Xianming Sun

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.

Multiangle dynamic light scattering analysis using angular intensity weighting determined by iterative recursion

Multiangle dynamic light scattering (MDLS) can provide better results for particle size distribution (PSD) determination than single-angle dynamic light scattering. Proper analysis of MDLS data requires data from each measurement angle to be appropriately weighted according to the intensity scattered by the particles at each scattering angle. The angular weighting coefficients may be determined by measuring the angular dependence of the scattered light intensity or estimated in various ways. In either case, any noise on the weighting coefficients will adversely affect the PSD determination. We propose a new iterative recursion method for estimating the weighting coefficients and demonstrate its effectiveness for recovering PSDs from both simulated and real experimental data. The new method gives better PSD results than those found using other weighting estimates.

Design of Multiple-Tau Photon Correlation System Implemented by FPGA

The photon correlation spectroscopy (PCS) experiment can measure the distribution of particle sizes by measuring dynamic fluctuations of intensity of scattered light. A way to analyse particle sizes from PCS is to calculate the auto-correlation function of the detected intensity. In order to get accurate result, we need a photon correlator with small sampling time and large-scale dynamic range. This paper presents not only a linear photon correlator but also a multiple-tau correlator implemented by high performance Xilinx field programmable gate array (FPGA). In the photon correlator, the works of counting, delaying, multiplying and accumulating are all completed in one FPGA chip. The Verilog-HDL is adopted in the design of FPGA modules. Experimental results indicate that this correlator can be applied in the analysing of ultra-fine particle sizing.

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.

Improved inversion procedure for particle size distribution determination by photon correlation spectroscopy

We propose a minimum variation of solution method to determine the optimal regularization parameter for singular value decomposition for obtaining the initial distribution for a Chahine iterative algorithm used to determine the particle size distribution from photon correlation spectroscopy data. We impose a nonnegativity constraint to make the initial distribution more realistic. The minimum variation of solution is a single constraint method and we show that a better regularization parameter may be obtained by increasing the discrimination between adjacent values. We developed the S-R curve method as a means of determining the modest iterative solution from the Chahine algorithm. The S-R curve method requires a smoothing operator. We have used simulated data to verify our new method and applied it to real data. Both simulated and experimental data show that the method works well and that the first derivative smoothing operator in the S-R curve gives the best results.

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.