  High-resolution optical microscopy suffers from a low contrast in scattering
media where a multiply scattered wave obscures a ballistic wave used for image
formation. To extend the imaging depth, various gating operations - confocal,
coherence, and polarization gating - have been devised to filter out the
multiply scattered wave. However, these gating methods are imperfect as they
all act on the detection plane located outside a scattering medium. Here, we
present a new gating scheme, called 'space' gating, that rejects the multiply
scattered wave directly at the object plane inside a scattering medium.
Specifically, we introduced a 30 $\mu$m-wide acoustic focus to the object plane
and reconstructed a coherent image only with the ballistic wave modulated by
acousto-optic interaction. This method allows us to reject the multiply
scattered wave that the existing gating methods cannot filter out and improves
the ratio of the ballistic wave to the multiply scattered wave by more than 100
times for a scattering medium more than 20 times thicker than its scattering
mean free path. Using the coherent imaging technique based on space gating, we
demonstrate the unprecedented imaging capability - phase imaging of optically
transparent biological cells fully embedded within a scattering medium - with a
spatial resolution of 1.5 $\mu$m.
