  Probing the collective spin state of an ensemble of atoms may provide a means
to reduce heating via the photon recoil associated with the measurement and
provide a robust, scalable route for preparing highly entangled states with
spectroscopic sensitivity below the standard quantum limit for coherent spin
states. The collective probing relies on obtaining a very large optical depth
that can be effectively increased by placing the ensemble within an optical
cavity such that the probe light passes many times through the ensemble. Here
we provide expressions for measurement resolution and spectroscopic enhancement
in such cavity-aided non-demolition measurements as a function of cavity
detuning. In particular, fundamental limits on spectroscopic enhancements in
$^{87}$Rb are considered.
