Direct spectroscopic biosignature characterization (hereafter "biosignature characterization") will be a major focus for future space observatories equipped with coronagraphs or starshades. Our aim in this article is to provide an introduction to potential detector and cooling technologies for biosignature characterization. We begin by reviewing the needs. These include nearly noiseless photon detection at flux levels as low as $<0.001~\textrm{photons}~s^{-1}~\textrm{pixel}^{-1}$ in the visible and near-IR. We then discuss potential areas for further testing and/or development to meet these needs using non-cryogenic detectors (EMCCD, HgCdTe array, HgCdTe APD array), and cryogenic single photon detectors (MKID arrays and TES microcalorimeter arrays). Non-cryogenic detectors are compatible with the passive cooling that is strongly preferred by coronagraphic missions, but would add non-negligible noise. Cryogenic detectors would require active cooling, but in return deliver nearly quantum limited performance. Based on the flight dynamics of past NASA missions, we discuss reasonable vibration expectations for a large UV-Optical-IR space telescope (LUVOIR) and preliminary cooling concepts that could potentially fit into a vibration budget without being the largest element. We believe that a cooler that meets the stringent vibration needs of a LUVOIR is also likely to meet those of a starshade-based Habitable Exoplanet Imaging Mission.
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