The peak constrained positive exponential sum method of inverting Laplace transform applied to correlation spectroscopy

Abstract

As a contribution to the basic problem of correlation spectroscopy, a method has been developed for the Laplace transform inversion with a given number of maxima in the nonnegative inverted functionΤΩ(Τ) (i.e. in the distribution function of decay timesΤ recalculated as a density function on a logarithmic scale) by the least squares method. The resulting solution consists of the given number ofδ-functions, each of which may be accompanied on one or both sides by one or several histogram bins decreasing away from theδ-function. When applied to simulated data for quasielastic light scattering (QELS), the method yields good agreement of the calculatedΤ distributions with the simulated ones, except that it yields sharp edges to the histogram bins and artefactδ-functions at the maxima of all the bands. An example shows the method to be a useful tool in interpreting QELS data.