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Pure and Applied Optics Journal of the European Optical Society Part A

Signal-to-noise ratio improvement by measuring the moment generating function of the number of photopulses for low intensity periodical signals

Fernando G. Moreno, Pedro J. Valle, Jose Maria Saiz, Felipe González

Published Sep 1, 1992• 1 citation
Publisher

Abstract

The authors show, through the analysis of a periodically modulated light beam with a square profile, the improvement in the signal-to-noise ratio by measuring the moment generating function of the number of photopulses, Q n (s, T), with respect to the measurement of the second normalized factorial moment, n (2) (T). An experimental verification in the low light level range (1-10 photoelectrons per period) for different values of the modulation factor has been made. The results and some conclusions are presented.

DOI
10.1088/0963-9659/1/5/004

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Optics Letters•Apr 15, 1994•1 citation
The authors show, through the analysis of a periodically modulated light beam with a square profile, the improvement in the signal-to-noise ratio by measuring the moment generating function of the number of photopulses, Q n (s, T), with respect to the measurement of the second normalized factorial moment, n (2) (T). An experimental verification in the low light level range (1-10 photoelectrons per period) for different values of the modulation factor has been made. The results and some conclusions are presented.
In this paper, we have characterized an intensity square wave modulated light beam of period P and visibility factor, V, by measuring the moment generating function of the number of photopulses, Qn(s,T), for only one value of the counting time, T. This has been done for different values of the parameter s. A least square fitting procedure has been used to obtain simultaneously the characterizing parameters, P and V. A set of experimental measurements has been carried out for different values of both, the mean intensity per period, m, and the visibility factor, V.
Theoretical expressions for the factorial moments of the triggered photon-counting distribution that corresponds to a light beam with a periodically modulated intensity are derived. Two triggering procedures are considered: the time-window triggering procedure (which has been experimentally checked for Gaussian light by other authors) and the first-photopulse triggering procedure (which is a faster procedure). The theoretical expressions that correspond to the latter procedure are experimentally checked in this paper by using a square-wave signal. The errors involved in the analysis of the information contained in the light beam, when this information is obtained from the measurement of the first-order factorial moment, are studied.
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.
A level-crossing detection method is presented and developed based on measurement of the normalized second factorial moment n((2))(T) of the photon-counting distribution of the resultant fluorescence. Expression n((2))(T) is obtained, and the errors expected in the determination of signal width and crossing field are theoretically studied. The validity of the approximations performed to establish the theoretical model is proved by an experiment with a square-wave periodically modulated light beam.