Non-contact Measurement of BOS Shock Wave Overpressure Based on Structure-Aware Variational Optical Flow Method

Background-Oriented Schlieren (BOS) technique has become a key measurement method in external-field experiments of explosion mechanics, thanks to its advantages of non-contact and high spatiotemporal resolution. However, factors such as strong light interference, product scattering, weak intrinsic signals of shock waves, and their complex morphologies make the automatic and accurate extraction of wavefronts from BOS images extremely challenging. Although existing methods have made progress, the accuracy of wavefront extraction and the handling of complex environments still need urgent improvement.To address this problem, this paper proposes a Structure-Aware Weighted Variational Optical Flow (SAW-VF) method, aiming to robustly quantify the high-speed transient displacement field of shock waves. The core of this method lies in minimizing a well-designed energy functional: first, its data fidelity term incorporates the first-order photometric constraint and second-order Hessian matrix invariance, which significantly enhances the sensitivity to the linear local geometric features of shock waves; second, a spatially adaptive weighting mechanism driven by Normalized Cross-Correlation (NCC) is introduced to dynamically suppress the negative impact of severely distorted regions in images; third, an anisotropic regularization term inspired by the Perona-Malik diffusion theory is adopted to effectively preserve the sharp motion boundaries of shock waves. The entire optimization process is embedded in a coarse-to-fine Gaussian pyramid framework to cope with large-displacement motion.On this basis, this study further proposes a physics-model-driven wavefront fitting method. Through maximum inlier set optimization combined with shock wave dynamics constraints, the wavefront is accurately extracted, and finally, non-contact quantitative overpressure measurement is achieved. In TNT explosion tests, the relative error of the measurement results of this method compared with pressure sensor data ranges from 0.93% to 9.85%, which verifies the effectiveness and accuracy of this automated system in non-intrusive overpressure measurement of shock waves.