  We propose a novel quantum diffraction imaging technique whereby one photon
of an entangled pair is diffracted off a sample and detected in coincidence
with its twin. The image is obtained by scanning the photon that did not
interact with matter. We show that when a dynamical quantum system interacts
with an external field, the phase information is imprinted in the state of the
field in a detectable way. The contribution to the signal from photons that
interact with the sample scales as $\propto I_{p}^{1/2}$, where $I_{p}$ is the
source intensity, compared to $\propto I_{p}$ of classical diffraction. This
makes imaging with weak-field possible, avoiding damage to delicate samples. A
Schmidt decomposition of the state of the field can be used for image
enhancement by reweighting the Schmidt modes contributions.
