A dynamic light scattering inversion method based on regularization matrix reconstruction for flowing aerosol measurement

Abstract

Tikhonov regularization, or truncated singular value decomposition (TSVD), is usually used for dynamic light scattering (DLS) inversion of particles in suspension. The Tikhonov regularization method uses a regularization matrix to modify all singular values in the kernel matrix. The modification of large singular values cannot effectively reduce the variance of the estimated values but may introduce bias in the solution, resulting in poor disturbance resistance in the inversion results. The TSVD method, on the other hand, truncates all small singular values, which leads to the loss of particle size information during the inversion process. The shortcomings of the two methods mentioned above do not have a significant impact on the inversion of high signal-to-noise ratio data. However, compared to the classical DLS particle size inversion for non-flowing suspended particles, the DLS inversion of flowing aerosols is more significantly affected by noise, and the extraction of particle size information is more difficult due to the effect of flow velocity, resulting in worse inversion results with increasing aerosol flow velocity for both methods. To improve the accuracy of the particle size distribution (PSD) of flowing aerosols, we introduced a kernel matrix into the regularization matrix, and based on the principles of the two methods, the spectral information of the kernel matrix was utilized to make the modification of small singular values by the regularization matrix. Correspondingly, weak or no modification was made according to the values of large singular values to reduce the introduction of bias. The inversion results of simulated and measured data indicate that the reconstruction of the regularization matrix improves the anti-disturbance performance and avoids the loss of particle size information during the regularization inversion process, thereby significantly improving the PSD accuracy, which is affected by the dual effects of flow velocity and noise in the DLS measurement of flowing particles. The peak error and distribution error of the inversion results by reconstructing the regularization matrix are lower than those of Tikhonov regularization.