NeDF: neural deflection fields for sparse-view tomographic background oriented Schlieren

Three-dimensional (3D) density-varying turbulent flows are widely encountered in high-speed aerodynamics, combustion, and heterogeneous mixing processes. Multi-camera-based tomographic background-oriented Schlieren (TBOS) has emerged as a powerful technique for revealing 3D flow density structures. However, dozens of cameras are typically required to obtain high-quality reconstructed density fields. Limited by the number of available optical windows and confined space in the harsh experimental environments, TBOS with only sparse views and limited viewing angles often becomes the necessary choice practically, rendering the inverse problem for TBOS reconstruction severely ill-posed and resulting in degraded tomography quality. In this study, we propose a novel TBOS reconstruction method, neural deflection field (NeDF), utilizing deep neural networks (DNNs) to represent the density gradient fields without using any pretrained neural network models. Particularly, state-of-the-art positional encoding techniques and hierarchical sampling strategies are incorporated to capture the density structures of high spatial frequencies. Required background images for TBOS reconstructions are synthesized based on a high-fidelity nonlinear ray-tracing method with the ground truth flows from conducting LES simulations on premixed turbulent flames. Owing to these synthesized BOS images, the superiority of the proposed method is quantitatively verified compared to the classical TBOS reconstruction methods, and the specific contributions from the position encoding and the hierarchical sampling strategy are also elucidated.