Simultaneous measurement of phonon and light signatures is an effective way to reduce the backgrounds and increase the sensitivity of CUPID, a next-generation bolometric neutrinoless double-beta decay ($0 ubetabeta$) experiment. Light emission in tellurium dioxide (TeO$_2$) crystals, one of the candidate materials for CUPID, is dominated by faint Cherenkov radiation, and the high refractive index of TeO$_2$ complicates light collection. Positive identification of $0 ubetabeta$ events therefore requires high-sensitivity light detectors and careful optimization of light transport. A detailed microphysical understanding of the optical properties of TeO$_2$ crystals is essential for such optimization. We present a set of quantitative measurements of light production and transport in a cubic TeO$_2$ crystal, verified with a complete optical model and calibrated against a UVT acrylic standard. We measure the optical surface properties of the crystal, and set stringent limits on the amount of room-temperature scintillation in TeO$_2$ for $beta$ and $alpha$ particles of 5.3 and 8 photons / MeV, respectively, at 90% confidence. The techniques described here can be used to optimize and verify the particle identification capabilities of CUPID.
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