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Regularized Inversion of the Laplace Transform: Accuracy of analytical and discrete inversion
Author(s) -
Ross Douglas A.,
Dhadwal Harbans S.
Publication year - 1991
Publication title -
particle and particle systems characterization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.877
H-Index - 56
eISSN - 1521-4117
pISSN - 0934-0866
DOI - 10.1002/ppsc.19910080151
Subject(s) - laplace transform , inversion (geology) , eigenfunction , regularization (linguistics) , mathematics , inverse transform sampling , mathematical analysis , statistical physics , physics , computer science , optics , eigenvalues and eigenvectors , quantum mechanics , paleontology , structural basin , artificial intelligence , biology , surface wave
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.