  The propagation of light in moving media is dragged by atomic motion. The
light-drag effect can be dramatically enhanced by reducing the group velocity
with electro-magnetically induced transparency (EIT). We develop a systematic
procedure to accurately reconstruct the complex wavefront of the slow light
with single-shot measurements, enabling precise, photon shot-noise limited
spectroscopic measurements of atomic response across EIT even in presence of
generic atomic number fluctuations. Applying the technique to an expanding
cloud of cold atoms, we demonstrate simultaneous inference of the atomic
density distribution and the velocity field from the complex imaging data. This
inline imaging technique may assist a wide range of cold atom experiments to
access spectroscopic and phase space information with in situ and minimally
destructive measurements.
