Abstract not found

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. I.

Thirty years ago, Bernard Picinbono and his colleagues carefully addressed an important problem: how an optical field is converted into a sequence of photoelectrons upon detection. Their choice of problem could not have been better, nor their timing more judicious. In a paper entitled "Photoelectron Shot Noise", published in the Journal of Mathematical Physics in 1970, when quantum optics was in its infancy, they obtained results that were to serve as an important building block in analyzing and generating many di#erent forms of light. We present some variations on the theme of cascaded stochastic processes in optics. Processus stochastiques en cascade d'importance en optique Resume--Il y a trente ans, Bernard Picinbono et ses collegues ont traite rigoureusement un probleme important : comment un champ optique est converti en une suite de photoelectrons apres detection. Leur choix de ce probleme ne pouvait pas etre meilleur et a revele un caractere pionnier. Dans un article intitule "Photoelectron Shot Noise", publie dans le Journal of Mathematical Physics en 1970, alors que l'optique quantique n'etait encore qu'a ses debuts, ils obtinrent des resultats qui constituerent un important point de depart pour analyser et generer de nombreuses et diverses formes de lumieres. Nous presentons des variations sur le theme des processus stochastiques en cascade, en optique. 1

noise in the human visual system at threshold: