Inversion Of Multimodal Particle Size Distribution Based On Improved Regualarization Method In Dynamic Light Scattering

In Dynamic Light Scattering measurement technique,getting particle size distribution need to solve the first kind Fredholm integral equation,which is an ill-conditioned linear problem,therefore,it was hard to acurately invert multimodal particle size distribution.In order to realize accurate inversion of multimodal particle size distribution,the paper studied the mehod based on regularization,which adding a smooth constraint penalty item in the objective function of regualarization and using several different regular parameters to address the regular matrix,and then applied these methods to inverse the dynamic light scattering data.The main research contents of this paper includs1.Particle size iniversion of multi-penalty regularization method.Inverting single and multi-angle dynamic light scattering data in single modal and multi-modal particle system with Tikhonov regularization method and multi-penalty regularization method,Tikhonov regularization method have a single penalty term,its adjustment ability is too big or too small,adding a penalty term can increase the resolving power of multimodal,and then make the inversion results more accurate.Adding a smooth constraint penalty term can effectively eliminate the spike and spurious peaks in reversed particle size distribution,improving the resolution of particle size distribution and increasing the antinoise ability.Sequentially,making better use of the advantage that Multi-angle Dynamic Light Scattering technique could be able to provide more information of ultrafine particle size distribution in medium and large size range,and then realize the accurate measurement of bimodal and multi-modal particle from nanometer to submicron size range.2.Particle size iniversion of multiparameter regularization method.The multiparameter regularization method by applied several different regular parameters reconstructed after truncated singular value to regular matrix,it can inhibit the small singular value impact on the inversion results,making its inversion ability,anti-noise ability and resolution power increased.Inverting multimodal particle size distribution with multiparameter regularization method can effectively eliminate the false peaks in reversed particle size distribution,at the same time,retaining more particle size information,and strengthen the ability of multimodal resolving.3.Particle size iniversion of weighted multi-penalty regularization method.Weighted regularization method by processing dynamic light scattering data at different delay time with different weight coefficients can enhanced the ability of extracting measurement information.However,with the influence of noise,false peaks and spikes appeared in the particle size distribution of bimodal and multimodal,and even appeared at the peak.Adding a smooth constraint penalty item in the objective function of weighted regualarization can effectively eliminate the false peaks in the inversed particle size distribution,and getting more accurate bimodal and multimodal particle size distribution.4.Particle size iniversion of segmented weighted multi-pennalty regularization method.Segmented weighted regularization method can suppresse the influence that caused by random noise of long delay time on bimodal and multimodal results,and improve the utilization rate of the particle sizing information.Adding a smooth constraint penalty item in the objective function of segmented weighted regualarization not only can effectively avoid the false peaks and spikes occurrenced in reversed particle size distribution,and greatly improved the inversion performance of bimodal and multimodal,then realizing accurate particle sizing in bimodal and multimodal particle system.It was a difficult problem that inverting multimodal particle size distribution accuracy in dynamic light scattering technique.In the paper,we using the modified regularization method to inverse the dynamic light scattering data of multimodal particle system,these methods can effectively improved the accuracy of dynamic light scattering measurement of multimodal particle system.