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Journal of Physics D Applied Physics

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

Carmen Cámara, Manuel P. Cagigal, Fernando G. Moreno, Felipe González

Published Aug 14, 1990• 8 citations
Publisher

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 4 T 1 state of Mn 2+ in an undoped TMMC crystal at room temperature.

DOI
10.1088/0022-3727/23/8/002

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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.
In this paper we present a method for processing the time-interval data obtained in a single-photon-decay spectroscopy experiment. This method is based on the measurement of the Laplace transform of P ƒ ( t) [the probability distribution function of the time of arrival of the first photon (PDFP) after the excitation pulse] instead of the direct measurement of P ƒ ( t) by means of a multichannel analyzer. With the use of this method, a good estimation of the lifetime of the signal can be obtained with a shorter measurement time than that used in the conventional method, in which the recorded time intervals are used to construct P ƒ ( t). A theoretical model of the error involved in determining the lifetime is obtained for the Laplace method, and it is compared with that corresponding to the measurement of P ƒ ( t) by means of a multichannel analyzer. Finally, a computer simulation of the experiment is performed to corroborate the theoretical predictions.
Time-correlated single photon counting is a technique to record low level light signals with very high time resolution. We first describe the experimental apparatus and briefly outline the statistical interpretation of the measurement series. After, we propose a stochastic model for the formulation of interference patterns based on doubly stochastic autoregressive model class. We suggest the application of optimal filtering technique conceived in [R. J. Elliott et al., (1997)] in order to estimate the underlying intensity process of the Poisson type measurement series. Finally, we present some results of the identification of realistic data that is although in coincidence with the general view of interference experiments, goes beyond the physical interpretation and may deepen our understanding of the quantum world.
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.