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Journal of the Optical Society of America

Observation of dead-time-modified photocounting distributions for modulated laser radiation

Malvin Carl Teich, Giovanni Vannucci

Published Oct 1, 1978• 32 citations
Publisher

Abstract

We report a series of optical experiments that verify the theoretical photocounting distributions obtained by Diament and Teich for triangularly and sinusoidally modulated laser radiation. Another series of experiments validates the (nonparalyzable) dead-time-modified versions of these formulas obtained by Cantor and Teich. A new expression is obtained for the counting distribution in the presence of modulation and paralyzable dead time. The results have application in photon counting, nuclear counting, and neural counting.

DOI
10.1364/josa.68.001338

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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.

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Determination of Decay Times from Photocount Statistics of Weak Modulated Luminescence Radiation

Čestmı́r Koňák, Petr Štěpánek, L. Dvořák +3 more

The experimental and theoretical photocount distribution of modulated weak luminescence radiation are compared, and the Mandel-Rice formula with modulation is shown to describe well the photon statistics of this radiation. It is shown, combining the square-wave and the exponential modulations, that one can deduce with good accuracy the decay time constants from the photocount distributions of weak modulated luminescence radiation.

Optica Acta International Journal of Optics•Aug 1, 1982•2 citations
We report a series of optical experiments that verify the theoretical photocounting distributions obtained by Diament and Teich for triangularly and sinusoidally modulated laser radiation. Another series of experiments validates the (nonparalyzable) dead-time-modified versions of these formulas obtained by Cantor and Teich. A new expression is obtained for the counting distribution in the presence of modulation and paralyzable dead time. The results have application in photon counting, nuclear counting, and neural counting.
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.
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.
Statistical properties such as the cumulants, and the central, factorial, and ordinary moments are obtained for photocounting distributions when the incident radiation is intensity-modulated with arbitrary statistics. The results are applied in some detail to the cases of triangular, sinusoidal, and square-wave modulation of multimode superposed coherent and chaotic radiation. The coefficient of variation, skewness, and kurtosis are obtained as a function of modulation depth. Comparison is made with experimental data in the cases of triangular and sinusoidal modulation of a laser source.
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.
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.