Numerical and experimental analysis of a focused reflected wave in a multi-layered material based on a ray model

A focal probe is used for the acoustic measurement of a thin layer of a material with unknown sound velocity. This is now possible, because an algorithm, based on the focused ray model, has been found. However, there are still several problems such as the assumption that the half-aperture angle equals the incident angle, the identification of the longitudinal-wave focus, and the composition of the signal. In this work, we study the multi-mode wave focus numerically and experimentally to identify the focused longitudinal waves. A theoretical multilayered focusing model has been introduced based on geometrical acoustics. In addition, a phase differentiation theory is proposed to find the incident angle for the focus of the tilted rays, which is referred to as maximum half-aperture angle in other studies. The V(z,t) curve of a single layer, with a thickness of 1.5 mm and 2.0 mm, and a multi-layer are obtained using vertical translational movement. Both thickness and sound velocity are derived from the curve simultaneously. Our single layer experiments show that it is possible to focus multimode waves. The single and multi-layer experiments confirm the multi-layered focused ray model and phase differentiation theory. Furthermore, experiments are conducted to analyze the measured results.