Photon-counting distribution of fluorescence from a blinking molecule

Photon-counting distribution of fluorescence from a single molecule is modeled as a doubly stochastic Poisson distribution. A two-state model is considered where fluorescence from a dye molecule jumps between an `onʹ (=high) intensity level and an `offʹ (=low, background) level. Those intensity jumps may be caused by sojourns of a molecule into a non-emissive triplet state. Illustrative examples of photon-counting distribution are calculated for three parameter regimes. In the slow blinking regime, the `onʹ and `offʹ lifetimes are much longer then the integration time (=bin time). In the intermediate regime at least one of the `onʹ and `offʹ lifetimes is comparable with the integration time. In the fast blinking regime, the `onʹ and `offʹ lifetimes are shorter then the integration time. The photon-counting distribution can be helpful in establishing whether an experimental intensity histogram is consistent with triplet blinking.