Regularized inversion of dynamic light scattering intensity data

This paper presents a new method of analyzing intensity correlation data obtained in dynamic light scattering measurements of particles in Brownian motion in a colloid. A second-order linewidth distribution is obtained directly from the intensity autocorrelation by the method of regularized inversion with a nonnegativity constraint, based on the regularization method of Tikhonov. The linewidth distribution, and consequently a particle size distribution, is obtained by deconvolving the second order linewidth. The method is illustrated using a variety of data obtained using a compact optical fiber based instrument developed by Dhadwal. It is shown that regularized inversion of intensity data, followed by a deconvolution to obtain the first order linewidth distribution, is superior in performance to the inversion of reduced first order data. The reduction of second order data by subtracting a baseline and taking the square root of the difference results in increased noise, and in distortion. Noise and distortion cause inaccurate or even completely spurious inversions. The method can resolve very narrow monomodal size distributions or much broader multimodal distributions.