  We establish a relation between entanglement of a many-body system and its
diffractive properties, where the link is given by structure factors. Based on
these, we provide a general analytical construction of multi-qubit entanglement
witnesses. The proposed witnesses contain two-point correlations. They could be
either measured in a scattering experiment or via local measurements, depending
on the underlying physical system. For some explicit examples of witnesses we
analyze the properties of the states that are detected by them. We further
study the robustness of these witnesses with respect to noise.
