Optimum filter-based analysis for the characterization of a high-resolution magnetic microcalorimeter

Ultrasensitive cryogenic calorimeters have become a favored technology with widespread application where eV-scale energy resolutions are needed. In this article, we characterize the performance of an x-ray magnetic microcalorimeter (MMC) using a $^{55}Fe$ source. Employing an optimum filter-based amplitude estimation and energy reconstruction, we demonstrate that a full-width half-maximum (FWHM) resolution of$ ΔE_{FWHM}=(1.25±0.17(stat)^{+0.05}_{−0.07}(syst))  eV$ can be achieved, leading to an unprecedented energy resolving power $E/ΔE_{FWHM}∼4700$ among existing energy-dispersive detectors for soft and tender x-rays. We also derive the best possible resolution and discuss limiting factors affecting the measurement. The analysis pipeline for the MMC data developed in this paper is furthermore an important step for the realization of the proposed superfluid helium-based experiment DELight, which will search for direct interaction of dark matter particles with masses below $100  MeV/c^2$.