Multi-Frequency Time-Reversal-Based Imaging for Ultrasonic Nondestructive Evaluation Using Full Matrix Capture

In this paper, two multi-frequency time-reversal (TR)-based imaging algorithms are explored for application to the nondestructive evaluation (NDE) imaging of defects in solids: time reversal with multiple signal classification (TR-MUSIC) and a related phase-coherent form (PC-MUSIC). These algorithms are tested with simulated and experimental ultrasonic array data acquired using the full matrix capture (FMC) process. The performance of these algorithms is quantified in terms of their spatial resolution and robustness to noise. The effect of frequency bandwidth is investigated and the results are compared with the single-frequency versions of these algorithms. It is shown that both TR-MUSIC and PC-MUSIC are capable of resolving lateral targets spaced closer than the Rayleigh limit, achieving super-resolution imaging. TR-MUSIC can locate the positions of scatterers correctly, whereas the results from PC-MUSIC are less clear because of the presence of multiple peaks in the vicinity of target. However, an advantage of PC-MUSIC is that it can overcome the elongated point spread function that appears in TR-MUSIC images, and hence provide enhanced axial resolution. For high noise levels, TR-MUSIC and PC-MUSIC are shown to provide stable images and suppress the presence of artifacts seen in their single-frequency equivalents.