly reduces the oscillations and false peaks and significantly improves the resolution of the peak position in the recovered PSDs as the noise in the data increases. The performance of the method was also verified using experimental DLS data.