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Multi-parameter Nonlinear Gain Correction of X-ray Transition Edge Sensors for the X-ray Integral Field Unit

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Abstract

With its array of 3840 Transition Edge Sensors (TESs), the Athena X-ray Integral Field Unit (X-IFU) will provide spatially resolved high-resolution spectroscopy (2.5 eV up to 7 keV) from 0.2 to 12 keV, with an absolute energy scale accuracy of 0.4 eV. Slight changes in the TES operating environment can cause significant variations in its energy response function, which may result in systematic errors in the absolute energy scale. We plan to monitor such changes at pixel level via onboard X-ray calibration sources and correct the energy scale accordingly using a linear or quadratic interpolation of gain curves obtained during ground calibration. However, this may not be sufficient to meet the 0.4 eV accuracy required for the X-IFU. In this contribution, we introduce a new two-parameter gain correction technique, based on both the pulse-height estimate of a fiducial line and the baseline value of the pixels. Using gain functions that simulate ground calibration data, we show that this technique can accurately correct deviations in detector gain due to changes in TES operating conditions such as heat sink temperature, bias voltage, thermal radiation loading and linear amplifier gain. We also address potential optimisations of the onboard calibration source and compare the performance of this new technique with those previously used.

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Notes

  1. In the following, \(_{\text {ref}}\) indicates ground calibration measurements under controlled operating conditions and \(_{\text {fl}}\) in-flight measurements. \(||.||_{2}\) indicates the \(L^{2}\) norm of the vector.

  2. Using the following setpoints \(\{T_{\text {bath}}, L_{\text {amp}} (V_{\text {bias}})\}\): {55, 0 (51.6)}, {56, 250 (51.65)}, {55, 1000 (51.7)}, {54, 250 (51.65)}, {54.5, 500 (51.55)}, {55.5, 500 (51.55)} (in {mK, ppm (nV\(_{\text {rms}}\))}).

  3. As we investigate optimisations of the MXS lines, baseline effects are neglected.

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Cucchetti, E., Eckart, M.E., Peille, P. et al. Multi-parameter Nonlinear Gain Correction of X-ray Transition Edge Sensors for the X-ray Integral Field Unit. J Low Temp Phys 193, 931–939 (2018). https://doi.org/10.1007/s10909-018-1912-5

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  • DOI: https://doi.org/10.1007/s10909-018-1912-5

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