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Particle size inversion of dynamic light scattering (DLS) is a typically ill-posed problem. Regularization is an effective method to solve the problem. The regularization involves imposing constraints on the fitted autocorrelation function data by adding a norm. The classical regularization inversion for DLS data is constrained by the L2 norm. In the optimization equation, the norm determines the smoothness and stability of the inversion result, affecting the inversion accuracy. In this paper, the Lp norm regularization model is constructed. When p is 1, 2, 10, 50, 100, 1000, and ∞, respectively, the influence of their norm models on the inversion results of data with different noise levels is studied. The results prove that overall, the inversion distribution errors show a downward trend with the increase of p. When p is larger than 10, there is no significant difference in distribution error. Compared with L2, L∞ can provide better performance for unimodal particles with strong noise, although this does not occur in weak noise cases. Meanwhile, L∞ has lower sensitivity to noise and better peak resolution, and its inverse particle size distribution is closer to the true distribution for bimodal particles. Thus, L∞ is more suitable for the inversion of DLS data. [ABSTRACT FROM AUTHOR]

Dynamic light scattering (DLS) from ultra-low concentration suspensions (the average number of particles in the scattering volume is less than ~100) gives rise to autocorrelation functions (ACFs) containing a non-Gaussian term due to particle number fluctuations. This term is difficult to characterize and account for and makes recovery of particle size distribution (PSD) information unreliable. We show that an initial analysis of the intensity ACF to determine parameters describing the amplitude and relaxation rate of the non-Gaussian term and then using these parameters to create a better theoretical non-Gaussian ACF model allows a more accurate recovery of the PSD. The modified model is consistent with the measured ACF data, and a reconstructed kernel matrix matching the measured data is obtained. When compared with the usual kernel function reconstruction (KFR) method, the proposed method gives significantly improved PSD recovery accuracy with experimental data. Furthermore, the PSDs obtained have no obvious differences to those obtained from measurements at normal particle concentrations. [Display omitted] • Fitting the measured ACF data with a non-Gaussian ACF model of lower concentration. • Reducing focused beam waist value to obtain non-Gaussian model at lower concentration. • Providing a solution for nanoparticle size measurement at ultra-low concentration. [ABSTRACT FROM AUTHOR]