Oct 03

## Photon counting with deadtime-Part 1

The main problem with photon counting detectors in medical x-ray systems is the large count rates, which can be greater than 10^{8}/sec. The maximum count rate is limited in part by the deadtime and a critical question is the effects of deadtime on the image quality. This post starts the derivation of a simplified model to understand these effects. I do not claim that the model describes a real detector in detail. Instead, I want to get an insight into the magnitude of the effects. For a given mean incident count rate what are small deadtimes that do not affect the results and what values are so large that the images are totally degraded? I start in this post by deriving formulas for the mean value and variance of the recorded counts as a function of deadtime. I found that books and papers that cover this topic, like Parzen and Yu and Fessler, refer to other much more mathematical books for the central limit theorem of renewal processes, which forms the basis for the derivation. Here, I present a derivation, which, although decidedly not mathematically rigorous, gives insight into the assumptions of the formulas. I then validate the formulas with a Monte Carlo simulation. As always, I provide the code and data to reproduce the simulation results.

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