Electromagnetic Crack Detection Inverse Problems Using Terahertz Interrogating Signals

Abstract

We apply an inverse problem formulation to determine characteristics of a defect from a perturbed electromagnetic interrogating signal. A defect (crack) inside of a dielectric material causes a disruption, from reflections and refractions off of the interfaces, of the windowed interrogating signal. We model the electromagnetic waves inside the material with Maxwell's equations. Using simulations as forward solves, our Newton-based, iterative optimization scheme resolves the dimensions and location of the defect. Numerical results are given in tables and plots, standard errors are calculated, and computational issues are addressed.

A computational and statistical framework for multidimensional domain acoustooptic material interrogation

“…With such noninvasive interrogating techniques one can study properties and defects in biological tissues with very little discomfort to the subjects. Other potential applications for such interrogation techniques are nondestructive damage detection in aircraft and spacecraft where very high frequency electromagnetic pulses can be used to detect the location and width of cracks that may be present [BGW03]. Additional applications are found in mine, ordnance and camouflage surveillance, and subsurface and atmospheric environmental modelling [BBL00].…”

Gap detection with electromagnetic terahertz signals

“…Therefore in our implementation we actually multiply the sine function by an exponential function (see [3] for details) rather than the traditional indicator function. However, for notational consistency we will continue to denote this function as…”

“…For tridiagonal matrices the factorization and the back substitution are both order O(N ). See [3] for computational issues encountered in implementation, including the use of the method of maps to allow for gap sizes (δ) smaller than the mesh size (h).…”

“…We did so here merely so that the full wavelength of the signal would be visible. See [3] for figures showing the signal recorded at receivers located at z = 0 and z = 1.…”

“…First we attempt to get very close approximations to d and δ using information about the travel times of the data signal, then we use these values as initial guesses in the optimization routine. See [3] for a complete discussion of the methods used in determining initial estimates.…”