Measurements of microscale shock velocity in water droplets using optical imaging and ray tracing analysis*

The microscale shock waves induced by laser ablation in liquids are relevant in many applications, including laser surgery and nanoparticle synthesis. Accurate measurements of shock properties, such as shock and particle velocities, are difficult to conduct due to the complexity of optical ablation and the small size of the system. To characterize such shocks, ~60 µm diameter water microdroplets were exposed to focused X-ray laser pulses, which ablate water more controllably and reproducibly than optical lasers. The ablation generated cylindrical shock waves, that were imaged optically inside the drop over a range of time delays. Because the image of the interior of the drop is magnified, we conducted a ray tracing analysis of the optical imaging system. The optical magnification depends on the distance from the center of the drop, being a function rather than a constant factor, and this function depends on the details of the imaging system and on the droplet size and shape. Using the magnification function, we determined the shock positions and velocities inside the drop as a function of time. We also determined the relation between shock and particle velocities by combining these shock velocity measurements with particle velocity measurements in smaller drops, for shocks generated by X-ray pulses with the same energy.