Analysis of ultrasonic focusing in silicon wafers using the angular spectrum approach and ray tracing

Understanding ultrasonic beam focusing in anisotropic media is crucial for optimizing nondestructive evaluation techniques, as many advanced materials exhibit anisotropic properties. This study investigates the focusing behavior of ultrasonic beams in silicon, a representative anisotropic material, across three crystallographic orientations (0°, 22.5°, and 45° offsets from the [1 0 0] axis) using the angular spectrum approach (ASA) and ray tracing to understand computational cost trade-offs between the two models while elucidating new focusing behaviors and profiles. The ASA model is used to construct three-dimensional wave field visualizations and localize focal depths. Ray tracing is then employed to map the focal profiles at the ASA-identified depths. The results demonstrate that focal behavior geometry and depth vary as the anisotropic orientation changes, with foci splitting for the 45° orientation and skewed focusing for the 22.5° orientation. For high-frequency approximations, the ASA method may effectively identify focal depths that can serve as focal planes for ray tracing, potentially reducing computational expense. This approach showed alignment in the present study for 25 MHz, though its validity depends on the material properties under consideration. These findings can be useful in devising alternative experimental configurations that optimize focusing within anisotropic solids.