Artefacts in the analysis of temporal response functions measured by photon counting

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The least-squares (LS) method in fluorescence decay analyses and in time-domain analyses of the diffuse scattering light for data measured by the time-correlated single photon counting (TCSPC) technique is experimentally evaluated, and the artefact in LS analysis for data with different counting statistics is discussed. In single exponential decay analysis, the error of the decay parameter by the LS method is smaller than 10% of the expected true value when the average number of counts per bin (N/k) is more than 1, and the fitting region covers a period on the order of the decay time. In multi-exponential analysis, the decay parameters are sensitively dependent on the counting statistics. In contrast, the fitting by the maximum likelihood estimation (MLE), assuming Poissonian statistics, greatly reduces such dependence of parameters on the counting statistics. In another application, time-domain diffuse scattering measurements, the LS method is only accurate at N/k > 50 (10% error in the absorption coefficient). In particular, the absorption coefficient is largely dependent on the count. In both examples, the problem of stability in the fitting process by MLE still remains: the convergence of the fitting is critically dependent on the selection of initial guesses of the parameters in contrast to the convergence in the LS method. Thus, a hybrid method using the LS method for the determination of the initial guesses is a practical solution to this problem.