Calibrations of the Compton Spectrometer and Imager

The Compton Spectrometer and Imager (COSI) is a balloon-borne soft $\gamma$-ray telescope (0.2-5 MeV) designed to study astrophysical sources. COSI employs a compact Compton telescope design and is comprised of twelve high-purity germanium semiconductor detectors. Tracking the locations and energies of $\gamma$-ray scatters within the detectors permits high-resolution spectroscopy, direct imaging over a wide field-of-view, polarization studies, and effective suppression of background events. Critical to the precise determination of each interaction's energy, position, and the subsequent event reconstruction are several calibrations conducted in the field before launch. Additionally, benchmarking the instrument's higher-level performance through studies of its angular resolution, effective area, and polarization sensitivity quantifies COSI's scientific capabilities. In May 2016, COSI became the first science payload to be launched on NASA's superpressure balloon and was slated for launch again in April 2020. Though the 2020 launch was canceled due to the COVID-19 pandemic, the COSI team took calibration measurements prior to cancellation. In this paper we provide a detailed overview of COSI instrumentation, describe the calibration methods, and compare the calibration and benchmarking results of the 2016 and 2020 balloon campaigns. These procedures will be integral to the calibration and benchmarking of the NASA Small Explorer satellite version of COSI scheduled to launch in 2025.