Instantaneous 3D pressure mapping in shock waves using optical tomography

While pressure measurements are essential for shock wave characterization, conventional techniques remain fundamentally limited to intrusive point probes that provide only spatially discrete data-a critical barrier for studying transient compressible phenomena. In this Letter, we present, to the best of our knowledge, the first optical tomographic approach for spatiotemporally resolved 3D pressure mapping in shock waves. The methodology begins with acquisition of time-resolved multi-angle background-oriented schlieren (BOS) imaging data through a fiber-coupled high-speed camera system, capturing shock wave evolution at 48 kHz frame rates. Tomographic reconstruction algorithms are then applied to resolve the 3D refractive index field of shock waves. Subsequent integration of the level-set method with the Gladstone-Dale relation enables simultaneous determination of velocity and density field distributions. Finally, volumetric pressure fields are derived through solving Rankine-Hugoniot equations utilizing the reconstructed velocity and density data. Demonstrations on a detonation tube exhaust plume show that the presented technique can reconstruct full-field pressure distributions (40.5 mm³ volume) in shock waves. Validation against pressure transducer data demonstrates acceptable accuracy.