A ray tracing approach to focusing ultrasonic beams in isotropic and anisotropic solids

Abstract

Focal depths in solid materials are generally calculated using analytical expressions that rely on the paraxial approximation (i.e., small angles related to shallow focusing). However, with increasing use of highly focused probes for acoustic microscopy and backscattering studies, these assumptions are often challenged. Additional challenges are posed by the presence of material anisotropy within the solid. In this presentation, we present a ray tracing based approach to characterize ultrasonic beam focusing when using highly focused ultrasonic transducers. The results are compared to traditional methods to calculate focal regions to evaluate the range of applicability for isotropic and anisotropic materials. For isotropic solids, a non-paraxial focusing equation is derived and compared to the conventional focusing equation for both normal incidence and oblique incidence immersion setups. Both focusing equations are compared through ray diagrams where the proximity to the true geometric focus is explored. The proposed focusing equation results in a closer approximation to the geometric focus, a smaller beam cross-section, and a greater time convergence compared to the conventional focusing equation. Lastly, the results are expanded to anisotropic media where potential for multiple foci and complex beam behavior arise.