  We show theoretically that the noise due to laser induced backaction acting
on a small nanosphere levitated in a standing-wave trap can be considerably
reduced by utilising a suitable reflective boundary. We examine the spherical
mirror geometry as a case study of this backaction suppression effect,
discussing the theoretical and experimental constraints. We study the effects
of laser recoil directly, by analysing optical force fluctuations acting on a
dipolar particle trapped at the centre of a spherical mirror. We also compute
the corresponding measurement imprecision in an interferometric,
shot-noise-limited position measurement, using the formalism of Fisher
information flow. Our results show that the standing-wave trapping field is
necessary for backaction suppression in three dimensions, and they satisfy the
Heisenberg limit of detection.
