Characterization of the Sound Field Generated by an Ultrasonic Transducer in a Solid Medium by Rayleigh-Sommerfeld Back-Propagation of Bulk Acoustic Waves Measured with Double-Pulsed TV Holography

Abstract

The established approach for the characterization of sound beams is the acquisition of experimental data by measuring the acoustic field pressure distribution in a fluid medium, which is usually done with point detectors (hydrophones, microphones) or arrays of detectors. From these point measurements, important characteristics of the sound field emitted by the transducer (such as the axial and transversal beam profiles, focal length or beam spread) can be derived. When the propagation medium is a solid, these characteristics are normally obtained from the measurement of pulse-echo signal amplitudes that arise from the interaction of the sound beam with targets placed in the material, such as metal balls embedded in plastics, or flat-bottom or side holes drilled in metallic blocks. These measurements are more difficult to perform and provide a sparser set of data compared to the immersion techniques. In this work we explore the capabilities of an alternative technique to characterize the acoustic field emitted by a piezoelectric transducer that is coupled to a thick metallic slab. This technique was originally developed for the nondestructive testing of metallic samples, and was successfully tested to locate the transversal dimensions and axial location of an internal artificial defect. It employs acoustic, optical and numerical methods and can be regarded as a combination of optical digital holography and acoustic holography. Firstly, a short burst of compression waves produced by the transducer is coupled to a thick metallic slab. The acoustic waves traverse the sample and emerge at the opposite surface, where a sequence of 2D maps of the out-of-plane displacement produced by the arrival of the successive wavefronts is recorded with double-pulsed TV holography. A 3D Fourier transform evaluation method applied to this data set yields a sequence of complex-valued 2D maps that contain the acoustic amplitude and phase of the wavefronts at that plane. Finally, the acoustic amplitude and phase are numerically reconstructed at other planes located at the desired depth within the material by Rayleigh-Sommerfeld back-propagation from one of these maps. In the present work, the technique described above is used with a homogeneous metallic specimen, since the aim is to study the acoustic field produced by the source. All the measurements are performed under the actual working conditions of the transducer. By choosing the appropriate reconstruction distance, a dense 2D map of the acoustic amplitude can be obtained at any plane within the volume delimited by the measurement and excitation surfaces, even at the interface sample-transducer. By generating a set of maps at regularly spaced reconstruction distances, the axial profile of any part of the beam can be obtained, as well as an estimation of the beam spread. The capability of the technique to assess a correct coupling between transducer and sample is also investigated with a set of experiments with artificial coupling defects.