Multiplexed single-photon counting. II. The statistical theory of time-correlated measurements

We present the statistical theory governing the operation of multiplexed time-correlated single-photon counting (MUX-TCSPC) fluorometers which incorporate multiple detection channels and a single time-to-amplitude converter. The requirement to reject coincident counts in different detection channels leads to binomial photon counting statistics. The overall data collection probability is mapped out in terms of the ‘‘start’’ repetition rate, the number of detection channels, the ‘‘stop-to-start’’ rate ratio per detector, and the dead time. The overall collection probability is shown not to be proportional to the number of detection channels, but to be maximized at ∼0.37, which still compares very favorably with the equivalent pileup limited probability of ∼0.01 for a single detection channel. Excellent agreement with our theory is demonstrated for experimental data with 2 and 16 detection channels. Potential sources of errors when using MUX-TCSPC to record fluorescence anisotropy and spectra are described. The theory we describe provides a model for photon counting with multiple detection channels which is quite general and also applicable to other fields such as time-resolved imaging using photon migration in tissue and optical time-domain reflectometry.