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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]

In the large inversion range, the wavelet-regularization inversion method (WRIM) is an effective method for improving the inversion accuracy of dynamic light scattering (DLS) data. However, the initial decomposition scale (IDS) of this method has a great effect on the inversion accuracy. The particle size distribution (PSD) obtained from inappropriate IDS is not optimal. We analyze the effect of the different IDS on the inversion result in this paper. The results show that IDS of the smallest relative error should be chosen as the optimal IDS. However, because the true PSD is unknown in the practical measurements, this optimal IDS criterion is infeasible. Therefore, we propose an application criterion determining the optimal IDS. Based on this criterion, an improved WRIM with the optimal IDS is established. By the improved WRIM, high accuracy inversion PSD is obtained from DLS data. The simulated and experimental data demonstrate the effectiveness of this algorithm. Besides, we also further study the effect of the data noise on the optimal IDS. These studies indicate that the optimal IDS usually shows a downward trend with an increase of noise level. [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]

Abstract: The measurement and analysis system of nanoparticle size distribution was developed by using virtual instrument technology, where the photon counting technology was applied in the system to replace the correlator; a high speed photon counter was designed with seamlessly counting technology to reduce the system cost and increase the accuracy. The data of nanoparticle dynamic light scattering (DLS) were analyzed in the mixed program of MATLAB and LabVIEW, where the autocorrelation functions of light scattering signals of 100nm unimodal as well as 90nm and 300nm bimodal particles were inversed by truncated singular value decomposition arithmetic. Experiment results show that the peak position, peak width and symmetry of particle size distributions (PSDs) are very close to the real particles. [Copyright &y& Elsevier]

Abstract: For ill-posed inversion problem of photon correlation spectroscopy (PCS), a wavelet-regularization inversion method (WRIM) which combines wavelet multiscale inversion strategy with classical regularization inversion method (CRIM) was proposed. By using this method, the original inversion problem is decomposed into several subproblems on different multiscale spaces. As a result, we can successively obtain solution of original inversion problem according to the particle sizes inverted from the coarsest scale to the finest scale. The simulation and experimental data was respectively inverted by two methods. The inversion results demonstrate that WRIM has better global convergence, higher accuracy and more strong noise immunity than CRIM. [Copyright &y& Elsevier]

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]

• For NNTSVD, accurate particle sizing rely on optimal sampling points selection. • The number of sampling points must be less than the number of ACF channels. • There is weak similarity between the relative error of PSD and the residual of ACF. • Optimal sampling points can be achieved by minimum residual criterion. The number of particle size distribution (PSD) sampling points is an important factor to affect the accuracy of dynamic light scattering (DLS) inversion. If the number of sampling points is not selected properly, the accuracy of inversion results will be reduced or results will deviate seriously from the true value. To solve the problem, combining non-negative truncated singular value decomposition (TSVD), by studying the relationship between number of sampling points, relative error (RE) of PSD and number of autocorrelation function (ACF) channels, it is concluded that the upper limit of optimal sampling points is limited by the number of ACF channels. Under different sampling points, the study of RE of PSD and the residual (RES) of electric field ACF shows that there is a weak similarity between them. Then a criterion for determining the optimal number of sampling point is constructed. Finally, a non-negative constrained TSVD method for PSD adaptive sampling (PSDAS-NNTSVD) is proposed according to the upper limit condition of optimal number of sampling points and its determination criterion. Simulated DLS data for unimodal particles of 160 channels and bimodal particles of 120 channels were inverted under three noise levels of 1 × 10−4, 1 × 10−3, 1 × 10−2, respectively. The results show that, the peak position of PSDs inverted by PSDAS-NNTSVD is closer to the true value and the proposed method has better anti-noise ability. The inversion results of bimodal measured particles from 60 to 203 nm also verified the performance of the method. [ABSTRACT FROM AUTHOR]

Dynamic light scattering (DLS) is a popular method for measuring particle size in the colloidal size range. However, like all light scattering techniques, the results can be problematic when dust or large contaminant particles are present in the sample. Dust particles are usually much larger than the colloids or nanoparticles of interest and, consequently, scatter light very strongly when they pass through the laser beam in the scattering volume. This biases the measured particle size to much larger values than expected. However, it also suggests a means to detect and, potentially, reduce the effect of dust particles on the measurement results. If the high count-rate data associated with dust can be detected and removed during the DLS measurement, the particle size results will be more reliable. An a priori electronic dust filtering method based on the long-time count rate statistics is proposed and demonstrated. This allows the identification of data sets which have an abnormal number of high count-rate events which are, presumably, associated with scattering from dust particles. These data can be rejected and an autocorrelation function calculated using the retained counts after removing unwanted outlier data. The particle size distribution is then recovered. By measuring a standard polystyrene suspension containing "dust" particles, the results show that the method can effectively discriminate and eliminate data contaminated by dust, thereby improving the measurement results. Unlabelled Image • An a priori electronic dust filtering method is proposed in dynamic light scattering. • The proposed method is based on the long-time count-rate statistics. • The method allows the identification and rejection of data sets contaminated by dust. [ABSTRACT FROM AUTHOR]

Highlights • The influence of the intensity deviation of Fraunhofer diffraction pattern from the Mie scattering pattern on the polydisperse PSD recovered by the C–S algorithm is analyzed for the first time. • The optimal range of angles is determined based on the inversion error of PSD recovered by the C–S algorithm from the Mie scattering light pattern in different angular ranges. • By analyzing the inversion error of recovered PSDs, the influence of different particle sizes and distribution widths on the optimal range of angle is determined. Abstract In laser diffraction particle sizing measurements, only light in the range of forward small scattering angles is used to recover the particle size distribution (PSD). The Chin–Shifrin (C–S) integral transform algorithm is used to recover the particle size distributions (PSDs). However, this algorithm is based on the Fraunhofer diffraction theory, which may be used to approximate the scattered light pattern at small scattering angles. By comparing the inversion results recovered using the C–S algorithm from the two series of simulated light scattering data we determine the optimal range of angular integration for which the Fraunhofer diffraction approximation and the C–S algorithm may be used to reconstruct the PSD. One series is simulated using Mie scattering to calculate the true intensity pattern and for the other series is used to approximate the intensity pattern. For both series the data is calculated over a range of scattering angles. The effect of the deviation of the Fraunhofer diffraction pattern from the Mie scattering pattern is studied and the optimal range of angles is determined based on the inversion error of recovered PSD. The results show that the intensity pattern deviation will lead to variations in the recovered PSD. Also, the larger the angular range, the poorer the results. The optimal range of integration angle of the C–S algorithm for the various PSDs with different distribution widths and particle sizes is analyzed. The results indicate that the smaller the particle size and the wider the PSD, the smaller the optimal angular range. [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]