Correcting Energy Estimation Errors Due to Finite Sampling of Transition-Edge Sensor Data

We are developing transition-edge sensor microcalorimeters for the X-ray integral field unit (X-IFU) on-board ESA’s Athena space telescope. These detectors will be read out using time-domain multiplexing. Due to the limitations on bandwidth and dynamic range of the readout, the optimally filtered pulse heights of the measured X-ray signals suffer from a nonlinear variation with the exact photon arrival time relative to the sampling points. The shape and magnitude of this variation depend on the photon energy. We describe a method to characterize this energy-dependent variation with few parameters, which can then be interpolated to correct event energies across the whole spectrum. We implement our method on measurements from 200 pixels in a prototype X-IFU kilo-pixel array readout using 8-column × 32-row TDM. We show that the interpolation errors between calibration points, over the energy range 4–12 keV, can be made sufficiently small that they do not adversely impact the measured energy resolution across the full spectral range.