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

The probability of photon measurement in some photon-counting instrumentation, such as the Optical Monitor (OM) on the XMM-Newton satellite, and the Ultraviolet/Optical Telescope (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 count rate as a function of the measured count rate by Fordham, Moorhead & Galbraith. We show that the measured count rate 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.