A Highly Linear Calibration Metric for TES X-ray Microcalorimeters

TL;DR

This paper introduces a new calibration metric, $E_{Joule}$, for TES X-ray microcalorimeters that exhibits significantly improved linearity over the traditional OFPH metric, reducing calibration errors and effort.

Contribution

The study demonstrates that $E_{Joule}$ provides a nearly linear calibration metric, outperforming OFPH in linearity and accuracy for TES X-ray microcalorimeters.

Findings

$E_{Joule}$ fits a linear function an order of magnitude better than OFPH.

Calibration functions using $E_{J}$ are linear within 2-3 eV noise.

$E_{Joule}$ reduces calibration errors and measurement complexity.

Abstract

Transition-edge sensor X-ray microcalorimeters are usually calibrated empirically, as the most widely-used calibration metric, optimal filtered pulse height (OFPH), in general has an unknown dependance on photon energy, $E_{\gamma}$. Because the calibration function can only be measured at specific points where photons of a known energy can be produced, this unknown dependence of OFPH on $E_{\gamma}$ leads to calibration errors and the need for time-intensive calibration measurements and analysis. A calibration metric that is nearly linear as a function of $E_{\gamma}$ could help alleviate these problems. In this work, we assess the linearity of a physically motivated calibration metric, $E_{Joule}$. We measure calibration pulses in the range 4.5 keV$<$$E_{\gamma}$$<$9.6 keV with detectors optimized for 6 keV photons to compare the linearity properties of $E_{Joule}$ to OFPH. In these test data sets, we find that $E_{Joule}$ fits a linear function an order of magnitude better than OFPH. Furthermore, calibration functions using $E_{J}$, an optimized version of $E_{Joule}$, are linear within the 2-3 eV noise of the data.