Optical ray tracing simulations to image water microdroplets and negative pressure modulations inside them*

The ablation of water microdroplets with X-ray lasers generates large negative pressure waves through shock reflection on the droplet surfaces. These negative pressures might be the largest produced by any method but were measured with low accuracy. Due to the droplets' small sizes direct pressure measurements were impossible, and the accuracy of computational fluid dynamics (CFD) simulations was limited by uncertainties in initial conditions, equation of state at negative pressures as well as phase-transition modeling. During the experiments, the droplets were imaged optically and the pressure waves were visible as darker regions due to pressure-induced changes in the refractive index. To understand and quantify wave images, we ran ray-tracing image simulations of droplets containing refractive index profiles predicted by CFD simulations. Previously, optical ray tracing was used to simulate images of cavitation bubbles, but more accurate simulations are needed to see the effect of refractive index gradients in a liquid drop. We found that improving the accuracy of image simulations requires modeling accurately complicated imaging optics, and modeling the illumination based on experimental calibrations. With these improvements we achieved a good qualitative agreement between simulated and experimental images. These ray-tracing simulations can in turn be used to refine and validate the CFD simulations, leading to an iterative procedure that improves the accuracy of pressure measurements.