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Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A computational and statistical framework for multidimensional domain acoustooptic material interrogation

Authors: H. T. Banks and V. A. Bokil
Journal: Quart. Appl. Math. 63 (2005), 156-200
MSC (2000): Primary 78M20, 78A25, 78A02, 78A46, 62F25
Published electronically: February 1, 2005
MathSciNet review: 2126573
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider an electromagnetic interrogation technique in two and three dimensions for identifying the dielectric parameters (including the permittivity, the conductivity and the relaxation time) of a Debye medium. In this technique, a travelling acoustic pressure wave in the Debye medium is used as a virtual reflector for an interrogating microwave electromagnetic pulse that is generated in free space. The reflections of the microwave pulse from the air-Debye interface and from the acoustic pressure wave are recorded at a remote antenna. The data is used in an inverse problem to estimate the locally pressure dependent dielectric parameters of the Debye medium. We present a time domain formulation that is solved using finite differences (FDTD) in time and in space. Perfectly matched layer (PML) absorbing boundary conditions are used to absorb outgoing waves at the finite boundaries of the computational domain, preventing spurious reflections from reentering the domain. Using the method of least squares for the parameter identification problem, we compare two different algorithms (the gradient based Levenberg-Marquardt method and the gradient free, simplex based Nelder-Mead method) in solving an inverse problem to calculate estimates for two or more dielectric parameters. Finally we use statistical error analysis to construct confidence intervals for all the presented estimates, thereby providing a probabilistic statement about the computational procedure with uncertainty aspects of estimates.

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Additional Information

H. T. Banks
Affiliation: Center for Research in Scientific Computation, North Carolina State University, Raleigh, N.C. 27695-8205
MR Author ID: 194993

V. A. Bokil
Affiliation: Center for Research in Scientific Computation, North Carolina State University, Raleigh, N.C. 27695-8205
MR Author ID: 741294

Keywords: Electromagnetic-acoustic interaction, Debye dielectric materials, pulsed antenna source microwaves, inverse problems, FDTD, statistical inference.
Received by editor(s): August 14, 2004
Published electronically: February 1, 2005
Article copyright: © Copyright 2005 by the authors