Energy calibration of nonlinear microcalorimeters with uncertainty estimates from Gaussian process regression

TL;DR

This paper introduces a Gaussian process regression-based method for calibrating nonlinear microcalorimeters, providing both improved energy calibration and quantitative uncertainty estimates, especially near well-constrained calibration points.

Contribution

It proposes using Gaussian process regression with spline approximation for microcalorimeter calibration, enabling uncertainty quantification in energy measurements.

Findings

Provides a method for uncertainty estimation in calibration

Improves calibration accuracy near anchor points

Demonstrates the effectiveness of Gaussian process regression

Abstract

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.