2012/06/27 by A. A. Deshpande, Deshpande, Avinash A., Harsha Raichur +1
Physics and Astronomy · #Statistical Mechanics and Entropy #Radiation Detection and Scintillator Technologies #Gamma-ray bursts and supernovae
paper · pdf · doi:10.48550/arxiv.1206.6181
Mutually uncorrelated random discrete events, manifesting a common basic process, are examined often in terms of their occurrence rate as a function of one or more of their distinguishing attributes, such as measurements of photon spectrum as a function of energy. Such rate distributions obtained from the observed attribute values for an ensemble of events will correspond to the "true" distribution only if the event occurrence were \it mutually exclusive. However, due to finite resolution in such measurements, the problem of event \it pile-up is not only unavoidable, but also increases with event rate. Although extensive simulations to estimate the distortion due to pile-up in the observed rate distribution are available, no restoration procedure has yet been suggested. Here we present an elegant analytical solution to recover the underlying \it true distribution. Our method, based on Poisson statistics and Fourier transforms, is shown to perform as desired even when applied to distributions that are significantly distorted by pile-up. Our recipes for correction, as well as for prediction, of pile-up are expected to find ready applications in a wide variety of fields, ranging from high-energy physics to medical clinical diagnostics, and involving, but not limited to, measurements of count-rates and/or spectra of incident radiation using Charge Coupled Devices (CCDs) or other similar devices.