Description of the time interval correlation function and its application to lifetime determination

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Abstract
A Poisson point process (PPP) presents a series of characteristics which may be used to define functions with an optimal signal-to-noise ratio. This work describes a statistical function, obtained by measuring time intervals in a PPP, which contains the same information about the signal to be analysed as the autocorrelation function. The advantage of this function is that it can be applied to cases of low light level in which the autocorrelation function gives a low SNR. As a particular case of low light level signals, the authors have used this method in a real experiment of single photon decay spectroscopy and measured the lifetime of the 4T1 state of Mn2+ in an undoped TMMC crystal at room temperature.