Eddy current testing (ECT) is used extensively as a nondestructive evaluation (NDE) method to detect cracks and corrosion in critical structures, particularly in the aerospace and nuclear industries. The major advantages of ECT is its non-contact nature allowing high-speed inspection, simplicity of operation and robustness in hazardous environments. While the detection of defects is relatively simple and straightforward in eddy current testing, the imaging problem, i.e. reconstruction of the defect profile is a challenging inverse problem. Iterative methods generally applied to solve the inverse problem for the defect profile are computationally intensive and are prone to be trapped in local minima. Non-iterative methods are required for real-time imaging capability. Monotonicity based imaging method is one class of non-iterative methods for reconstructing defect profiles from pulsed eddy current measurements.This dissertation presents two major contributions to the fields of NDE and eddy current imaging:1. Formulated two important properties, namely monotonicity of time constants and monotonicity of transfer function, in time-domain eddy current measurements.2. Developed non-iterative, real-time imaging algorithms based on the monotonicity.The transient response of the eddy current system can be characterized by a discrete set (countable) of real, non-negative time constants. Time constants are global properties of the specimen under test and they are monotonic with the anomaly profile: $D_\alpha \subseteq D_\beta \Rightarrow \tau_\alpha^k \geq \tau_\beta^k$, where $D_\alpha$ and $D_\beta$ are two anomalies and $\tau_\alpha^k$ and $\tau_\beta^k$ are the associated time constants arranged in decreasing order. This property is exploited in this thesis to implement a non-iterative imaging method which determines if a voxel/test element in the sample is part of the anomaly or not by comparing the time constants. However, the implementation of this method has two major challenges, namely non-uniqueness of solutions due to the isometry and extraction of time constants. In this thesis, additional conductive blocks are introduced as part of the inspection system to break the isometry. Different algorithms are implemented to extract the time constants from transient waveforms. A Laplace-Pad\`{e} approximant approach is shown to be able to extract a few significant time constants.An alternate monotonicity property found in transient eddy current measurements is the monotonicity of the transfer function: $D_\alpha \subseteq D_\beta \Rightarrow \mathbf{Z}_\alpha - \mathbf{Z}_\beta$ is negative semidefinite, where $\mathbf{Z}$ is the transfer function evaluated on the negative real axis. An imaging method based on this property is also studied and compared to the earlier method using time constants. Validation results using simulated and experimental data are presented.
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