Optical Calibration of a Frequency-Domain-Multiplexed X-Ray TES Microcalorimeter Array via Photon-Number-Resolved Statistics

Transition-edge sensor (TES) microcalorimeters for future X-ray space observatories require accurate low-energy calibration, a regime where conventional X-ray sources are limited by intrinsic linewidth, count rate, or experimental complexity. In this work, we investigate fiber-coupled optical photons as a compact calibration tool for an Athena-like TES array. Optical pulses at 405 nm were generated with an acousto-optic modulator and delivered through an optical fiber onto a selected TES pixel inside a dilution refrigerator, via a dedicated cryogenic alignment interface. Externally triggered pulses were processed with an optimal-filter pipeline, including baseline subtraction, drift correction, and multi-Gaussian reconstruction of the pulse-height spectrum. The reconstructed spectra show resolved photon-number peaks consistent with the Poissonian statistics expected from an attenuated coherent source, reaching equivalent energies above 400 eV with a mean photon number exceeding 100 per pulse. The detector response was further tested for linearity by comparing the measured photon-number distributions against those predicted from the independently calibrated number of photons sent to the detector and a single, globally estimated detection efficiency, confirming Poissonian, linear behaviour across nearly two orders of magnitude in photon number. These results demonstrate that fiber-delivered optical photons can probe the few-eV to sub-keV response of Athena-like TES microcalorimeters, offering a practical and extensible framework for future low-energy calibration studies.