Time reversal and microwave techniques for solving inverse problem in Non-Destructive Evaluation

Abstract

Non-Destructive Evaluation (NDE) methods are used to inspect materials without damaging their usefulness. The key problem in NDE is the inverse problem which involves reconstructing materials’ physical profiles, like inner discontinuity etc., using information in the measured NDE signal. Inverse problem solutions in NDE can be classified as model-based and system-based approach. In model-based approach, an accurate forward model is used in an iterative framework. This approach provides a resultant materials' physical profile that minimizes the error between the measured signal and a simulated signal. However, this approach requires repeated calculations of a numerical model in each iteration, making it computationally demanding. This paper presents a model-based method that also provides a direct approach to inversion using principles of time reversal. Time reversal focusing is based on the fact that when a wave solution is reversed in time and back-propagated the wave comes to focus at the source. Using a computational model, this paper applies principles of time reversal to microwave NDE data to solve the inverse problem of defect detection in dielectric materials. A two-dimensional finite difference time domain (FDTD) model, for simulating the propagation of forward and time reversed wave fields, is developed. A dielectric sample with artificial defects, illuminated by a Gaussian modulated pulse, is used in the simulations. The microwave measurements are recorded, time reversed and propagated using the FDTD model to highlight the scatterer/defect. Maxima in the energy image indicate locations of defects. Simulation results demonstrate the feasibility of the technique to detect defects in dielectric materials. The FDTD model is validated using experimental data.