Shockwave velocimetry using wave-based image processing to measure anisotropic shock emission

Abstract

Noninvasive optical measurements of the shockwave propagation velocity using multiple pulse illumination allow deducing the shockwave pressure amplitude through Hugoniot relations and an appropriate equation of state of the medium. This technique is particularly useful for spatially resolved measurements near the shockwave emission site. Due to diffraction, however, a shockwave front can significantly change its morphology, rendering precise velocity measurements non-trivial. As solution we propose a wave front evolution (WaFE) velocimetry technique, which applies Huygens principle. We take a shadowgraph of the wave front at subsequent times as initial condition for the acoustic Helmholtz equation and numerically propagate the fronts in time. From the instance of time, when two subsequently taken wave front shadows numerically interfere and form one sharp wave front, the local shock velocity is obtained and the local shock pressure amplitude measured. With artificial test images, it is shown that this technique has excellent sub-pixel accuracy, robustness to noise, and can work with low contrast images and even overlapping and interfering wave fronts. The software is made available freely and can be applied to general shock front velocity measurements. We apply WaFE to determine the anisotropic shockwave emission from an elongated laser-induced plasma in water from shadowgraphs of the shockwave front imaged four times onto the same camera frame using multiple pulse illumination at a repetition rate of 60 MHz. The direction dependence of attenuation of the shockwave pressure amplitude is measured at distances of 50–300 μm to the plasma.