Submicron particle size distributions by dynamic light scattering with non-negative least-squares algorithm

A method is proposed using the non-negative least-squares (NNLS) algorithm of Lawson and Hanson to analyze dynamic light scattering (DLS) data for the size distribution of particles in a colloidal dispersion. The NNLS algorithm gives sparse solutions, which are sensitive to the domains used for reconstructing the solutions. The method uses the algorithm to construct an optimal solution from a set of sparse solutions of different domains but of the same dimension. The sparse solutions are superimposed to give a general solution with its dimension being treated as a regularization parameter. An optimal solution is specified by a suitable value for the dimension, which is determined by either Morozov's criterion or the L-curve method. Simulated DLS data are generated from a unimodal and a bimodal distribution for evaluating the performance of the method, which is then applied to analyze experimental DLS data from the ocular lenses of a fetal calf and a Rhesus monkey to obtain optimal size distributions of the α-crystallins and crystallin aggregates in the ocular lenses.