Theoretical and experimental responses for a large-aperture broadband spherical transducer probing a liquid–solid boundary

Abstract

A theoretical analysis of a spherical focusing transducer for broadband acoustic microscopy is proposed. The originality of the present contribution is the particular attention we have paid to describe, as rigorously as possible, the diffraction phenomena. Our analysis starts in the harmonic domain with the well-known angular spectrum method, and then gets into the time domain. A new formulation of the angular spectrum in the focal plane has been obtained and compared to other expressions previously reported. This article is deliberately limited to isotropic semi-infinite plane reflectors in order to carry out the inverse Fourier transform in an analytical way. The analytical approach is helpful for the physical interpretation of particular interesting phenomena observed in the transient analysis. A new kind of contribution to the echographic response has been identified and named “geometrical edge waves.” The weight and the arrival time of each discontinuity of the impulse response is analytically evaluated and the physical meaning of each of them is clearly established with the help of a ray model. In the last part of this article, a broadband polyvinylidene fluoride transducer excited by short pulses is used for the experimental validation of the model. The excellent quantitative agreement observed on the time waveforms confirms the efficiency of our approach both in the time domain and in the harmonic one. The comparison between theory and experiment is limited here to some typical examples, but similar results have been obtained on a wide range of defocus and for a large variety of materials. Applications for the characterization of materials will be discussed in future publications.