Particle Size Inversion Constrained by L_∞ Norm for Dynamic Light Scattering

Area of Science:

• Materials Science
• Physical Chemistry
• Data Analysis

Background:

• Particle size inversion from dynamic light scattering (DLS) data is an ill-posed problem.
• Regularization techniques, particularly L2 norm, are commonly used to stabilize DLS data inversion.
• The choice of norm significantly impacts the accuracy and stability of the inversion results.

Purpose of the Study:

• To investigate the performance of L_p norm regularization models for DLS particle size inversion.
• To compare the effectiveness of different L_p norms (p=1, 2, 10, 50, 100, 1000, ∞) across various noise levels.
• To determine the optimal norm for accurate DLS data inversion.

Main Methods:

• Construction of an L_p norm regularization model for DLS data inversion.
• Systematic evaluation of inversion accuracy and error distribution using L_p norms with increasing p values.
• Comparative analysis of L2 and L∞ norms under different noise conditions for unimodal and bimodal particle distributions.

Main Results:

• Inversion distribution errors generally decrease as the value of p increases.
• L∞ norm demonstrates superior performance for unimodal particles in high-noise scenarios compared to L2 norm.
• L∞ norm exhibits lower noise sensitivity, enhanced peak resolution, and more accurate inverse particle size distributions for bimodal particles.

Conclusions:

• The L∞ norm is more suitable for DLS data inversion than the traditional L2 norm.
• Increasing the p value in L_p regularization generally improves inversion accuracy.
• The L∞ norm provides a robust and accurate method for particle size determination using DLS, especially in the presence of noise.