Energy Calibration of Nonlinear Microcalorimeters with Uncertainty Estimates from Gaussian Process Regression

The nonlinear energy response of cryogenic microcalorimeters is usually corrected through an empirical calibration. X-ray or gamma-ray emission lines of known shape and energy anchor a smooth function that generalizes the calibration data and converts detector measurements to energies. We argue that this function should be an approximating spline. The theory of Gaussian process regression makes a case for this functional form. It also provides an important benefit previously absent from our calibration method: a quantitative uncertainty estimate for the calibrated energies, with lower uncertainty near the best-constrained calibration points.