Particle Size Inversion Constrained by L(∞) Norm for Dynamic Light Scattering

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 L(2) norm. In the optimization equation, the norm determines the smoothness and stability of the inversion result, affecting the inversion accuracy. In this paper, the L(p) 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 L(2), 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.