This paper reports 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 of simulated buoyancy-driven flow and both simulated and experimental BOS measurements of hypersonic flow over a sphere. Moreover, the model is embedded in a neural reconstruction algorithm, which is demonstrated with a total variation penalty and 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.

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This material is based upon work supported by NSF under Grant No. 2227763, NASA under Grant No. 80NSSC19M0194, FAU Erlangen-Nürnberg, and a DoD NDSEG Fellowship. The views and conclusions contained herein are those of the authors and should not be interpreted as representing the official policies or endorsements, either expressed or implied, of NSF, NASA, DoD, or the U.S. Government. The authors also gratefully acknowledge K. Kim and other members of the Combs Research Group at the University of Texas at San Antonio for helping with the background-oriented schlieren setup and operating the wind tunnel facility.

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Received24 February 2024
Accepted15 August 2024
Published online1 October 2024

Forward and Inverse Modeling of Depth-of-Field Effects in Background-Oriented Schlieren

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