What is the Shortest Lifetime that can be Measured

It is frequently asked what is the shortest lifetime that can be measured with a given TCSPC system. A simple estimation can be made by using the first moments of the photon distributions measured for the IRF and the fluorescence. The first moment, Mj, or the centroid of the function/[t) is defined as 

For discrete time channels containing discrete numbers of photons is 

In the early days of TCSPC the moment or centroid shift method was used to calculate fluorescence and excited nuclear state lifetimes from measurement data [348, 549]. For fluorescence lifetime measurements this method has now entirely been replaced with curve fitting procedures. However, the first-moment technique has recently been revived for use in functional brain imaging [325]. A benefit of the first-moment technique is that the statistical accuracy of r calculated via the first moments can be easily estimated. Let the standard deviation of the photon arrival times in the IRF recording be Jjj. The standard deviation of the first 

For fluorescence lifetimes much shorter than the IRF width, the shapes of the recorded IRF and the recorded fluorescence curve are almost identical. Provided the same number of photons, N, is recorded both in the IRF and the fluorescence curve, the standard deviation,, of the calculated fluorescence lifetime, t, is  

With a femtosecond laser and an MCP PMT cr is about 10 ps. For a total number of recorded photons of A = 10 both in the IRF and the fluorescence, which is certainly a conservative assumption, the standard deviation of a short lifetime is 14 fs. This value is surprisingly low. 

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