Calibration of Transition-edge Sensor (TES) Bolometer Arrays with Application to CLASS

TL;DR

This paper presents a simplified and robust calibration method for TES bolometer arrays used in CMB experiments, utilizing daily $I$-$V$ measurements and Moon calibration to achieve high accuracy and stability.

Contribution

It introduces a direct calibration approach linking responsivity and time constant to measured TES current, improving calibration robustness and accuracy for large detector arrays.

Findings

Median calibration error within bins is 0.3%

Moon-based calibration shows 0.5% TES ratio error

Bias correction improves calibration stability over time

Abstract

The current and future cosmic microwave background (CMB) experiments fielding kilo-pixel arrays of transition-edge sensor (TES) bolometers require accurate and robust gain calibration methods. We simplify and refactor the standard TES model to directly relate the detector responsivity calibration and optical time constant to the measured TES current $I$ and the applied bias current $I_{\mathrm{b}}$. The calibration method developed for the Cosmology Large Angular Scale Surveyor (CLASS) TES bolometer arrays relies on current versus voltage ($I$-$V$) measurements acquired daily prior to CMB observations. By binning Q-band (40GHz) $I$-$V$ measurements by optical loading, we find that the gain calibration median standard error within a bin is 0.3%. We test the accuracy of this "$I$-$V$ bin" detector calibration method by using the Moon as a photometric standard. The ratio of measured Moon amplitudes between detector pairs sharing the same feedhorn indicates a TES calibration error of 0.5%. We also find that for the CLASS Q-band TES array, calibrating the response of individual detectors based solely on the applied TES bias current accurately corrects TES gain variations across time but introduces a bias in the TES calibration from data counts to power units. Since the TES current bias value is set and recorded before every observation, this calibration method can always be applied to raw TES data and is not subject to $I$-$V$ data quality or processing errors.