Flaw shape reconstruction using topological gradient for 2D scalar wave equation

This study is concerned with a non-linear inverse scattering technique called Time-Domain Topological Gradient (TDTG) for 2D wave equation. The TDTG is a recently developed shape optimization technique for elastodynamic problems with several potential advantages. The method, however, hasn't been used in the context of array ultrasonic imaging. In this study, performance of the TDTG is investigated numerically and experimentally by solving two example problems. The first is a numerical example in which a vertical slit in a plate is reconstructed from simulated data. The second one is a reconstruction from experimental data. Ultrasonic signals from a side-drilled hole in a steel block specimen are measured by an array transducer. The profile of the hole is reconstructed from those ultrasonic signals in the second problem. The results show that the TDTG can effectively use the phase focused beam fields, and very accurate in reconstructing not only a flat object but also a round one.