Optical-flow-based background-oriented schlieren technique for measuring a laser-induced underwater shock wave

The background-oriented schlieren (BOS) technique with the physics-based optical flow method (OF-BOS) is developed for measuring the pressure field of a laser-induced underwater shock wave. Compared to BOS with the conventional cross-correlation method that is also applied for particle image velocimetry (here called PIV-BOS), by using the OF-BOS, the displacement field generated by a small density gradient in water can be obtained at the spatial resolution of one vector per pixel. The corresponding density and pressure fields can be further extracted. It is demonstrated in particular that the sufficiently high spatial resolution of the extracted displacement vector field is required in the tomographic reconstruction to correctly infer the pressure field of the spherical underwater shock wave. The capability of the OF-BOS method is critically evaluated based on synchronized hydrophone measurements. Special emphasis is placed on direct comparison between the OF-BOS and PIV-BOS methods.