Particle size distribution inversion in dynamic light scattering by adaptive step-size non-negative least squares

Abstract

The non-negative least squares algorithm is widely used in dynamic light scattering, however, it suffers the shortcomings of sparse solutions and poor anti-noise performance. It is found that the construction of the kernel matrix of the algorithm is of great significance to the accuracy of the final results. In this paper, we propose an adaptive strategy to find the optimal step-size to construct the kernel matrix. By calculating the L2-norm between the measured and reconstructed light intensity autocorrelation function, the optimal step-size is determined corresponding to the minimum difference error. Then the kernel matrix constructed by this optimal step-size is used in the inversion. The final result is obtained by fitting the solution to a predefined model, such as a Gaussian model. This strategy improves the sparsity of NNLS solution, and thus the accuracy and stability of NNLS inversion results. The simulation and experiments demonstrate that the adaptive step-size strategy improves the stability and accuracy of the non-negative least squares inversion algorithm for dynamic light scattering.