Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics A Mathematical and General

Dead-time effects in photon counting statistics

S. K. Srinivasan

Published Nov 1, 1978• 4 citations
Publisher

Abstract

The paper deals with the modifications in photocount distributions due to dead-time following every registered count. In order to study the effects due to dead-time, the distribution of the interval between successive photocounts is studied. For the case of a constant dead-time, the mean count rate is derived using the dead-time neglected two-fold counting generating function. The result is also generalised to cover the case when the dead-time has a distribution with the different dead-times independently and identically distributed. In view of the complexity of the problem, a lower bound is obtained for the mean square number of photocounts in an arbitrary interval.

DOI
10.1088/0305-4470/11/11/015

Related papers

Dead-time corrections to the statistical distribution of photoelectrons

Gabriel Bédard

The corrections to the photocount distributions, due to dead-time effects, are evaluated by use of the time-interval probability density of the counts. The normalized cumulative distribution function J k ( T , τ), associated with the detection of fluctuating light beams during a counting time interval T , with a counter having a constant dead-time τ, appear naturally as a convenient quantity to be used in comparing experimental results with theoretical predictions. The quantities J k ( T , τ) obey a simple recurrence relation and are readily derived from the photocount distribution p ( k, T , τ). A general expression is derived for J k ( T , τ) and p ( k, T , τ) associated with the detection of fluctuating light beams. Typical cumulative distribution functions, relating to the detection of thermal light, are evaluated as functions of the degree of polarization of the light, of the average number of photocounts < n 0 > in the absence of dead-time effects and of the ratio τ/ T . The distributions J k ( T , τ) and p ( k, T , τ) relating to detection of laser light are also calculated in a typical case.

Proceedings of the Physical Society•Jan 1, 1967•75 citations

Dead-time-corrected photocounting distributions for laser radiation*

Barry I. Cantor, Malvin Carl Teich

Exact forward photocounting distributions for a source of optical radiation with arbitrary statistics are obtained in the presence of photodetector dead time. In particular, we examine the counting and pulse-interval distributions that arise from amplitude-stabilized radiation, from chaotic radiation, and from a Van der Pol laser with arbitrary excitation. The exact dead-time-corrected Poisson distribution is graphically compared with a previous approximate result and with the uncorrected Poisson. Plots of the Bose–Einstein distribution clearly indicate the dramatic anti-bunching effects of the dead time in overcoming the inherent bunching of this distribution. A simplified approximate solution is also found. for the Van der Pol laser above threshold; this result is similar to light from an amplitude-stabilized source incident on a photodetector with a gaussian-distributed dead time. Information about photodetector dead-time variation can therefore be obtained either by using an amplitude-stabilized source or by properly choosing system parameters such that irradiance fluctuations are averaged out.

Journal of the Optical Society of America•Jul 1, 1975•68 citations

Photocounting distributions for exponentially decaying sources

Malvin Carl Teich, HOWARD C. CARD

Exact photocounting distributions are obtained for a pulse of light whose intensity is exponentially decaying in time, when the underlying photon statistics are Poisson. It is assumed that the starting time for the sampling interval (which is of arbitrary duration) is uniformly distributed. The probability of registering n counts in the fixed time T is given in terms of the incomplete gamma function for n >/= 1 and in terms of the exponential integral for n = 0. Simple closed-form expressions are obtained for the count mean and variance. The results are expected to be of interest in certain studies involving spontaneous emission, radiation damage in solids, and nuclear counting. They will also be useful in neurobiology and psychophysics, since habituation and sensitization processes may sometimes be characterized by the same stochastic model.

Optics Letters•May 1, 1979•15 citations

Determination of the Statistical Properties of Light by Photodetectors with a Finite Dead Time

Sushma Gupta, C. L. Mehta

The problem of obtaining the probability density of the fluctuating light intensity from the knowledge of photocounting statistics, when the detectors have a finite dead time, is considered. The integral relation for the probability of registering $n$ photocounts in the time interval $T$ in the presence of a dead time $\ensuremath{\tau}$ is inverted, and an expression is obtained for the probability density of the fluctuating intensity of the incident light radiation. The method is illustrated with a few specific examples.

Physical Review A•Sep 1, 1973•1 citation

Dead-time modified photocount distributions for chaotic radiation with arbitrary coherence times

Gerard Lachs, Lin Wen-Tsung

A computer simulation method is employed to investigate the dead-time modified photocount detection distribution where the ratio of coherence time of the incident radiation to the counting time τc/T ≦ 1. The principal result is to demonstrate that a dead-time correction formula that was derived for τc/T ≫ 1 may be modified to be applicable to arbitrary coherence times. The simulation technique was verified by comparing simulated results with known results for dead-time modified photocount distribution for radiation with τc/T ≫ 1 and for unmodified photocount distribution for radiation with τc/T ≦ 1.

