Efficient numerical frameworks for modelling ultrasonic beams propagating across interfaces

Abstract

Two different frameworks are developed to model the wave field generated by a transducer and propagating through one or more interfaces, and a Quasi-Monte Carlo (QMC) integration scheme is used to numerically evaluate their results. The first method is based on the Rayleigh-Sommerfeld Integral (RSI), further developing a formulation in the literature and improving its capabilities, while the second relies on a high-frequency approximation, using a ray tracing principle. The advantages and limitations of each model are then compared via in-depth investigations on several use cases, culminating in an efficiency and scope assessment. It was found that the RSI-based model performs well if a large number of field points is needed, such as when modelling a full image of the field. Conversely, for a large number of interfaces, such as when modelling the field through a thin-layered material, the most efficient model was the ray tracing formulation, since it was unnecessary to propagate the field between all the interfaces first. This was especially noticeable for applications requiring only the evaluation of the field at a few points on the other side of multiple interfaces.