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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 L2 norm. In the optimization equation, the norm determines the smoothness and stability of the inversion result, affecting the inversion accuracy. In this paper, the Lp 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 L2, 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. [ABSTRACT FROM AUTHOR]

Simulated and experimental data were used to investigate the particle size distribution (PSD) recovery from a flowing aerosol via dynamic light scattering (DLS). It is found that, for a unimodal PSD, increasing the flow velocity leads to an increase in the error of the peak position, a decrease in the peak height and a broadening of the PSD. This is exacerbated for larger aerosol particles. For a bimodal PSD, the separation of the two peaks decreases and results in a single-peak PSD as the velocity increases. The effect of velocity on the measurement is similar to adding signal noise, which increases with the velocity. This effect is related to the measured aerosol particle size. The larger the particles, the lower the signal-to-noise ratio. By comparing DLS measurement results for flowing and non-flowing aerosol samples, it is possible to determine the maximum flow rate at which measurements can be usefully made. [ABSTRACT FROM AUTHOR]

Neural network technology shows certain superiority in the field of dynamic light scattering (DLS) inversion. However, due to the complex problems of training sample and parameter selection, its application has certain limitations. At present, it has not been applied to the inversion of bimodal particle size distribution (PSD). Aiming at training sample generation and smoothing parameter optimization of generalized regression neural network (GRNN), a DLS inversion method combining Tikhonov regularization and parameter-optimized GRNN (Tikhonov-PGRNN) is proposed. In this method, the PSD of Tikhonov regularization inversion is used as prior information to generate the training samples, the one-dimensional search method is used to obtain the optimal smoothing parameter, and the normalized field autocorrelation function data is input into GRNN to estimate the PSD. Simulated data for narrow and broad 522 nm unimodal, 216 nm/667 nm bimodal PSDs were inverted by Tikhonov-PGRNN and Tikhonov under different noise levels. The results show that Tikhonov-PGRNN can realize the inversion of unimodal and bimodal PSDs. Compared with Tikhonov, the peak position error and the distribution error of PSDs inverted by Tikhonov-PGRNN are smaller and the method has higher anti-noise performance. The inversion results of experimental data are consistent with the conclusion of simulation data. The peak position errors of 203 nm, 555 nm unimodal and 33 nm/203 nm, 306 nm/974 nm bimodal particle systems inverted by Tikhonov-PGRNN are 1.48%, 0.39% and 3.55%/0.76%, 7.90%/1.74% respectively, which are better than the inversion results of Tikhonov. [Display omitted] • A DLS inversion method of Tikhonov-PGRNN is proposed. • Tikhonov inversion result is used as prior information to generate training samples. • Optimal smoothing parameter is obtained by one-dimensional search method. • Tikhonov-PGRNN has higher anti-noise performance. • Tikhonov-PGRNN can obtain a high-accuracy inversion result. [ABSTRACT FROM AUTHOR]

Dynamic light scattering (DLS) is a popular method of particle size measurement, but at ultra-low particle concentrations, the occurrence of number concentration fluctuations limits the use of the technique. Number fluctuations add a non-Gaussian term to the scattered light intensity autocorrelation function (ACF). This leads to an inaccurate particle size distribution (PSD) being recovered if the normal DLS analysis model is used. We propose two methods for inverting the DLS data and recovering the PSDs when number fluctuations are apparent. One is to directly establish the relationship between the non-Gaussian ACF and the PSD by the kernel function reconstruction (KFR) method while including the non-Gaussian term to recover the PSD. The other is to remove the effect of the non-Gaussian term in the ACF by the baseline reset (BR) method. By including the number fluctuation term, the ideal recovered PSD can be obtained from the simulated data, but this will not happen in the experimental measurement data. This is because the measured intensity ACF contains more noise than the simulated ACF at ultra-low concentration. In particular, the baseline noise at the tail of long delay time of ACF overwhelms the number fluctuation term, making it difficult to recover reliable PSD data. Resetting the baseline can effectively remove the digital fluctuation term in ACF, which is also a feasible method to improve PSD recovery under ultra-low concentration. However, increasing noise at ultra-low concentrations can lead to errors in determining an effective baseline. This greatly reduces the accuracy of inversion results. Results from simulated and measured ACF data show that, for both methods, noise on the ACF limits reliable PSD recovery. [ABSTRACT FROM AUTHOR]

• The velocity of flow aerosol is obtained based on cumulants of the intensity autocorrelation function (ACF). • The flow velocity acquisition based on cumulants of ACF is used for both unimodal and bimodal distribution of aerosols. • In the inversion of dynamic light scattering for flow aerosol measurement, the noise widens the distribution, shifts the peak value, and increases the peak height ratio. In the dynamic light scattering (DLS) measurement for a flowing aerosol, an anemometer, is needed to measure the flow velocity to invert the aerosol particle size. In this work, a cumulative analysis method has been used to obtain the aerosol velocity through the light intensity autocorrelation function (ACF) based on the relation between the particle velocity and the second cumulant of the electric field ACF of flowing aerosol particles. Additionally, the particle size distribution (PSD) has been inversed by the regularization method, which enables the online measurement of flowing aerosol to be realized. The simulation results at different noise levels show that the accurate velocity and PSD for flowing aerosols can be obtained by the proposed method at low noise levels and high noise levels. It has been observed that higher noise causes the PSD broadening and the peak offset. For aerosol particles with a bimodal distribution, the increase of noise leads to the increase of peak height ratio and peak of small particles in bimodal distribution disappears, leaving only unimodal distribution. Furthermore, the increase of noise has no significant effect on the calculated velocity value both for unimodal and bimodal aerosol distributions. The experimental results of DLS measurements on unimodal and bimodal aerosols verified the above statements. [ABSTRACT FROM AUTHOR]

Dynamic light scattering (DLS) from ultra-low concentration suspensions (the average number of particles in the scattering volume is less than ~100) gives rise to autocorrelation functions (ACFs) containing a non-Gaussian term due to particle number fluctuations. This term is difficult to characterize and account for and makes recovery of particle size distribution (PSD) information unreliable. We show that an initial analysis of the intensity ACF to determine parameters describing the amplitude and relaxation rate of the non-Gaussian term and then using these parameters to create a better theoretical non-Gaussian ACF model allows a more accurate recovery of the PSD. The modified model is consistent with the measured ACF data, and a reconstructed kernel matrix matching the measured data is obtained. When compared with the usual kernel function reconstruction (KFR) method, the proposed method gives significantly improved PSD recovery accuracy with experimental data. Furthermore, the PSDs obtained have no obvious differences to those obtained from measurements at normal particle concentrations. [Display omitted] • Fitting the measured ACF data with a non-Gaussian ACF model of lower concentration. • Reducing focused beam waist value to obtain non-Gaussian model at lower concentration. • Providing a solution for nanoparticle size measurement at ultra-low concentration. [ABSTRACT FROM AUTHOR]