Jin Shen

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.

Analysis of noisy dynamic light scattering data using constrained regularization techniques.

Dynamic light scattering (DLS) from colloidal particles often contains noise, which makes inversion of the correlation function to obtain the particle size distribution (PSD) unreliable. In this work, poor-quality correlation function data with baseline error were analyzed using constrained regularization techniques. The effect of baseline error was investigated, and two strategies were proposed to compensate for baseline error. One strategy is based on edge proportion detection of spurious peaks at large size in the PSD, and the other is based on the solution norm. Results from simulated and experimental data demonstrate the effectiveness of our proposed strategies. The L-curve rules for standard Tikhonov and for constrained regularization, the generalized cross-validation (GCV) rule, and the robust GCV rule were investigated for determination of the regularization parameter. A comparison of these rules was done using both simulated and experimental data. It is shown that correction of baseline error with baseline compensation as well as a reasonable regularization parameter choice improves the accuracy of PSD recovery in poor-quality DLS data analysis.

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.

Accurate Retrieval of Bimodal Particle Size Distribution in Dynamic Light Scattering

Dynamic light scattering (DLS) is one of the most popular techniques for the particle size distribution (PSD) determination of particles under Brownian motion. However, the accurate retrieval of PSD from bimodal particles with a peak position ratio less than 2:1 is still an open problem in single-angle DLS measurement. In this letter, we proposed a new weighted constrained regularization (CR) method to improve the accuracy of inversion PSD for single-angle bimodal DLS data. The weighted CR method significantly improves the accuracy of inversion PSD for various bimodal particles, and, for the first time, reasonably resolves bimodal particles with a peak position ratio less than 2:1, such as 1.75:1, 1.50:1, and 1.68:1.

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.

Depolarization and Polarization of Light Scattering by Dustlike Tropospheric Aerosols

Measurement of the polarization and depolarization characteristics of light scattering by aerosols is a powerful remote sensing technique for retrieving the microphysics of aerosol particles. In this paper, we model dust-like aerosols using mixtures polydisperse, randomly oriented spheroids with varying aspect ratios from 0.6 μm to 2.0 μm at the wavelength of 0.443 μm and 0.865 μm. The Stokes scattering matrix elements averaged over wide shape distributions of spheroids are compared with those computed for polydisperse randomly oriented single scattering spheroids. The shape-averaged phase function for a mixture of spheroids is smooth, featureless, and nearly flat at side-scattering angles and closely resembles those typically measured for natural sand and dust particles. The linear and circular depolarization ratios were computed using the rigorous T-matrix method. We also show that there is no simple relationships between the depolarization ratio and aspect ratio, and an single spheroidal shape particles cannot be used to model natural dust aerosols.

Novel photon correlator with less hardware resource

Photon correlator is kernel component of Photon Correlation Spectroscopy particle sizing instrumentation, which must calculate autocorrelation function in real time. The correlation processing can be carried out by hardware or software. Hardware implemented with photon correlator has good real-time processing ability, but the cost for hardware resource is pretty high. Software correlator is comparably cheap but not competent for real-time processing. Hardware and software photon correlator architecture is analyzed, and a novel least hardware resource real-time correlator architecture taking advantage of fast processing speed of FPGA devices and vast memory space of microprocessor is presented in this paper. In this new architecture, high speed and middle speed correlator channels are implemented in FPGA, within which counter, shift register and multiplier are built with logic resources. At sample times longer than 100μs, photon pulse count, the output of 16-bit counter in FPGA, is sent to DSP to finish correlation calculation. The 300Mhz float-point DSP chip TMS320C6713 is chosen, which can finish 256-channel calculation task in 100μs. The combination of FPGA and DSP significantly decreases the hardware cost of correlator on the premise of real-time processing, and brings great flexibility to the designing of correlator.