Acta Photonica Sinica, Volume. 51, Issue 11, 1101002(2022)
Regularization Inversion with Preconditioner for Flowing Aerosols in Dynamic Light Scattering
Dynamic Light Scattering (DLS) is a technique for submicron and nano Particles Size Distribution (PSD) measurement. With convenience and rapidity and no interference to the measured particle system, it is widely used in science and engineering. Generally, the DLS measurements are carried out with non-flowing samples in suspension, in which particles move only in the form of Brownian motion. In this situation, the fluctuations of scattered light of particles are only caused by the Brownian motion. Different from the DLS measurement of non-flowing particles in suspension, the translational motion of flowing particles leads to extra fluctuations of scattered light, making DLS measurement for flowing aerosols more difficult.The key of flowing aerosol measurement is that the PSD is difficult to accurately recover, because the increase of velocity aggravates the ill-conditioned state of the inversion equation, which is manifested as the increase of the condition number of the kernel matrix. Regularization is a common equation. However, the effectiveness of regularization is restricted by increasing the velocities of flow particles. To solve this problem, in this paper, the inversion equation was preconditioned to reduce the condition number of the kernel matrix before the Tikhonov regularization was used, which significantly improved the accuracy of recovered PSDs for flowing particles.To verify the effectiveness of the proposed method, the recovered PSDs of the 600 nm unimodal aerosols and 200 nm/700 nm bimodal aerosols with different velocities were simulated. The results show that the peak position error (EP) and the distribution fitting error (EF) of recovered PSDs become significant as the flowing velocity increases, which is represented that the particle size at the peak position is smaller than the true value and the distributions are wider than true distributions. Under the same flowing velocity, the recovered PSDs by preconditioned Tikhonov regularization (Pre-Tik) are closer to the true PSD than Tikhonov regularization (Tik). And the effect of preconditioning is increasingly obvious with the flow velocity increase. When the particle velocity is 2.0 m/s, the EP and EF of the PSD obtained by the Tik is 0.046 7 and 0.006 9 respectively, and by the Pre-Tik is 0.026 7 and 0.005 7 respectively. The simulated inversions of the 200 nm/700 nm bimodal PSDs show similar results in the particle size at both peaks position and the width of distribution, which results in the value of EPs and EFs rising. However, the performance indices of the inversion results of the two methods were quite different. When the flowing velocity is 2.0 m/s, the EP and EF of the PSD obtained by the Tik method are 0.660 0/0.274 3 and 0.012 1 respectively, while the EP and EF of the PSD obtained by the Pre-Tik method are 0.460 0/0.091 4 and 0.009 1 respectively. The accuracy of the recovered PSDs is improved by using the Pre-Tik method.To further compare the performance of the Tik method and the Pre-Tik method, DLS experiments of flowing aerosols were carried out. The measured ACF data were obtained from a homemade DLS measurement platform for flowing aerosols. For unimodal flowing aerosols at 1.77 m/s, the EP and EF of PSDs reduced from 0.087 7 and 0.012 4 by using the Tik method to 0.052 6 and 0.008 6 by the Pre-Tik method. The recovery of the latter method is better than the former. For bimodal aerosol PSDs, the results are similar to unimodal aerosol PSDs. The EPs and EFs of the PSD recovered by the Pre-Tik method are smaller than those obtained by the Tik method, which agrees with the simulations.The inversion results of simulated and experimental data show that the limitations of the regularization method in DLS measurements of flowing particles can be broken through by preconditioning. In this paper, the preconditioner in the form of a diagonal matrix constructed with priori velocity and delay time can weaken the ill-condition state of the inversion equation and makes regularization less sensitive to velocities. Compared with the Tikhonov regularization, the preconditioned Tikhonov regularization can improve the inversion performance significantly for flowing aerosols in DLS measurement.