Tomographic background-oriented schlieren techniques for three-dimensional density field reconstruction in shock-containing flows

Two measurement techniques for acquiring pixel displacement data for tomographic background oriented schlieren are compared; the first analyses image pairs of an optimised random-dot pattern using a conventional cross-correlation algorithm. The second evaluates optical flow displacements for image pairs of a fractal texture background composed of multi-scale wavelet noise. Quasi-3D tomographic reconstruction is performed under the parallel-ray assumption using an algebraic method, initialised with large-gradient regions from a filtered back-projection gradient inversion, for improved clarity and noise reduction. Reconstruction of the near-field density of a highly underexpanded jet from an elliptical nozzle of aspect ratio 2:1 is performed using both optical flow and cross-correlation displacement fields. Diffraction effects at the Mach disk are seen to produce strong artefacts in reconstructed gradient fields. Differences in gradient components from optical flow and cross-correlation are effectively smoothed by Poisson integration, yielding similar final density distributions, stressing that selection of a suitably accurate method for integration of the Poisson equation is required to preserve increased fidelity of gradient fields. Good qualitative agreement in shock structure is found with respect to existing studies.