Lifetimes of chemical species is typically estimated, on a pixel-by-pixel basis by either fitting time correlated single photon counting (TCSPC) histograms or, more recently, through phasor analysis from time-resolved photon arrivals. While both methods yield lifetimes in a computationally efficient manner, they have limitations. First, both TCSPC and phasor analysis set the number of chemical species by hand before lifetimes can be determined. Yet the number of species itself is encoded in photon arrival times and need not be set by hand a priori. Next, even to determine lifetimes under the assumption of a known number of species, both methods rely on heavy data post-processing of the signal thereby requiring large amounts of data to retrieve lifetimes. As a result, the sample is exposed to orders of magnitude more light than is required and the ability to resolve fast processes is compromised. Here we propose a direct photo-by-photon analysis of data drawn from pulsed excitation experiments to infer, simultaneously and self-consistently, the number of species and their associated lifetimes from as little as a few thousand photons for two species. We do so by leveraging new mathematical tools within the Bayesian nonparametric (BNP) paradigm that we have previously exploited in the analysis of single photon arrivals from single spot confocal microscopy. We benchmark our method on simulated as well as experimental data for one, two, three, and four species with data sets from both immobilized and freely diffusing molecules.
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