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Journal of Modern Optics

The Measurement of the Triggered Probability Density as an Alternative to the Direct Evaluation of the Triple Correlation

L. Vega, Manuel P. Cagigal, Pedro M. Prieto

Published Mar 1, 1994• 0 citations
Publisher

Abstract

Evaluations of the triple correlation function for different time delays are performed from combinations of the triggered probability density values corresponding to a series of counting times. This technique can only be applied to very low light level signals, but ultimately, the signal-to-noise ratio obtained by this method is better, for short time delays, than that obtained from a direct measurement of the triple correlation function.

DOI
10.1080/09500349414550541

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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 4 T 1 state of Mn 2+ in an undoped TMMC crystal at room temperature.
The theoretical expression of the first-order factorial moment of a triggered delayed photocount distribution and a description of its SNR have been developed. We explain the adventages of this thecnique, in comparison with the second-order correlation function, when we measured a temporal signal under low light level. We derived the theoretical errors involved in determining a parameter by measuring both functions for a signal with a periodically modulated intensity, since this kind of signals usually appear in spectroscopy. We conclude that the first-order factorial moment of a triggered delayed photocount distribution is a useful tool for characterizing a signal at low; light level conditions.