Particle Size Inversion Based on <i>L</i>_1,∞-Constrained Regularization Model in Dynamic Light Scattering

Abstract

Dynamic light scattering (DLS) is a highly efficient approach for extracting particle size distributions (PSDs) from autocorrelation functions (ACFs) to measure nanoparticle particles. However, it is a technical challenge to get an exact inversion of the PSD in DLS. Generally, Tikhonov regularization is widely used to address this issue; it uses the L2 norm for both the data fitting term (DFT) and the regularization constraint term. However, the L2 norm’s DFT has poor robustness, and its regularization term lacks sparsity, making the solution susceptible to noise and a reduction in accuracy. To solve this problem, the Lp,q norm restrictive model is formulated to examine the impact of various norms in the DFT and regularization term on the inversion results. On this basis, combined with the robustness of DFT and the sparsity of regularization terms, an L1,∞-constrained Tikhonov regularization model was constructed. This model improves the inversion accuracy of PSD and offers a better noise-resistance performance. Simulation tests reveal that the L1,∞ model has strong noise resistance, exceptional inversion precision, and excellent bimodal resolution. The inversion outcomes for the 33 nm unimodal particles, the 55 nm unimodal, and the 33 nm/203 nm bimodal experimental particles show that L1,∞ reduces peak errors by at most 6.06%, 5.46%, and 12.12%/3.94% compared to L2,2, L1,2, and L2,∞ models, respectively. These simulations are validated by experimental data.

Keywords

• optical scattering
• particle sizing
• regularization inversion
• data fitting term
• regularization term
• norm