Thomas point process in pulse, particle, and photon detection.

Multiplication effects in point processes are important in a number of areas of electrical engineering and physics. We examine the properties and applications of a point process that arises when each event of a primary Poisson process generates a random number of subsidiary events with a given time course. The multiplication factor is assumed to obey the Poisson probability law, and the dynamics of the time delay are associated with a linear filter of arbitrary impulse response function; special attention is devoted to the rectangular and exponential case. Primary events are included in the final point process, which is expected to have applications in pulse, particle, and photon detection. We refer to this as the Thomas point process since the counting distribution reduces to the Thomas distribution in the limit of long counting times. Explicit results are obtained for the singlefold and multifold counting statistics (distribution of the number of events registered in a fixed counting time), the time statistics (forward recurrence time and interevent probability densities), and the counting correlation function (noise properties). These statistics can provide substantial insight into the underlying physical mechanisms generating the process. An example of the applicability of the model is provided by betaluminescence photons produced in a glass photomultiplier tube, when Cherenkov events are also present.

[1]  I. Miller.  Probability, Random Variables, and Stochastic Processes , 1966 .

[2]  Bahaa E. A. Saleh,et al.  Discrimination of shot-noise-driven poisson processes by external dead time: Application to radioluminescence from glass , 1981 .

[3]  R. E. Burgess,et al.  Homophase and heterophase fluctuations in semiconducting crystals , 1959 .

[4]  B E Saleh,et al.  Effects of random deletion and additive noise on bunched and antibunched photon-counting statistics. , 1982, Optics letters.

[5]  L. Mandel,et al.  Image fluctuations in cascade intensifiers , 1959 .

[6]  Emanuel Parzen,et al.  Stochastic Processes , 1962 .

[7]  J. C. Steinberg,et al.  Noise measurements , 1931, Electrical Engineering.

[8]  M. Teich,et al.  Fluctuation properties of multiplied-Poisson light: Measurement of the photon-counting distribution for radioluminescence radiation from glass , 1981 .

[9]  K. Pearson,et al.  Biometrika , 1902, The American Naturalist.

[10]  J. B. Birks,et al.  The Theory and Practice of Scintillation Counting , 1965 .

[11]  B.E.A. Saleh,et al.  Multiplied-Poisson noise in pulse, particle, and photon detection , 1982, Proceedings of the IEEE.

[12]  M. Teich,et al.  Poisson branching point processes , 1984 .

[13]  M C Teich,et al.  Role of the doubly stochastic Neyman type-A and Thomas counting distributions in photon detection. , 1981, Applied optics.

[14]  Giovanni Vannucci,et al.  Dead-time-modified photocount mean and variance for chaotic radiation , 1981 .

[15]  Bahaa E. A. Saleh,et al.  Cascaded Poisson processes , 1982 .

[16]  W. Viehmann,et al.  Noise limitations of multiplier phototubes in the radiation environment of space , 1976 .

[17]  Bahaa E. A. Saleh,et al.  Statistical properties of a nonstationary Neyman - Scott cluster process , 1983, IEEE Trans. Inf. Theory.

[18]  Bahaa E. A. Saleh,et al.  Interevent-time statistics for shot-noise-driven self-exciting point processes in photon detection , 1981 .

[19]  I. Rubin,et al.  Random point processes , 1977, Proceedings of the IEEE.

[20]  H. Pollak,et al.  Amplitude distribution of shot noise , 1960 .

[21]  Aldert Van der Ziel,et al.  Noise in measurements , 1976 .

[22]  M. Thomas.  A generalization of Poisson's binomial limit for use in ecology. , 1949, Biometrika.

[23]  W Viehmann,et al.  Photomultiplier window materials under electron irradiation: fluorescence and phosphorescence. , 1975, Applied optics.

[24]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[25]  Jerzy Neyman,et al.  On a New Class of "Contagious" Distributions, Applicable in Entomology and Bacteriology , 1939 .