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 dependence on photon energy, Eγ\documentclass[12pt]{minimal}
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\begin{document}$$E_{\gamma }$$\end{document}. 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 Eγ\documentclass[12pt]{minimal}
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\begin{document}$$E_{\gamma }$$\end{document} 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 Eγ\documentclass[12pt]{minimal}
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\begin{document}$$E_{\gamma }$$\end{document} could help alleviate these problems. In this work, we assess the linearity of a physically motivated calibration metric, EJoule\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {Joule}}$$\end{document}. We measure calibration pulses in the range 4.5 keV <Eγ<\documentclass[12pt]{minimal}
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\begin{document}$$<E_{\gamma }<$$\end{document} 9.6 keV with detectors optimized for 6 keV photons to compare the linearity properties of EJoule\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {Joule}}$$\end{document} to OFPH. In these test data sets, we find that EJoule\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {Joule}}$$\end{document} fits a linear function an order of magnitude better than OFPH. Furthermore, calibration functions using EJ\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {J}}$$\end{document}, an optimized version of EJoule\documentclass[12pt]{minimal}
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\begin{document}$$E_{\mathrm {Joule}}$$\end{document}, are linear within the 2–3 eV noise of the data.
