Accurate Analysis of Fluorescence Decays from Single Molecules in Photon Counting Experiments

In time-resolved, single-photon counting experiments, the standard method of nonlinear least-squares curve fitting incorrectly estimates the fluorescence lifetimes. Even for single-exponential data, errors may be up to +-15%, and for more complex fits, may be even higher, although the fitted line appears to describe the data. The origin of this error is not a result of the Poisson distribution, as is often stated, but is entirely due to the weighting of the fit. An alternative weighting method involving a minor change in the fitting method eliminates this problem, enabling accurate fitting even in difficult cases, including the small data sets observed in single molecule experiments and with a precision similar to that of maximum likelihood methods.