A Highly Linear Calibration Metric for TES X-ray Microcalorimeters

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, $E_{\text{Joule}}$ . We measure calibration pulses in the range $4.5\text{keV}<E_{\gamma }<\text{9.6}\text{keV}$ with detectors optimized for 6 keV photons to compare the linearity properties of $E_{\text{Joule}}$ to OFPH. In these test data sets, we find that $E_{\text{Joule}}$ fits a linear function an order of magnitude better than OFPH. Furthermore, calibration functions using $E_{\text{J}}$ , an optimized version of $E_{\text{Joule}}$ , are linear within the 2-3 eV noise of the data.