I assume that this is a photoluminescence decay measurement.

In this case it is governed by the excited state decay kinetics -

dNex/dt = - kem*Nex

Nex(t) = Nex(0) exp (-kem*t)

Crudely assuming the emission Intensity, Iem, is related to Nex

Iem(t) = Iem(0) exp (-kem*t)

a plot of Log (Iem) vs time should give you a straight line of slope kem, the emisison rate, or the inverse of the characteristic lifetime.

Your plot shows essentially this, until a time of about 3 microseconds, afterwhich it looks like the light levels reach those of the background.

I have no idea what you mean by 1/e, 1/e2, 1/e3.

Thanks, Hugh J Byrne, for your help.