Quantitative x ray phase contrast imaging of oblique shock wave–interface interactions

Oblique shock wave–interface interactions of gases and liquids have been extensively studied in shock tubes using optical methods to measure equation-of-state (EOS) parameters. However, this is difficult with solids due to their opaqueness to visible light. X ray phase contrast imaging (XPCI) has the penetrative strength to probe solids while still being sensitive to mass density and enhancing the visibility of material boundaries. We investigate the accuracy and repeatability of measuring the mean value of the average mass density (areal density divided by thickness) over region S (BS) and flow deflection angle (θ) from XPCI images of a sample. To that end, a Hough transform-based method for measuring θ is developed. To measure BS, the XPCI image intensity probability density function (PDF) is modeled accounting for the spatial distribution of x ray energy, scintillator response, and pulse-to-pulse variation in the x ray intensity. In addition, a Monte Carlo-based algorithm for computing the BS PDF is developed. Both methods are validated on an impact-generated oblique shock wave interacting at a solid polymer-to-polymer interface. This is accomplished through a comparison to hydrodynamic simulations using well-established EOS. Under the modeling framework for the XPCI image intensity, BS is computed with an accuracy of <0.1% and precision of 3%–5%, while θ has an uncertainty of 0.2°, respectively. This shows that the XPCI-based model that is developed here could be an invaluable tool for high-fidelity testing of hydrodynamic models in shock polar configurations.