  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 ($0\nu\beta\beta$)
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 $0\nu\beta\beta$ 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.
