Enhancing spatial resolution of background-oriented Schlieren using deep learning: An experimental and numerical approach

Abstract

High-speed flow visualization using the background-oriented Schlieren (BOS) method is constrained by a trade-off between frame rate and spatial resolution. The potential of deep learning-based super-resolution to the periodic patterns of the wavelet-based BOS (W-BOS) remains largely unexplored. This study proposes a method to enhance the spatial resolution of the W-BOS technique for unsteady supersonic flows by employing deep learning-based super-resolution. We integrated the enhanced deep super-resolution networks with the W-BOS method to visualize a supersonic jet ejected from a small-volume shock tube, along with the induced shock wave. To mitigate the high cost of acquiring training data, we evaluated the use of synthetic BOS images generated through computational fluid dynamics (CFD). Quantitative analysis indicated that models trained on BOS-specific periodic luminance patterns outperformed conventional bicubic interpolation. At a magnification ratio of 8, models trained on experimental and CFD-generated images reduced the root-mean-squared error of the density gradient field by 20.3% and 15.4%, respectively. However, models trained exclusively on idealized CFD images demonstrated overfitting when applied to experimental data containing optical noise. Incorporating only 25% of the experimental images into the CFD dataset suppressed overfitting and achieved restoration accuracy comparable with that of models trained solely on experimental data, reducing the required volume of experimental data by 75%. Application of the trained model to high-magnification visualizations suppressed noise, revealing shock waves and supersonic jet structures. The combination of deep learning-based super-resolution and CFD-assisted training demonstrates significant potential for high-fidelity visualization of complex compressible flows.