Terahertz-Based Electromagnetic Interrogation Techniques for Damage Detection

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dc.contributor.advisor H. Thomas Banks, Committee Chair en_US
dc.contributor.advisor Hien T. Tran, Committee Member en_US
dc.contributor.advisor Kazufumi Ito, Committee Member en_US
dc.contributor.advisor Negash G. Medhin, Committee Member en_US
dc.contributor.author Gibson, Nathan Louis en_US
dc.date.accessioned 2010-04-02T19:05:55Z
dc.date.available 2010-04-02T19:05:55Z
dc.date.issued 2004-06-24 en_US
dc.identifier.other etd-06232004-175831 en_US
dc.identifier.uri http://www.lib.ncsu.edu/resolver/1840.16/5000
dc.description.abstract We apply an inverse problem formulation to determine characteristics of a defect from a perturbed electromagnetic interrogating signal. A defect (gap) inside of a dielectric material causes a disruption, via reflections and refractions at the material interfaces, of the windowed interrogating signal. We model these electromagnetic waves inside the material with Maxwell's equations. In order to resolve the dimensions and location of the defect, we use simulations as forward solves in our Newton-based, iterative scheme which optimizes an innovative cost functional appropriate for reflected waves where phase differences can produce ill-posedness in the inverse problem when one uses the usual ordinary least squares criterion. Our choice of terahertz frequency allows good resolution of desired gap widths without significant attenuation. Numerical results are given in tables and plots, standard errors are calculated, and computational issues are addressed. An inverse problem formulation is also developed for the determination of polarization parameters in heterogeneous Debye materials with multiple polarization mechanisms. For the case in which a distribution of mechanisms is present we show continuous dependence of the solutions on the probability distribution of polarization parameters in the sense of the Prohorov metric. This in turn implies well-posedness of the corresponding inverse problem, which we attempt to solve numerically for a simple uniform distribution. Lastly we address an alternate approach to modeling electromagnetic waves inside of materials with highly oscillating dielectric parameters which involves the technique of homogenization. We formulate our model in such a way that homogenization may be applied, and demonstrate the necessary equations to be solved. en_US
dc.rights I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. en_US
dc.subject non-destructive evaluation en_US
dc.subject inverse problems en_US
dc.subject polarization en_US
dc.title Terahertz-Based Electromagnetic Interrogation Techniques for Damage Detection en_US
dc.degree.name PhD en_US
dc.degree.level dissertation en_US
dc.degree.discipline Applied Mathematics en_US

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