Analytical approach to the recovery of short fluorescence lifetimes from fluorescence decay curves

Considerable effort in instrument development has made possible detection of picosecond fluorescence lifetimes by time-correlated single-photon counting. In particular, efforts have been made to narrow markedly the instrument response function (IRF). Less attention has been paid to analytical methods, especially to problem of discretization of the convolution integral, on which the detection and quantification of short lifetimes critically depends. We show that better discretization methods can yield acceptable results for short lifetimes even with an IRF several times wider than necessary for the standard discretization based on linear approximation (LA). A general approach to discretization, also suitable for nonexponential models, is developed. The zero-time shift is explicitly included. Using simulations, we compared LA, quadratic, and cubic approximations. The latter two proved much better for detection of short lifetimes and, in that respect, they do not differ except when the zero-time shift exceeds two channels, when one can benefit from using the cubic approximation. We showed that for LA in some cases narrowing the IRF beyond FWHM = 150 ps is actually counterproductive. This is not so for quadratic and cubic approximations, which we recommend for general use.