Study On The Dynamic Light Scattering Weighted Inversion Algorithms

Dynamic light scattering(DLS)is a widely applied technique for measuring submicronand nanoparticle size distribution in science and industry.In this technique,the particle size distributions(PSD)are acquired by inverting the autocorrelation function(ACF)of the scattered light intensity.The recovery of the PSDs involves solving a Fredholm integral equation of the first kind,which is a highly ill-posed problem.In particular,the measurement of unimodal broad PSDs and closely-spaced bimodal PSDs with the peak position ratio of less than 2:1 has not been well solved.The weighted inversion algorithm provides the possibility for its accurate measurement.In the ACF,the particle size information is mainly distributed in the attenuation delay section,and the noise is mainly distributed in the long delay section.In order to make full use of the particle size information in the decay delay section and effectively suppress the noise in the long delay section,it is necessary to weight the ACF,that is,different weights are given in different section.However,due to the limitations of the algorithm itself,it can not dynamically test whether the particle size information is fully utilized,so there are some errors in the measurement results.And in the multi-angle dynamic light scattering(MDLS),the angular weighting coefficient is easy to be affected by the noise,so it is difficult to obtain it accurately.In this paper,the problem of particle size weighted inversion is studied from the aspects of how to maximize the use of particle size information and how to accurately calculate the angular weighting coefficient.And the main work of this paper consists of,1.The basic theory of weighted inversion is analyzed.The measurement information of particles is mainly distributed in the decay delay period of the ACF.In order to extract the particle size information from the ACF,the ACF needs to be weighted.In the section with relatively concentrated particle size information,a larger weight is given,and in the section with noise,a smaller weight is given.And the particle size information of closely-spaced bimodal distribution in the ACF is significantly less than that of far bimodal distribution,which is also the main reason of the difficulty in inversion of closely-spaced bimodal distribution..2.The deviation weighted inversion of dynamic light scattering method based on ACF reconstruction was studied.In order to make full use of the effective particle size information of the decay delay section of the ACF,a weighted inversion method of information deviation is proposed.The PSD can be obtained by information character weighted inversion,and then the ACF can be reconstructed.Compared with the real ACF,it can see whether they are coincident.If not,the weighted matrix can be reconstructed by using the difference between them to correct the last information weighting,and then the inversion can be carried out.By usingdeviation weighted inversion successively,the next deviation is reduced until the minimum of the information deviation is reached,that is,the ACF corresponding to the PSD obtained by last inversion will tend to be in conformity with the ACF obtained from the correlator.This method realizes the maximum utilization of particle size information in the ACF by dynamically testing the utilization effect of information and weighting the deviation successively.3.The multi-angle dynamic light scattering analysis based on successive updating of the angular weighting method was studied.How the benefit brought by the information character weighted inversion algorithm benefits the calculation of the angular weighting coefficient is studied.A novel successive updating of the angular weighting method is proposed.By using information character weighting,the angular weighting coefficient and the character weighting matrix are updated once with each additional angle.The effect of autocorrelation function(ACF)denoising and information extraction is improved by using information character weighting step-by-step.The results for broad unimodal and closely-spaced bimodal PSDs demonstrate the effectiveness of this method.Compared with another routinely-used inversion method,it is found that the increase in PSD information retrieved from MDLS depends not only on increasing the number of angles,but also on the calculation of the angular weightings.An accurate weighting algorithm can reduce the number of scattering angles required.Using the AWSU method for PSD recovery with 4 scattering angles can give better results than the usual method with 6 scattering angles.It is also found that the AWSU method not only improves the accuracy of the weightings,but it also contributes directly to the PSD recovery by reconstructing the ACF with the PSD obtained by the weighted inversion.The combination of these two contributions not only reduces the number of scattering angles needed,but also keeps the PSD recovery results from getting worse because of excessive scattering angles.4.The iteration deviation weighting method was studied.In particle size inversion,any small disturbance will affect the stability of the solution.In the angular weighting update step by step method,the accuracy of PSD affects the accuracy of angular weighting coefficient,while the accuracy of angular weighting coefficient affects the accuracy of information weighting,and the accuracy of final information weighting coefficient directly affects the accuracy of PSD.So in order to ensure the stability of PSD,this paper proposes an iterative deviation weighting method was proposed in this paper.When the recovered PSD is used for the calculation of the next angular weighting coefficient,first use this PSD to reconstruct the ACF,carry out the information utilization effect test,and then carry out the information deviation weighting according to the test results,until a stable distribution is obtained.The error in the update process is greatly reduced,and more accurate measurement results of theunimodal broad PSDs and the closely-spaced bimodal PSDs are obtained.The accurate measurement of the unimodal broad PSDs and the closely-spaced bimodal PSDs with the peak position ratio less than 2:1 and containing large particles has always been a difficult point in the DLS measurement.In this paper,through the exploration and research of the weighted inversion method of the dynamic light scattering data,we strive to effectively improve the accuracy of the dynamic light scattering particle measurement of the unimodal particle system and the closely-spaced bimodal particle system,so as to promote this technology and seeks to obtain more accurate PSD to meet the increasingly social requirements of complicated PSDs.