Sequential Extraction of Late Exponentials (SELE): A technique for deconvolving multimodal correlation curves in Dynamic Light Scattering

Abstract

Abstract:In techniques such as Dynamic Light Scattering (DLS), Fluorescence Correlation Spectroscopy, and image mining, motion is tracked by the autocorrelation of a signal over logarithmic time scales. For instance the tracking signal in DLS is the scattered light intensity; it remains correlated at time scales where scant changes in the arrangement of the scattering particles occur, but decays exponentially at the time scales of their diffusion. When there are multiple time scales of motion (for instance due to scatterers of different sizes), the correlation curve has more than one exponential fall. Extracting the decay constants or hydrodynamic sizes due to each exponential fall in a multi-species field correlation curve becomes an ill-conditioned mathematical problem. We describe a new algorithm to invert a multi-modal correlation curve by Sequential Extraction of the Late Exponentials (SELE). The idea is that while the inversion of a multi-exponential equation may be ill posed, that of a single exponential is not. So we fit data windows towards to base of the correlation curve to extract the largest contribution species, remove the species contribution from the correlation curve, and repeat the process with the remnant curve. The single exponent can be robustly fitted by least-square minimization with initial guesses generated by an adapted cumutant technique (power-series) that includes stretch coefficients (measure of sample dispersity). The proposed algorithm resolves particle sizes separated by 3X, and is reliable against fluctuations in the correlation curve and to localized regions of suboptimal data. The algorithm can be used to track particle dynamics in solution in multi-species problems such as self-assembly.