Singular value analysis and reconstruction of photon correlation data equidistant in time

Abstract

The application of the algorithm of Zeiger and McEwen to the analysis of noisy photon correlation data is investigated. For the particular case where the data are sampled at equidistant time intervals a complete solution is given allowing reliable reconstruction of the spectrum of exponential decay rates without any a priori knowledge. A particular attractive feature of the method is that the singular value analysis of the Hankel matrix of autocorrelation functions offers a practical criterion for the decomposition of the data into a signal and a noise part. Some tests of the method are illustrated with experiments on monodisperse latices, gold sols, and binary mixtures of monodisperse latices. In the latter case comparable and even better results are obtained in significantly shorter computing time when compared to an analysis with Contin and the maximum entropy method. Since the present method does not require any a priori parameter setting, it is also complementary to these methods.