Effect of acoustical properties of a lens on the pulse-echo response of a single element transducer

The purpose of this study is to compare two methods for calculating the electroacoustic response of a transducer at the focal point through an acoustic focusing lens. The theoretical conditions depend on the degrees of freedom taken into account as well as on the boundary conditions for the propagation. The most widely used conditions, i.e. longitudinal vibration and rigid baffle boundary condition are considered here. The theoretical approach consists in calculating the electroacoustic response using each electroacoustic model, both of these results being then propagated with the Rayleigh integral for a focused source. The first section consists in a modeling of the electroacoustic response based either on the modified classical KLM electrical equivalent circuit (1D) or on the finite element method (FEM) ATILA (axisymmetric 2D). Both models are applied to an axisymmetric configuration, and a classical propagation operation is used to obtain the response at the focal point. The second part deals with the experimental verification of the modeling methods. Measurements on a series of 10 MHz focused transducers are compared to theoretical curves, and results are discussed as a function of geometry and properties of the acoustical lens.