Time reversal microwave methods for solving inverse problems in non-destructive evaluation

Non-Destructive Evaluation (NDE) methods are use to inspect a material and components without damaging their usefulness. NDE is used in different industries to inspect the reliability of critical components, product quality, or detect material failure. The techniques used in NDE range from simple visual methods to microwaves, ultrasound, x-rays, and thermography. The key problem in NDE is the inverse problem which involves reconstructing defect profiles using the information in the output signal of the system. 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 to estimate the defect shape that minimizes the error between the measured and simulated signals. However, this approach results in repeated executions of a three dimensional forward model in each iteration, making it computationally demanding.;This thesis presents 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 it comes to focus at the source. Research on time reversal techniques of ultrasound fields has demonstrated the reliability of the technique for detecting small defects in complex geometries. This thesis uses a computational model to study the feasibility of applying principles of time reversal to microwave NDE data for solving the inverse problem of defect detection in dielectric materials.;Microwave NDE methods are well suited for inspection of dielectric materials because electromagnetic waves can propagate through and interact with such materials. The interaction is influenced by the electrical and magnetic properties of the material and hence the response of this interaction contains information of discontinuities of permittivity in the material.;A two-dimensional finite difference time domain (FDTD) model, for simulating the propagation of forward and time reversed wave fields is developed. A dielectric slab used in the simulations is illuminated by a gaussian modulated pulse. The measured microwave NDE measurements are recorded, time reversed and propagated backwards once through the FDTD model to highlight the scatterer/defect. Maxima in the energy image indicates the location of the defect. Simulation results demonstrate the ability of the technique to accurately detect defects in dielectric and lossy dielectric materials. Experiments were performed in free space to validate the FDTD model. The signals recorded in the experiment were time reversed and input to the FDTD model. Errors in source position, using the model, were attributed to experimental measurements.