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Applied Optics

Statistical properties of triggered photocounting distribution

Takeaki Yoshimura, Toshiro Nakajima, Nobuo Wakabayashi

Published Sep 1, 1981• 12 citations
Publisher

Abstract

The triggered photocounting distribution (TPCD) of practical fields has been investigated. The moment generating function and the factorial moment are exactly deduced from theory and experimentally justified by the measurement of Gaussian-Lorentzian light. It is found that the first-order factorial moment of the TPCD has the spectral information of incident light corresponding to the second-order factorial moment of ordinary photocounting distribution.

DOI
10.1364/ao.20.002993

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Analysis of a light beam with a periodically modulated intensity by triggered photon counting

M. Á. Rebolledo, J. M. Alvarez, Julio Cesar Amare

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.

Journal of the Optical Society of America A•Jan 1, 1986•6 citations
The triggered photocounting distribution (TPCD) of practical fields has been investigated. The moment generating function and the factorial moment are exactly deduced from theory and experimentally justified by the measurement of Gaussian-Lorentzian light. It is found that the first-order factorial moment of the TPCD has the spectral information of incident light corresponding to the second-order factorial moment of ordinary photocounting distribution.
The expression corresponding to the normalized first-order factorial moment (NFOFM) of a double triggered photocount distribution (DTPCD) has been developed. It is found that the NFOFM of a DTCPD has the spectral information of incident light corresponding to the third-order autocorrelation function. A theoretical error model was developed and checked by using a computer simulation method. We also compare the results obtained from the measurement of the NFOFM of a DTPCD with those obtained from the second- and third-order correlation functions.
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.
It is well known that the photocount distribution associated with the photoelectric detection of fluctuating light beams carries information about the probability density of the light intensity. In this paper, we present an exact solution to a problem of particular interest which arises in connection with the photoelectric detection of narrow-band Gaussian (thermal or pseudothermal) light, namely, the problem of determining the photocount distribution when the counting-time interval is not necessarily short compared to the coherence time of the light. The method developed in this paper is applied to the case where the spectral profile of the light is Lorentzian; it leads to an exact expression for the photocount generating function and it provides simple recurrence relations for the photocount distribution and for its factorial moments.
We study the photocounting statistics and the integrated intensity distribution of partially polarized Gaussian light. Expressions for the characteristic functions of the two distributions are obtained in terms of the eigenvalues of an associated integral equation. Closed-form expressions for these characteristic functions are derived for the special case when the spectral profile of the light is Lorentzian. Results from a numerical evaluation of the factorial moments of the number of photoelectrons in a given time interval and of the integrated intensity distribution are also presented.
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.