Reconstruction refinement of hybrid background-oriented schlieren tomography

This paper introduces a hybrid method that leverages the advantages of both the window-based separate algorithm and the regularization-based unifying algorithm to refine the three-dimensional refractive index field measured by the background-oriented schlieren (BOS) tomography. Two image-warping approaches, under paraxial and non-paraxial ray-tracing assumption, are developed as a connecting link between coarse and refined reconstruction. An orthogonal test is conducted to examine the influence of various factors on the reconstruction fields in the hybrid approach, providing insights into the impact of factors such as the ray-tracing assumption, initial value for refractive index iteration, and image displacement algorithm. Various synthetic and real BOS cases demonstrate that our hybrid method reconstructs a more detailed and robust field, outperforming conventional BOS reconstruction methods in scenarios with small or large density gradients, as well as laminar or turbulent structures.