An Inversion Algorithm Of Dynamic Light Scattering Based On Singular Value Decomposition

Nanoparticle has been widely used in many aspects of industry, agriculture and daily life, because of its special physical and chemical properties such as: surface effect, small size effect, quantum size effect, macroscopic quantum tunneling effect etc. The use of the Nanoparticle materials can effectively improve the performance, the quality of materials and crop yield, and is very important for the development of human. As an important research topic, the measurement of nano particle size has great important value of theory and practical application.Dynamic light scattering has been widely used in the measurement of nano particle size, as it is easy to use, and has low cost and high accuracy. And it has been a standard method for the measurement of nano particle size in dilute solution. But when we use the light intensity autocorrelation datas to inverse the particle size, we need to solve the first kind Fredholm integral equation, but it’s a typical ill-posed equation. To solve the problem better, the traditional inversion of dispersion particle size distribution requires prior knowledge or constraints for the solution.A new inversion algorithm based on singular value decomposition is proposed in the paper. Firstly, construct a Hankel matrix with the intensity autocorrelation datas. Then calculate the singular value decomposition of the Hankel matrix. And get the rank of the reconstruction matrix based on the singular value’s contribution. At last, calculate the characteristic value decomposition of the new matrix and the particle size distribution is obtained. So it can get a good result without any prior knowledge. In the paper, has some experiments to test and verify this algorithm, and the result is consistent with the theoretical analysis.And a filtering algorithm of photon correlation spectroscopy based on singular value decomposition is also proposed in the paper. Based on the singular value’s contribution, it can effectively filter out the noise from autocorrelation datas. Adding this algorithm to the traditional inversion, it can get better inversion result. And the result of experiment is consistent with the theoretical analysis.At last, a new dynamic light scattering particle measurement system is proposed in the paper. In the system, we use the photon counting card and the supporting software to replace the traditional digital autocorrelator. It can improve the portability of the system, and is easy to make some development for users. At the same time, it can greatly reduce the cost of research.