Event-based high temporal resolution measurement of shock wave motion field

TL;DR

The paper tackles the challenge of accurately measuring shock-wave motion with high spatiotemporal resolution. It introduces a multi-event-camera framework that uses polar coordinate encoding, adaptive ROI extraction, and a slope-iterative shock-front extraction to preserve microsecond timing ($1\,\mu s$). By deriving a geometric model linking event data to shock radii and applying multi-view reconstruction, it achieves 3D motion-field visualization and explosive-charge equivalence inversion, with velocity measurements closely matching pressure sensors and empirical formulas (errors as low as $0.06\%$ and up to $5.20\%$). Experimental validation on a TNT charge demonstrates the method's accuracy and practical utility for power-field testing and damage assessment, offering a flexible, high-resolution alternative to traditional measurement approaches.

Abstract

Accurate measurement of shock wave motion parameters with high spatiotemporal resolution is essential for applications such as power field testing and damage assessment. However, significant challenges are posed by the fast, uneven propagation of shock waves and unstable testing conditions. To address these challenges, a novel framework is proposed that utilizes multiple event cameras to estimate the asymmetry of shock waves, leveraging its high-speed and high-dynamic range capabilities. Initially, a polar coordinate system is established, which encodes events to reveal shock wave propagation patterns, with adaptive region-of-interest (ROI) extraction through event offset calculations. Subsequently, shock wave front events are extracted using iterative slope analysis, exploiting the continuity of velocity changes. Finally, the geometric model of events and shock wave motion parameters is derived according to event-based optical imaging model, along with the 3D reconstruction model. Through the above process, multi-angle shock wave measurement, motion field reconstruction, and explosive equivalence inversion are achieved. The results of the speed measurement are compared with those of the pressure sensors and the empirical formula, revealing a maximum error of 5.20% and a minimum error of 0.06%. The experimental results demonstrate that our method achieves high-precision measurement of the shock wave motion field with both high spatial and temporal resolution, representing significant progress.

Figures (13)

• Figure 1: Overview of the proposed framework. By processing the event stamp through three modules, the asymmetry of the shock wave is estimated, and the motion field is reconstructed.
• Figure 2: Extraction process of LED marker. The density and polarity information of each pixel triggering event are used for extraction.
• Figure 3: Method of intermediate steps in shock wave extraction: Events are re-encoded into polar coordinate form firstly. Subsequently, for any propagation angle, construct a $d-t$ graph. Furthermore, the adaptive ROI extraction algorithm is utilized.
• Figure 4: Method of the slope-iterative extraction algorithm. As the search process advances, the slope is updated iteratively in small increments.
• Figure 5: Geometric model relating the radius of the shock wave to the events. By employing this model, the transformation from event coordinates to 3D radius can be achieved.