Application of background-oriented schlieren (BOS) technique to a laser-induced underwater shock wave

We build an ultra-high-speed imaging system based on the background-oriented schlieren (BOS) technique in order to capture a laser-induced underwater shock wave. This BOS technique is able to provide two-dimensional density-gradient field of fluid and requires a simple setup. The imaging system consists of an ultra-high speed video camera, a laser stroboscope, and a patterned background. This system takes images every 0.2 $\mu$s. Furthermore, since the density change of water disturbed by the shock is exceedingly small, the system has high spatial resolution $\sim$ 10 $\mu$m/pixel. Using this BOS system, we examine temporal position of a shock wave. The position agrees well with that measured by conventional shadowgraph, which indicates that the high-speed imaging system can successfully capture the instantaneous position of the underwater shock wave that propagates with the speed of about 1500 m/s. The local density gradient can be determined up to $O$(10$^3$ kg/m$^4$), which is confirmed by the gradient estimated from the pressure time history measured by a hydrophone.