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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.

A principal component analysis (PCA) of clean microcalorimeter pulse records can be a first step beyond statistically optimal linear filtering of pulses toward a fully nonlinear analysis. For PCA to be practical on spectrometers with hundreds of sensors, an automated identification of clean pulses is required. Robust forms of PCA are the subject of active research in machine learning. We examine a version known as coherence pursuit that is simple and fast and well matched to the automatic identification of outlier records, as needed for microcalorimeter pulse analysis.

The analysis of data from x-ray microcalorimeters requires great care; their excellent intrinsic energy resolution cannot usually be achieved in practice without a statistically near-optimal pulse analysis and corrections for important systematic errors. We describe the essential parts of a pulse-analysis pipeline for data from x-ray microcalorimeters, including steps taken to reduce systematic gain variation and the unwelcome dependence of filtered pulse heights on the exact pulse-arrival time. We find these steps collectively to be essential tools for getting the best results from a microcalorimeter-based x-ray spectrometer.