Counting statistics of X-ray detectors at high counting rates.

Modern synchrotron radiation sources with insertion devices and focusing optics produce high fluxes of X-rays at the sample, which leads to a requirement for photon-counting detectors to operate at high counting rates. With high counting rates there can be significant non-linearity in the response of the detector to incident X-ray flux, where this non-linearity is caused by the overlap of the electronic pulses that are produced by each X-ray. A model that describes the overlap of detector pulses is developed in this paper. This model predicts that the correction to the counting rate for pulse overlap is the same as a conventional dead-time correction. The model is also used to calculate the statistical uncertainty of a measurement and predicts that the error associated with a measurement can be increased significantly over that predicted by Poisson (N(-1/2)) statistics. The error differs from that predicted by a conventional dead-time treatment.