  Point source localization is a problem of persistent interest in optical
imaging. In particular, a number of widely used biological microscopy
techniques rely on precise three-dimensional localization of single
fluorophores. As emitter depth localization is more challenging than lateral
localization, considerable effort has been spent on engineering the response of
the microscope in a way that reveals increased depth information. Here we
consider the theoretical limits of such approaches by deriving the quantum
Cram\'{e}r-Rao bound (QCRB). We show that existing methods for depth
localization with single-objective detection exceed the QCRB by a factor
$>\sqrt{2}$, and propose an interferometer arrangement that approaches the
bound. We also show that for detection with two opposed objectives, established
interferometric measurement techniques globally reach the QCRB.
