Quantitative reconstruction of ultrasound fields in optically transparent isotropic solids

This contribution reports on a method of utilizing light refractive tomography (LRT) to reconstruct ultrasound dilatation fields in optically transparent isotropic solids. Furthermore, it proposes the description of ultrasound in solids using a normal stress component, which shares the same unit with sound pressure and can be approximately derived from dilatation. After giving the theoretical support for this novel application, we reconstruct the distribution of normal stress σ_zz in a cross section within poly(methyl methacrylate) (PMMA). Because of the lack of techniques for verifying the measurement results directly, systematic errors of the LRT measurements in PMMA are checked by comparing the results from LRT and hydrophone measurements in water. The small differences relative to the maximum pressure (e.g., <;2% at the center) indicate the reliability of the corresponding LRT measurements in PMMA. With the aid of numerical simulations, the uncertainty of the reconstructed dilatation is determined to be about 5% near the rotation axis. We also succeed in reconstructing ultrasound fields throughout water and PMMA in time and in three spatial dimensions. The reconstructed fields match the corresponding numerical simulation quite well; e.g., the simulation predicts most of the phenomena emerging in the reconstructed images. The reliability of the measurement is then verified by calculating two quantities; each of them is computed with two different methods. Small differences between results are achieved in both cases (i.e., -5.1% and -1.3%).