Simulation of ultrasonic fields radiated by a circular source through a layer with nonparallel boundaries

Abstract

Active elements of ultrasonic transducers are separated from the medium by thick protective layers, which may have nonparallel front and back surfaces. The objective of this work was to develop a simple method suitable for fast calculation of ultrasonic fields radiated through a layer with parallel or nonparallel boundaries and enabling one to take into account multiple reflections inside the layer. The main presumption of the proposed method is the following: after refraction at the boundary between two media, the ultrasonic field consists of plane and edge waves as before refraction. The proposed simulation method is based on transformation of a multi-layered medium into a virtual one without internal boundaries and equivalent to the actual medium from the point of a view of the times of flight of the direct plane and edge waves. The method enables simulation of radiated ultrasonic fields even after multiple reflections within the layer with parallel or nonparallel boundaries. The examples of simulated and experimentally measured ultrasonic fields of the transducer with a nonparallel front surface of protection layer, radiating into the water, are presented.