Time reversal imaging for gradient sensor networks over the Lamb-wave field

Combining the time reversal mirror (TRM) with the spatio-temporal gradient analysis has an ability to localize a scatterer such as a defect in a thin plate. Time-reversed signals propagate backwards through the time-independent medium and go through all the multiple scattering, reflections, and refraction. As a result, the TRM provides the means for converging wave front narrowly in time and space. If the focal point coincides with a point-like, the converging cylindrical wave provides the orthogonal pair of out-of-plane-surface shear strains to be linearly independent. The proposed imaging method utilizes the determinant of the covariance matrix defined over the shear strain field. The determinant denotes the distributions of correlated intensity modulation (DCIM) of two or more converging wave fronts. The DCIM increases significantly in the near-field of the focal point. In this paper, we explore analytically and numerically the defect imaging by time reversal method based on the spatio-temporal gradient analysis.