Regularized Inversion of the Laplace Transform: Accuracy of analytical and discrete inversion

Dynamic light scattering is a technique used for the optical determination of a colloidal particle size distribution. A simple procedure, based on a trapezoidal model for the linewidth distribution function, is given for obtaining a constrained regularized inversions of correlation data obtained in dynamic light scattering experiments, and estimating the accuracy of such inversions. Based on the eigenfunction decomposition of the Laplace integral equation, error bars, which are directly related to the accuracy of the correlation data, may be placed on both analytical and discrete inversions. By using a regularization procedure, and a nonnegativity constraint, problems with statistical noise in data may be handled effectively.