Title: Pile-up Reduction, Bayesian Decomposition and Applications of Silicon Drift Detectors at LCLS,
Abstract: Silicon drift detectors (SDDs) revolutionized spectroscopy in fields as
diverse as geology and dentistry. For a subset of experiments at ultra-fast,
x-ray free-electron lasers (FELs), SDDs can make substantial contributions.
Often the unknown spectrum is interesting, carrying science data, or the
background measurement is useful to identify unexpected signals. Many
measurements involve only several discrete photon energies known a priori. We
designed a pulse function (a combination of gradual step and exponential decay
function) and demonstrated that for individual pulses the signal amplitude,
peaking time, and pulse amplitude are interrelated and the signal amplitude and
peaking time are obtained for each pulse by fitting. Avoiding pulse shaping
reduced peaking times to tens of nanoseconds, resulting in reduced pulse
pile-up and allowing decomposition of remaining pulse pile-up at photon
separation times down to 100~ns while yielding time-of-arrival information with
precision of 10~nanoseconds. At pulsed sources or high photon rates, photon
pile-up still occurs. We showed that the area of one photon peaks is not
suitable for estimating high photon rates while pile-up spectrum fitting is
relatively simple and preferable to pile-up spectrum deconvolution. We
developed a photon pile-up model for constant intensity sources, extended it to
variable intensity sources (typical for FELs) and used it to fit a complex
pile-up spectrum, demonstrating its accuracy. Based on the pile-up model, we
developed a Bayesian pile-up decomposition method that allows decomposing
pile-up of single events with up to 6 photons from 6 monochromatic lines with
99% accuracy. The usefulness of SDDs will continue into the x-ray FEL era of
science. Their successors, the ePixS hybrid pixel detectors, already offer
hundreds of pixels, each with similar performance to an SDD, in a compact,
robust and affordable package.