  In this article we explore the requirements for enabling high quality
optically detected magnetic resonance (ODMR) spectroscopy in a conventional
gradient force optical tweezers using nanodiamonds containing nitrogen-vacancy
(NV$^{-}$) centres. We find that modulation of the infrared (1064 nm) trapping
laser during spectroscopic measurements substantially improves the ODMR
contrast compared with continuous wave trapping. The work is significant as it
allows trapping and quantum sensing protocols to be performed in conditions
where signal contrast is substantially reduced. We demonstrate the utility of
the technique by resolving NV$^{-}$ spin projections within the ODMR spectrum.
Manipulating the orientation of the nanodiamond via the trapping laser
polarisation, we observe changes in spectral features. Theoretical modelling
then allows us to infer the crystallographic orientation of the NV$^{-}$. This
is an essential capability for future magnetic sensing applications of
optically trapped nanodiamonds.
