The non-negative truncated singular value decomposition for adaptive sampling of particle size distribution in dynamic light scattering inversion

Abstract

The number of particle size distribution (PSD) sampling points is an important factor to affect the accuracy of dynamic light scattering (DLS) inversion. If the number of sampling points is not selected properly, the accuracy of inversion results will be reduced or results will deviate seriously from the true value. To solve the problem, combining non-negative truncated singular value decomposition (TSVD), by studying the relationship between number of sampling points, relative error (RE) of PSD and number of autocorrelation function (ACF) channels, it is concluded that the upper limit of optimal sampling points is limited by the number of ACF channels. Under different sampling points, the study of RE of PSD and the residual (RES) of electric field ACF shows that there is a weak similarity between them. Then a criterion for determining the optimal number of sampling point is constructed. Finally, a non-negative constrained TSVD method for PSD adaptive sampling (PSDAS-NNTSVD) is proposed according to the upper limit condition of optimal number of sampling points and its determination criterion. Simulated DLS data for unimodal particles of 160 channels and bimodal particles of 120 channels were inverted under three noise levels of 1 × 10−4, 1 × 10−3, 1 × 10−2, respectively. The results show that, the peak position of PSDs inverted by PSDAS-NNTSVD is closer to the true value and the proposed method has better anti-noise ability. The inversion results of bimodal measured particles from 60 to 203 nm also verified the performance of the method.