  We report a novel "cone-ray" model of background-oriented schlieren (BOS)
imaging that accounts for depth-of-field effects. Reconstructions of the
density field performed with this model are far more robust to the blur
associated with a finite aperture than conventional reconstructions, which
presume a "thin-ray" pinhole camera. Our model is characterized and validated
using forward evaluations based on simulated and experimental BOS measurements
of buoyancy-driven flow and hypersonic flow over a sphere. Moreover, we embed
the model in a neural reconstruction algorithm, which is demonstrated with a
total variation penalty as well as the compressible Euler equations. Our
cone-ray technique dramatically improves the accuracy of BOS reconstructions:
the shock interface is well-resolved in all our tests, irrespective of the
camera's aperture setting, which spans f-numbers from 22 down to 4.
