  We have constructed a counterpropagating optical tweezers setup embedded in a
Sagnac interferometer in order to increase the sensitivity of position tracking
for particles in the geometrical optics regime. Enhanced position determination
using a Sagnac interferometer has previously been described theoretically by
Taylor et al. [Journal of Optics 13, 044014 (2011)] for Rayleigh-regime
particles trapped in an antinode of a standing wave. We have extended their
theory to a case of arbitrarily-sized particles trapped with
orthogonally-polarized counterpropagating beams. The working distance of the
setup was sufficiently long to optically induce particle oscillations
orthogonally to the axis of the tweezers with an auxiliary laser beam. Using
these oscillations as a reference, we have experimentally shown that
Sagnac-enhanced back focal plane interferometry is capable of providing an
improvement of more than 5 times in the signal-to-background ratio,
corresponding to a more than 30-fold improvement of the signal-to-noise ratio.
The experimental results obtained are consistent with our theoretical
predictions. In the experimental setup, we used a method of optical
levitator-assisted liquid droplet delivery in air based on commercial inkjet
technology, with a novel method to precisely control the size of droplets.
