  Classical imaging works by scattering photons from an object to be imaged,
and achieves resolution scaling as $1/\sqrt{t}$, with $t$ the imaging time. By
contrast, the laws of quantum mechanics allow one to utilize quantum coherence
to obtain imaging resolution that can scale as quickly as $1/t$ -- the
so-called "Heisenberg limit." However, ambiguities in the obtained signal often
preclude taking full advantage of this quantum enhancement, while imaging
techniques designed to be unambiguous often lose this optimal Heisenberg
scaling. Here, we demonstrate an imaging technique which combines unambiguous
detection of the target with Heisenberg scaling of the resolution. We also
demonstrate a binary search algorithm which can efficiently locate a coherent
target using the technique, resolving a target trapped ion to within 0.3% of
the $1/e^2$ diameter of the excitation beam.
