Discrimination of shot-noise-driven poisson processes by external dead time: Application to radioluminescence from glass

Abstract

The shot-noise-driven doubly stochastic Poisson point process (SNDP) describes the photodetection statistics for several kinds of luminescence radiation (e.g., cathodoluminescence). This process, which is bunched (clustered) in character and is associated with multiplied Poisson noise, has many applications in pulse, particle, and photon detection. In this work we describe ways in which dead time can be used to constructively enhance or diminish the effects of point processes that display such bunching, according to whether they are signal or noise. We discuss in some detail the subtle interrelations between photocount bunching arising in the SNDP and the antibunching character arising from dead-time effects. We demonstrate that the dead-time-modified count mean and variance for an arbitrary doubly stochastic Poisson point process (DSPP) can be obtained from the Laplace transform of the single-fold and joint moment-generating functions for the driving rate process. The dead time is assumed to be small in comparison with the correlation time of the driving process. Specific calculations have been carried out for the SNDP. The theoretical counting efficiency ε <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf> and normalized variance ε <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">υ</inf> fox shot-noise light with a rectangular impulse response function are shown to depend principally on the dead-time parameter and on the number of primaxy events in a correlation time of the driving rate process. The values of ε <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf> and ε <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">υ</inf> are significantly reduced below those obtained with the constant-rate Poisson because of the clustering associated with the SNDP. The theory is in good accord with the experimental values of these quantities for radioluminescence radiation in three transparent materials (fused silica, quartz, and glass). Various parameter values for each material have been extracted. For large counting times, the experimental photon-counting distributions are shown to be well described by the Neyman Type-A theoretical distribution, both in the absence and in the presence of dead time.