Background oriented schlieren image displacement estimation method based on global optical flow

Background oriented schlieren (BOS) technology is a recent non-contact optical diagnostic technology, which can be used for the visualization of variable density flow and the quantitative measurement of the refractive index field. The accuracy of BOS image displacement estimation directly determines the accuracy of refractive index field reconstruction. For BOS images, the optical path construction method, vibration and uneven illumination, blurring and defocusing effects, and the refocusing effect of volume refraction make it difficult for the BOS image sequence to satisfy the constant brightness assumption. In this study, the optical flow algorithm based on the assumption of a constant gradient in PIV is improved and applied to BOS image displacement estimation. A data item based on the assumption of constant brightness combined with the assumption of constant gradient is proposed. The first-order div-curl regularization constraint is used as the spatial smoothing condition, and the non-convex Charbonnier penalty function is used to determine the displacement field by the variational method to minimize the energy function. The proposed method is tested on the synthetic images obtained by two-dimensional turbulent direct numerical simulation (DNS), the BOS synthetic images with brightness changes, and the actual experimental BOS images of the flow field above a premixed butane/air combustion flame with different equivalence ratios. Compared with the current advanced optical flow algorithm, this method has higher accuracy and robustness. Overall, the proposed method can not only obtain more accurate results when the brightness of the BOS synthetic image and experimental image changes, but also helps in retaining the flow details such as small divergence and vorticity structure of the heat flow field while reducing the outliers.