The measurement errors in the Swift-UVOT and XMM-OM

TL;DR

This paper investigates the measurement errors in photon counting instruments like Swift-UVOT and XMM-OM, revealing that their errors follow a binomial distribution rather than the commonly assumed Poisson distribution, especially at high count rates.

Contribution

The authors extend existing formalism to accurately derive the incident count rate error, accounting for binomial measurement errors in photon counting instruments.

Findings

Measurement errors follow a binomial distribution.

Error in incident count rate exceeds Poisson error at high rates.

Extended formalism improves accuracy of count rate error estimation.

Abstract

The probability of photon measurement in some photon counting instrumentation, such as the Optical Monitor on the XMM-Newton satellite, and the UVOT on the Swift satellite, does not follow a Poisson distribution due to the detector characteristics, but a Binomial distribution. For a single-pixel approximation, an expression was derived for the incident countrate as a function of the measured count rate by Fordham, Moorhead and Galbraith (2000). We show that the measured countrate error is binomial, and extend their formalism to derive the error in the incident count rate. The error on the incident count rate at large count rates is larger than the Poisson-error of the incident count rate.