Comparison of displacement estimation techniques for background-oriented schlieren of high-speed compressible turbulent flows

Background-oriented schlieren (BOS) is a non-intrusive optical method for measuring density gradients in a fluid flow based on changes of local refractive index. The density gradients can be obtained by observing the displacement between two images of a background pattern, with and without the presence of the flow. Existing methods to estimate displacements include block matching and optical flow. Image registration in computer vision seeks reasonable transformations between two images such that one matches the other and has been under-utilized in determining the displacement for BOS image processing. Deformable image registration (DIR) methods allow non-global transformations and are proposed as displacement estimation methods for processing BOS images. Numerical ray tracing simulations are performed to generate synthetic BOS images of various flows. The estimated density gradient results of block matching, optical flow, and DIR methods are compared to the ground truth (the path-averaged density gradient of the schlieren object used in ray tracing) to assess and compare their performances. The performances of these methods are also validated on experimental BOS images to determine the displacement estimation method that is most suitable for high-speed, turbulent flows.