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Near-Field Imaging of Interior Cavities

Published online by Cambridge University Press:  22 January 2015

Peijun Li  and
Yuliang Wang
Peijun Li*
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
Yuliang Wang
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
*
*Email addresses: lipeijun@math.purdue.edu (P. Li), wang2049@math.purdue.edu (Y.Wang)
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Abstract

A novel method is developed for solving the inverse problem of reconstructing the shape of an interior cavity. The boundary of the cavity is assumed to be a small and smooth perturbation of a circle. The incident field is generated by a point source inside the cavity. The scattering data is taken on a circle centered at the source. The method requires only a single incident wave at one frequency. Using a transformed field expansion, the original boundary value problem is reduced to a successive sequence of two-point boundary value problems and is solved in a closed form. By dropping higher order terms in the power series expansion, the inverse problem is linearized and an explicit relation is established between the Fourier coefficients of the cavity surface function and the total field. A nonlinear correction algorithm is devised to improve the accuracy of the reconstruction. Numerical results are presented to show the effectiveness of the method and its ability to obtain subwavelength resolution.

Keywords

65N2178A46Inverse scatteringnear-field imagingHelmholtz equation
Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 2 , February 2015 , pp. 542 - 563
Copyright
Copyright © Global Science Press Limited 2015 

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