  Optically levitated microspheres are an excellent candidate for force and
acceleration sensing. Here, we propose an acceleration sensing protocol based
on an optically levitated microsphere array (MSA). The system consists of an
$N$-microsphere array levitated in a driven optical cavity via holographic
optical tweezers. By positioning the microspheres suitably relative to the
cavity, only one of the collective modes of the MSA is coupled to the cavity
mode. The optomechanical interaction encodes the information of acceleration
acting on the MSA onto the intracavity photons, which can then be detected
directly at the output of the cavity. The optically levitated MSA forms an
effective large mass-distributed particle, which not only circumvents the
problem of levitating a large mass microsphere but also results in a
significant improvement of sensitivity. Compared with the traditional
single-microsphere measurement scheme, our method presents an improvement in
sensitivity by a factor of $\sqrt{N}$.
