  The covalent functionalization of single-walled carbon nanotubes (SWCNTs)
with luminescent quantum defects enables their application as near-infrared
single-photon sources, as optical sensors, and for in-vivo tissue imaging.
Tuning the emission wavelength and defect density are crucial for these
applications. While the former can be controlled by different synthetic
protocols and is easily measured, defect densities are still determined as
relative rather than absolute values, limiting the comparability between
different nanotube batches and chiralities. Here, we present an absolute and
unified quantification metric for the defect density in SWCNT samples based on
Raman spectroscopy. It is applicable to a range of small-diameter nanotubes and
for arbitrary laser wavelengths. We observe a clear inverse correlation of the
D/G$^{+}$ ratio increase with nanotube diameter, indicating that curvature
effects contribute significantly to the defect-activation of Raman modes.
Correlation of intermediate frequency modes with defect densities further
corroborates their activation by defects and provides additional quantitative
metrics for the characterization of functionalized SWCNTs.
