Guided wave topological imaging of isotropic plates

Abstract

Topological imaging is a recent method. So far, it has been applied to bulk waves, and high resolution has been demonstrated for imaging scatterers even with a single ultrasonic insonification of the inspected medium. This method consists of (i) emitting waves and measuring the response of the medium; (ii) solving two propagation problems: the direct problem, where the experimental source is simulated, and the adjoint problem, where the source is the time-reversed difference between the measured wave field and that obtained from the direct problem; (iii) computing the image by simply multiplying both wave fields together in the frequency domain, and integrating over the frequency. The speed of the method depends only on the cost of the field computations that are performed in the defect-free medium. The present work deals with the application of topological imaging to plate guided waves. Combining modal theory and Fourier analysis, the computations are performed in a very short time. In the investigated cases, two-dimensional in-plane imaging is based on propagation of the single S0 Lamb mode. Despite very high dispersion of that mode, scatterers are accurately located and the spatial resolution is equal to about one wavelength.