### What is the fluorescence lifetime?

The fluorescence lifetime - the average decay time of a fluorescence molecule's excited state - is a quantitative signature which can be used to probe structure and dynamics at micro- and nano scales. FLIM (Fluorescence Lifetime Imaging Microscopy) is used as a routine technique in cell biology to map the lifetime within living cells, tissues and whole organisms. The fluorescence lifetime is affected by a range of biophysical phenomena and hence the applications of FLIM are many: from ion imaging and oxygen imaging to studying cell function and cell disease in quantitative cell biology using FRET.

For fluorescent molecules the temporal decay can be assumed as an exponential decay probability function:

$P_{decay}(t)={1/\tau} e^{-{t/\tau}},\quad t\gt 0$

where $$t$$ is time and $$\tau$$ is the excited state lifetime.

More complex fluorophores can be described using a multiple exponential probability density function:

$P_{multiple-decay}(t)={\sum_{i=1}^{N}}\alpha_i\cdot P_{\tau_i}(t),\quad t\gt 0$

where $$t$$ is time, $$\tau_i$$ is the lifetime of each component and $$\alpha_i$$ is the relative contribution of each component.