Fitting the correlation function

The whole correlation function of the intensity of scattered light is usually determined from a single realization of the photocurrent. As a result, the values of the correlation function at different delay times are not statistically independent. A standard least-squares fitting procedure is not optimal for an analysis of such data. However, the benefits of mathematically rigorous but highly nonlinear and less stable methods are not known. We consider the test case of a Gaussian signal with a single-exponential correlation function without shot noise. In this case the fitting procedure, which is based on the maximum-likelihood principle for the observed signal, permits an analytical solution. We demonstrate that such a rigorous statistical analysis produces an approximately two times more-accurate result for the relaxation time than does the standard least-squares fit. This gain, however, is greatly reduced by the presence of shot noise, which introduces additional uncorrelated errors into the values of the correlation function.