Study On The Inversion Algorithms Of Particle Size Distributuion In Dynamic Light Scattering Particle Sizing

The dynamic light scattering (DLS) technique, as a powerful tool for characterizing submirco and nano paticle size, has been widely used in fluid mechanics, polymer materials, medicine and biochemistry fields. However, the reconstruction of the particle size distribution, a very difficult inverse problem, should be dealed with, which also has been received wide spread attention. Because of the difficulties in solving the inverse problem, the diversity of particle size distributions and some prior knowledge assumed by many inversion algorithms, the existing algorhtms are suffered from limitations. Consequently, the improvement of current algorithms and development of novel excellent algorithms are urgent issues in the dynamic light scattering technique. Based on the nonnegative characteristics of particle size distribution, the baseline error effect, and the characteristic of inversion algorithms with the scattered intensity data subject to the denoising by wavlet packet transform, the main work of this paper consists of:1. The characteristics of various inversion algorithms were analyzed, and the comparisons of the performance between the common algorithms (NNLS, ML, PSO, CONTIN) were presented. The results show that the Tikhonov algorithm cannot guarantee the non-negative characteristic of the solutions, which reduces the accuracy of solution; the particle size distribution given by the NNLS algorithm is susceptible to the noise, and the ML algorithm supplies results which are over-smooth; the PSO algorithm and the CONTIN algorithm create the smooth distribution which are also superior to the ML and CONTIN algorithms.2. The inversion algorithms of Tikhonov regularization, the truncated singular value decomposition (TSVD) and the truncated conjugate gradient (TCG) were sdudied in dynamic light scattering inversion. The results show that the Tikhonov regularization is better than the TSVD and the TCG when the noise level is high. In addition, the selection criteria of the regularization parameter was studied, results demostrate that the L-curve rule is more robust than Morozov discrepancy principle and GCV rule.3. The use of CONTIN and Marino algorithms in dynamic light scattering data inversion were presented, following that the performance of the corresponding algorithms were completed. The second-order difference operator is superior to the indentity difference operator in terms of recovered particle size distribution. The L-curve is valid in the CONTIN algorithm. Compared with the CONTIN algorithm, Marino algorithm offers a smaller error of peak position. 4. A constraint Tikhonov regularization algorithm was proposed based on trust region Newton reflection and active set algorithms. In the presented approach, the effect of regularization parameter on the particle size distribution was investigated, and the selection rules of regularization parameter were discussed. In view of the difficulty in choosing regularization parameter, we proposed a novel regularization parameter selection rule, which is based on the optimiazatoin traces of optimization algorithms.5. To ensure a nonnegative solution to the TSVD algorithm, we proposed a nonnegative least square TSVD algorithm of particle size distribution inversion. There is a weak symmetry relationship between the relative error of particle size distribution and solution norm, and we use this relationship to determine the optimal regularization parameter. Simulated and experimental results demonstrate the validity of our nonnegative least square TSVD algorithm.6. We proposed an improved method for particle size distribution inversion based on the relationship between first order electric field correlation function and second order correlation function of light intensity. Simulated and experimental results show that the improved algorithm delivers results with a smaller error, in condition that partilce size distribution is unimodal.7. Dynamic light scattering intensity was processed by wavelet packet transform, which was analyzed by Cumulants method. The results demonstrate that wavelet packet denoising method is effective when the mean photon number is greater than one within the coherence time. At a certain wavelet packet threshold within 0.5-0.8, there is an optimal value of the particle size as well as a least mean square error, in the analysis of 300nm,503nm and 1035nm data with Cumulant method.The inversion of the particle size distribution remains the main factor that prevents improvement of the accuracy of the dynamic light scattering particle sizing. By now, sophisticated particle size distribution still embrasses the dynamic light scattering particle sizing. This work seeks to improve the accuracy from the aspect of inversion algorithm, contributing to meet the increasingly social demand of prtilce sizing for shophiscated particle size distributions.