Pile-up rejection: Limitations and corrections for residual errors in energy-dispersive spectrometers

Pile-up rejection is commonly achieved through use of an auxiliary inspection channel with short time constants but low energy events can be missed because of electronic noise. A formula is derived to predict the detection efficiency of such a channel and the effect of adjusting the discriminator threshold or changing the time constants is demonstrated. When pulses are missed, spectrum distortion and counting losses are greater than would be predicted from the specified pulse pair resolution time so it is important to optimize the inspector adjustment. A mathematical analysis leads to formulae which can be used to correct for residual counting losses and sum peaks, and the relationship between empirical parameters obtained for these formulae and time constants in the electronics is demonstrated. The present state of the art in noise performance dictates that 1 μs is about the best resolution time that can be achieved for 1 ke V pulses. For further improvements, a fast beam switching technique could be used which would improve pulse pair resolution by a factor of three or more and thus afford adequate protection for the very low energy pulses that would be encountered with thin-window or windowless solid-state detectors.