Measuring high-resolution 3D density field in buoyant plumes using Optical-flow based Tomographic Background-Oriented Schlieren (TBOS) with sinogram interpolation

Tomographic Background-Oriented Schlieren (TBOS) is a three-dimensional density measurement technique in transparent media where the density gradients are related to the refractive index through the Gladstone-Dale relation. The line-integrated density gradient, based on the apparent deflection of a background pattern, from eight projection angles, is used to reconstruct the instantaneous 3D density field. Traditionally, background pattern deflections are calculated using a window-based cross-correlation approach, which, however, introduces spatial averaging and limits resolution. We employ an optical flow technique, specifically the Horn and Schunk implementation, to obtain the pattern deflection at each pixel, thus resulting in a highly dense displacement field.

The analytical tomographic reconstruction technique such as Filtered Back Projection (FBP) based on the Fourier slice theorem suffers from low reconstruction accuracy when there are fewer projection angles. Whereas, the Algebraic reconstruction techniques (ART), which are iterative, provide better reconstruction accuracy with limited projection angles and noisy data. Simultaneous Iterative Reconstruction Technique (SIRT), a variation of ART, is used to develop an in-house code to reconstruct the instantaneous density field using the data obtained from BOS measurements. The accuracy of this reconstruction is further enhanced using a sinogram interpolation technique.

Our test cases involve buoyant plumes generated by releasing a Helium-Air mixture (20 slpm Helium and 15 slpm Air) from a 35 mm diameter cylindrical nozzle into the ambient atmosphere. We validate our measurements against theoretical density profiles. Our results demonstrate that the optical flow algorithm combined with sinogram interpolation significantly enhances the resolution of the reconstructed density field compared to traditional cross-correlation methods.