Simulation of self-focusing by an array on a crack in an immersed specimen

An ultrasonic measurement model is developed to simulate self-focusing by a curved array of transducers on an interior crack. The far field radiated b y each transducer element is modeled by rays with a Gaussian distribution o f amplitudes over the beam width. The ray tracing method is used to determi ne the focused wave field in the immersed specimen and the travel times fro m each array element to the crack. The self-focusing array is modeled for b oth sonification and reception focusing. The transducers in the array are e xcited with the appropriate time delays to achieve sonification focusing. A fter the incident wave field on the crack has been obtained, the crack open ing volume is calculated. For a pair of transducers, a reciprocal identity for two media in contact is used to determine the amplitudes of signals sca ttered back from the crack. The field transmitted and received by the entir e array is obtained by superposition. Reception focusing is used to adjust the differences in signal arrival times for in-phase signal summation. Cons iderable signal amplification can be achieved by the self-focusing procedur e, as has been shown by comparison of scattered fields. (C) 1999 Elsevier S cience B.V. All rights reserved.