Positive exponential sum method of inverting Laplace transform applied to photon correlation spectroscopy

A computer program for the positive exponential sum method of inverting Laplace transform of photon autocorrelation curves has been written and applied to both simulated and experimental data. The method recovers the decay time spectra from autocorrelation curves by replacing the decay time distribution by a set of delta peaks whose envelope roughly follows this distribution. Spacing of this set becomes slightly denser with decreasing noise and is about two peaks per decade under usual conditions (noise level about 10^–3). Occasional irregularities in peak spacing and an appearance of weak artifact peaks in regions where the decay time spectrum is of zero density may make the physical interpretation of results difficult.