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

A theoretical analysis of a spherical focusing transducer for broadband aco ustic microscopy is proposed. The originality of the present contribution i s the particular attention we have paid to describe, as rigorously as possi ble, the diffraction phenomena. Our analysis starts in the harmonic domain with the well-known angular spectrum method, and then gets into the time do main. A new formulation of the angular spectrum in the focal plane has been obtained and compared to other expressions previously reported. This artic le is deliberately limited to isotropic semi-infinite plane reflectors in o rder to carry out the inverse Fourier transform in an analytical way. The a nalytical approach is helpful for the physical interpretation of particular interesting phenomena observed in the transient analysis. A new kind of co ntribution to the echographic response has been identified and named "geome trical edge waves." The weight and the arrival time of each discontinuity o f the impulse response is analytically evaluated and the physical meaning o f 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 e xcited by short pulses is used for the experimental validation of the model . The excellent quantitative agreement observed on the time waveforms confi rms the efficiency of our approach both in the time domain and in the harmo nic one. The comparison between theory and experiment is limited here to so me typical examples, but similar results have been obtained on a wide range of defocus and for a large variety of materials. Applications for the char acterization of materials will be discussed in future publications. (C) 199 9 American Institute of Physics. [S0021-8979(99)07417-4].