Theoretical and Experimental Investigations of Coincidences in Poisson Distributed Pulse Trains and Spectral Distortion Caused by Pulse Pileup.

Part one of this two-part study is concerned with the multiple coincidences in pulse trains from X-ray and gamma radiation detectors which are the cause of pulse pileup. A sequence of pulses with inter-arrival times less than tau, the resolving time of the pulse-height analysis system used to acquire spectra, is called a multiple pulse string. Such strings can be classified on the basis of the number of pulses they contain, or the number of resolving times they cover. The occurrence rates of such strings are derived from theoretical considerations. Logic circuits were devised to make experimental measurements of multiple pulse string occurrence rates in the output from a NaI(Tl) scintillation detector over a wide range of count rates. Markov process theory was used to predict state transition rates in the logic circuits, enabling the experimental data to be checked rigorously for conformity with those predicted for a Poisson distribution. No fundamental discrepancies were observed. Part two of the study is concerned with a theoretical analysis of pulse pileup and the development of a discrete correction algorithm, based on the use of a function to simulate the coincidence spectrum produced by partial sums of pulses. Monte Carlo simulations, incorporating criteria for pulse pileup inherent in the operation of modern ADC's, were used to generate pileup spectra due to coincidences between two pulses, (1st order pileup) and three pulses (2nd order pileup), for different semi-Gaussian pulse shapes. Coincidences between pulses in a single channel produced a basic probability density function spectrum which can be regarded as an impulse response for a particular pulse shape. The use of a flat spectrum (identical count rates in all channels) in the simulations, and in a parallel theoretical analysis, showed the 1st order pileup distorted the spectrum to a linear ramp with a pileup tail. The correction algorithm was successfully applied to correct entire spectra for 1st and 2nd order pileup; both those generated by Monte Carlo simulations and in addition some real spectra acquired with a laboratory multichannel analysis system.