Statistical properties of measured X-ray intensities affected by counting loss

The statistical properties of X-ray intensities measured with counting systems have been experimentally investigated. A formula of statistical variance for the intermediately extended dead-time model is proposed and compared with the experimentally evaluated variance obtained from repeated measurements based on Chipman's foil method applied to X-ray detection systems of laboratory and synchrotron powder diffractometers. It has been found that the variance of the observed intensities is smaller than the average of count, as has been suggested by conventional theoretical models for counting loss. It is shown that the statistical errors can be predicted by applying an intermediately extended dead-time model including dead-time τ and degree of extension ρ as fixed parameters.