  Quantum physics allows an object to be detected even in the absence of photon
absorption, by the use of so-called interaction-free measurements. We provide a
formulation of this protocol using a three-level system, where the object to be
detected is a pulse coupled resonantly into the second transition. In the
original formulation of interaction-free measurements, the absorption is
associated with a projection operator onto the third state. We perform an
in-depth analytical and numerical analysis of the coherent protocol, where
coherent interaction between the object and the detector replaces the
projective operators, resulting in higher detection efficiencies. We provide
approximate asymptotic analytical results to support this finding. We find that
our protocol reaches the Heisenberg limit when evaluating the Fisher
information at small strengths of the pulses we aim to detect -- in contrast to
the projective protocol that can only reach the standard quantum limit. We also
demonstrate that the coherent protocol remains remarkably robust under errors
such as pulse rotation phases and strengths, the effect of relaxation rates and
detunings, as well as different thermalized initial states.