Journal of the Optical Society of America A•Oct 1, 1985•1 citation

Influence of coherent properties of an optical field on the photocount statistics

В. Г. Астафуров, G. N. Glazov

The asymmetry of photocount statistics in respect of the spatial and temporal coherence factors is demonstrated and explained. This asymmetry appears because of the of a counter receiving a non-Poisson photoelectron flux. A statistical model of an optical field, photoelectron flux, and counting flux is used in a computer study of the dependences of the distributions and moments of the number of counts in a given time interval on the ratio of the coherence factors. An explanation of the features of these dependences is provided. A determination is made of the range of conditions in which the asymmetry is significant. In particular, the asymmetry disappears in the case of a Poisson photoelectron flux and for a very short dead time.

Soviet Journal of Quantum Electronics•Jan 31, 1985•0 citations
The paper deals with the modifications in photocount distributions due to dead-time following every registered count. In order to study the effects due to dead-time, the distribution of the interval between successive photocounts is studied. For the case of a constant dead-time, the mean count rate is derived using the dead-time neglected two-fold counting generating function. The result is also generalised to cover the case when the dead-time has a distribution with the different dead-times independently and identically distributed. In view of the complexity of the problem, a lower bound is obtained for the mean square number of photocounts in an arbitrary interval.
The corrections to the photocount distributions, due to dead-time effects, are evaluated by use of the time-interval probability density of the counts. The normalized cumulative distribution function J k ( T , τ), associated with the detection of fluctuating light beams during a counting time interval T , with a counter having a constant dead-time τ, appear naturally as a convenient quantity to be used in comparing experimental results with theoretical predictions. The quantities J k ( T , τ) obey a simple recurrence relation and are readily derived from the photocount distribution p ( k, T , τ). A general expression is derived for J k ( T , τ) and p ( k, T , τ) associated with the detection of fluctuating light beams. Typical cumulative distribution functions, relating to the detection of thermal light, are evaluated as functions of the degree of polarization of the light, of the average number of photocounts < n 0 > in the absence of dead-time effects and of the ratio τ/ T . The distributions J k ( T , τ) and p ( k, T , τ) relating to detection of laser light are also calculated in a typical case.
Exact forward photocounting distributions for a source of optical radiation with arbitrary statistics are obtained in the presence of photodetector dead time. In particular, we examine the counting and pulse-interval distributions that arise from amplitude-stabilized radiation, from chaotic radiation, and from a Van der Pol laser with arbitrary excitation. The exact dead-time-corrected Poisson distribution is graphically compared with a previous approximate result and with the uncorrected Poisson. Plots of the Bose–Einstein distribution clearly indicate the dramatic anti-bunching effects of the dead time in overcoming the inherent bunching of this distribution. A simplified approximate solution is also found. for the Van der Pol laser above threshold; this result is similar to light from an amplitude-stabilized source incident on a photodetector with a gaussian-distributed dead time. Information about photodetector dead-time variation can therefore be obtained either by using an amplitude-stabilized source or by properly choosing system parameters such that irradiance fluctuations are averaged out.
Exact photocounting distributions are obtained for a pulse of light whose intensity is exponentially decaying in time, when the underlying photon statistics are Poisson. It is assumed that the starting time for the sampling interval (which is of arbitrary duration) is uniformly distributed. The probability of registering n counts in the fixed time T is given in terms of the incomplete gamma function for n >/= 1 and in terms of the exponential integral for n = 0. Simple closed-form expressions are obtained for the count mean and variance. The results are expected to be of interest in certain studies involving spontaneous emission, radiation damage in solids, and nuclear counting. They will also be useful in neurobiology and psychophysics, since habituation and sensitization processes may sometimes be characterized by the same stochastic model.
The problem of obtaining the probability density of the fluctuating light intensity from the knowledge of photocounting statistics, when the detectors have a finite dead time, is considered. The integral relation for the probability of registering nnn photocounts in the time interval TTT in the presence of a dead time $\ensuremath{\tau}$ is inverted, and an expression is obtained for the probability density of the fluctuating intensity of the incident light radiation. The method is illustrated with a few specific examples.
A computer simulation method is employed to investigate the dead-time modified photocount detection distribution where the ratio of coherence time of the incident radiation to the counting time τc/T ≦ 1. The principal result is to demonstrate that a dead-time correction formula that was derived for τc/T ≫ 1 may be modified to be applicable to arbitrary coherence times. The simulation technique was verified by comparing simulated results with known results for dead-time modified photocount distribution for radiation with τc/T ≫ 1 and for unmodified photocount distribution for radiation with τc/T ≦ 1.
The asymmetry of photocount statistics in respect of the spatial and temporal coherence factors is demonstrated and explained. This asymmetry appears because of the of a counter receiving a non-Poisson photoelectron flux. A statistical model of an optical field, photoelectron flux, and counting flux is used in a computer study of the dependences of the distributions and moments of the number of counts in a given time interval on the ratio of the coherence factors. An explanation of the features of these dependences is provided. A determination is made of the range of conditions in which the asymmetry is significant. In particular, the asymmetry disappears in the case of a Poisson photoelectron flux and for a very short dead time.