Optimizing Fitting Statistics in Photon Correlation Spectroscopy

Abstract

We have performed an experiment to test our understanding of the run time, T, necessary to achieve a specified precision in the value of the intensity coherence time, τc, extracted from correlation functions taken in the strong signal limit, and to test predictions for the values of some experimental parameters that optimize the precision. Using ensembles of 10 correlation functions taken at 5 different choices of sample time, we found that the ensemble estimators for the error in τc were well described by the expression δτ/τ c =4.2/T/τ c , in agreement with the work of Degiorgio and Lastovka (1971). The sample times used were chosen so that the number of coherence times spanned by the 128 channels of the correlator, α, covered the range 1 ≤ α ≤ 16; in this range, we found no evidence of a minimum in δτ/τc to suggest an optimum value of α. These results were independent of whether we used three-parameter or two-parameter least-squares fits to extract τc. However, we did find that the two fits gave systematically different values of τc, and both show a similar dependence on α.