Yajing Wang

Nonnegative least-squares truncated singular value decomposition to particle size distribution inversion from dynamic light scattering data

The weak symmetry relationship between the relative error and solution norm holds in our developed nonnegative least-squares truncated singular value decomposition method. By using this relationship to specify the optimal regularization parameters, we applied the proposed algorithm to recover particle size distribution from dynamic light scattering (DLS) data. Simulated results and experimental validity demonstrate that the proposed method, which compliments the CONTIN algorithm, might serve as a powerful and simple approach to the inverse problem in DLS.

Effect of scattering angle error on particle size determination by multiangle dynamic light scattering

Dynamic light scattering (DLS) is a popular method of particle size measurement. Multiangle dynamic light scattering (MDLS) collects DLS data at multiple angles and analyzes the data simultaneously to improve the particle size measurement. Using data from several scattering angles admits the possibility of introducing noise caused by scattering angle error in the measurement, which may have an impact on the performance of the MDLS technique. We investigate the effect of scattering angle noise on recovered particle size distributions (PSDs) using simulated and measured MDLS data and various levels of angular noise. Our results show that, for unimodal PSDs, those with small particle sizes are more strongly affected by the noise than are medium and large particle size systems. For bimodal PSDs, those containing small-sized particles are also more affected by the noise than the systems of larger particles. Furthermore, broad PSDs are more vulnerable to angular noise than narrow PSDs.

Wavelet denoising experiments in dynamic light scattering

Dynamic light scattering (DLS) is widely used for particle size measurement. Recovering accurate particle sizes from noisy DLS measurements (short duration and/or low count rate) is problematic. We demonstrate that denoising of the light scattering signal using wavelet packet filtering is beneficial and leads to more accurate particle sizes being recovered.

Non-negative constraint research of Tikhonov regularization inversion for dynamic light scattering

In dynamic light scattering (DLS) technology, a non-negative constraint on the solution can improve the inversion accuracy of the particle size distribution (PSD). Different non-negative constraint methods have different effects on the inversion results. Combined with the Tikhonov regularization inversion method, the following non-negativity constraint methods: negative to zero (N-to-Z), multi-negative to zero (Multi-N-to-Z), Lin-projected gradient (LPG), oblique projected Landweber (OPL), projected sequential subspace optimization (PSESOP), interior point Newton (IPN), gradient projection conjugate gradient (GPCG) and trust-region method based on the interior reflective Newton (TR-IRN) method are studied in DLS inversion. In different inversion ranges and noise levels, autocorrelation functions of unimodal and bimodal particle distributions were inverted using different non-negativity constraint methods. From the inversion results, the characteristics of the various methods were obtained, which can be treated as a reference for the implementation of non-negative constraints in Tikhonov regularization inversion of DLS.

Wavelet Noise Reduction in Dynamic Light Scattering

Particle size determination with dynamic light scattering (DLS) is limited by noise. We have used a wavelet transform method to reduce noise in the DLS data. A digital storage oscilloscope (DSO) was used to capture the time-history of the scattered light intensity and signal denoising was implemented with a multi-scale packet wavelet transform. The experimental results indicate that, for a threshold of 0, corresponding to no denoising, the DLS signal with noise, does not give good results because the number of samples used to compute the correlation function was only 20k or 10k and the data are noisy. However, denoising with thresholds in the range 0.5-0.8 can give both better particle size values and smaller root mean square error from the same raw light scattering data.

Research on ultrafine particle size measurement using small amounts of data

The paper puts forward a new method of ultrafine particle size measurement using small amounts of data of a dynamic light-scattering signal, and establishes an arithmetic model of the measurement by wavelet package transform. First, through the wavelet package transform, the ultrafine particle dynamic light-scattering signals were decomposed into multifrequency bands. Then, the noise of signals of different frequency bands were removed and the power spectrum of the wavelet packet coefficients of each frequency band was calculated. Finally, the ultrafine particle size distribution information could be deduced from inversing the power spectrum. The standard polystyrene particles of 100, 300, and 400 nm were measured using this method, and the inversion results indicated that this method can effectively remove noise and improve the accuracy of particle size measurement using small amounts of data.

Inversion of photon correlation spectroscopy based on truncated singular value decomposition and cascadic multigrid technology

For the low accuracy of single-scale inversion method in photon correlation spectroscopy technology, a cascadic multigrid (CMG)-truncated singular value decomposition (TSVD) inversion method that combines the TSVD regularization with CMG technology is proposed. This method decomposes the original problem into several subproblems in different scale grid space. According to the particle sizes inverted from the coarsest scale to the finest scale, the solution of an original inversion problem can be obtained. For the inversion of each subproblem, TSVD method is used. The simulation and experimental data were respectively inverted by TSVD and CMG-TSVD methods. The inversion results demonstrate that the CMG-TSVD method has higher accuracy, more strong noise immunity and better smoothness than the TSVD method.

Simulation of the light signal scattered by brownian colloidal particles

In dynamic light scattering experiments, the light intensity scattered by brownian colloidal particles is regarded as a stationary stochastic process. According to the theory of stationary stochastic process, a method for generating the light scattering signal is proposed. This method establishes an auto-regressive (AR) model by the autocorrelation function (ACF) of scattered light signal. When white noises pass this AR model, scattering light signal can be obtained. The numerical results show the ACF of simulated signal performs a good agreement with its theory value. Therefore, this method is feasible for the simulation the light signal scattered by brownian colloidal particles. In addition, by analyzing influence of simulation parameters on simulation precision, the paper acquires the relationship of simulation parameters and simulation precision.

Appropriate sampling quantity and its influence on particle sizing results in PCS technique

In photon correlation spectroscopy(PCS)particle sizing technique, the measurement accuracy is concerned with total sampling quantity N. the larger N is, the closer to true value will measured autocorrelation function be. However, large amount of sampling quantity means long measurement duration, and significant addition of memory cells is desired for software correlation in batch process mode. The reasonable sampling quantity can be determined through the estimation of relative error of autocorrelation function. Relative error of autocorrelation for correlator of M channels is approximate to±(M/N)1/2. For different particle systems and correlator channels, measurement duration ranges from several seconds to minutes. In practice, noise is another important factor concerned with the choice of sampling quantity. For the same particle system and the same number of correlator channels, measurement repeatability and deviation varies under different error level, can be improved through increasing the sampling quantity and adding correlator channels. Autocorrelation functions of simulated scattered light signal of 50nm, 100nm and 300nm particles were inversed under noise levels of 0, 0.01 and 0.1 respectively. Results show that, if theres no noise, only with small sampling quantity can ideal test result be achieved, while under noise level nonzero, to enhance measurement repeatability and minimize deviation, the desired sampling quantity need to increases with the increase of noise. Increasing sampling quantity will decrease fitting errors caused by the noises, which make the inverse algorithm produce better results.