@article{ZHOU2026, 
author = {Zhigang ZHOU and Changli WANG and Zhenghao WU and Changyan XIAO and Ming KE and Xin ZHANG and Bingwen QIAN},
title = {Non-contact measurement of BOS shock wave overpressure based on structure-aware variational optical flow method},
year = {2026},
journal = {Explosion and Shock Waves},
volume = {46},
number = {6},
keywords = {shock wave, non-contact measurement, background-oriented schlieren, variational optical flow, overpressure measurement, wavefront extraction},
url = {https://www.sciopen.com/article/10.11883/bzycj-2025-0269},
doi = {10.11883/bzycj-2025-0269},
abstract = {Background-oriented schlieren (BOS) imaging, owing to its non-contact nature and high spatiotemporal resolution, has become an important measurement technique in field experiments of explosion mechanics. However, due to strong illumination interference, scattering from detonation products, and the inherently weak and morphologically complex shockwave signature, automatic and accurate extraction of the shock front from BOS images remains highly challenging. To address this issue, we propose a structure-aware weighted variational optical flow method (SAW-VF) for robust quantification of the high-speed transient displacement field of shockwaves. The proposed approach minimizes a purpose-designed energy functional. Specifically, the data fidelity term combines a first-order photometric constraint with a second-order Hessian-invariance constraint, substantially enhancing sensitivity to the local line-like geometric features of shock fronts. In addition, a spatially adaptive weighting mechanism driven by normalized cross-correlation (NCC) is introduced to dynamically suppress the adverse influence of severely distorted regions on the estimation. Moreover, an anisotropic regularization term inspired by Perona-Malik diffusion is employed to effectively preserve the sharp motion boundaries of the shock front. To cope with large displacements, the optimization is embedded in a coarse-to-fine Gaussian pyramid framework. Building upon the estimated displacement field, we further develop a physics model–driven shock-front fitting method, in which the shock front is accurately extracted via maximum-inlier-set optimization coupled with shockwave dynamical constraints. Finally, the shock radius and propagation velocity are estimated using geometric calibration and temporal information, and the overpressure is quantitatively determined in a non-contact manner based on the Rankine-Hugoniot theory. In TNT explosion experiments, the proposed method achieves a relative error of 0.93%−9.85% with respect to pressure sensor measurements, demonstrating its effectiveness and accuracy for non-intrusive overpressure measurement of shockwaves.}
}