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Applied Optics

Level-crossing detection through measurement of the second factorial moment of photon-counting distribution

M. Á. Rebolledo, J. J. Sanz

Published Aug 1, 1980• 15 citations
Publisher

Abstract

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.

DOI
10.1364/ao.19.002533

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Spectroscopy Letters•Mar 1, 1989•2 citations

Analysis of a periodically modulated light beam by measurement of the moment-generating function of the number of photopulses

Felipe González, Fernando G. Moreno

We analyze a low-intensity square-wave modulated light signal by measuring the moment-generating function of the number of photopulses, Qn(s, T). The behavior of the experimental errors in the determination of the period and the modulation factor of the signal is studied by means of a theoretical error model. A set of experimental measurements was carried out, and the results found through the Qn(s, T) measurement and by the normalized second-order factorial moment n(2)(T) are compared.

Journal of the Optical Society of America B•Oct 1, 1992•1 citation
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.
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.