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Reconstruction of Scatterer Shape from Relative Intensity of Scattered Field by Using Linearized Boundary Element Method
Junichiro SUGISAKA Takashi YASUI Koichi HIRAYAMA
Publication
IEICE TRANSACTIONS on Electronics
Vol.E103C
No.2
pp.3038 Publication Date: 2020/02/01 Publicized: 2019/08/22 Online ISSN: 17451353
DOI: 10.1587/transele.2019ECP5013 Type of Manuscript: PAPER Category: Electromagnetic Theory Keyword: inverse scattering problem, boundaryintegral equation, boundary element method, scattering theory,
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Summary:
A method to reconstruct the surface shape of a scatterer from the relative intensity of the scattered field is proposed. Reconstruction of the scatterer shape has been studied as an inverse problem. An approach that employs boundaryintegral equations can determine the scatterer shape with low computation resources and high accuracy. In this method, the reconstruction process is performed so that the error between the measured far field of the sample and the computed far field of the estimated scatterer shape is minimized. The amplitude of the incident wave at the sample is required to compute the scattered field of the estimated shape. However, measurement of the incident wave at the sample (measurement without the sample) is inconvenient, particularly when the output power of the wave source is temporally unstable. In this study, we improve the reconstruction method with boundaryintegral equations for practical use and expandability to various types of samples. First, we propose new boundaryintegral equations that can reconstruct the sample shape from the relative intensity at a finite distance. The relative intensity is independent from the amplitude of the incident wave, and the reconstruction process can be performed without measuring the incident field. Second, the boundary integral equation for reconstruction is discretized with boundary elements. The boundary elements can flexibly discretize various shapes of samples, and this approach can be applied to various inverse scattering problems. In this paper, we present a few reconstruction processes in numerical simulations. Then, we discuss the reason for slowconvergence conditions and introduce a weighting coefficient to accelerate the convergence. The weighting coefficient depends on the distance between the sample and the observation points. Finally, we derive a formula to obtain an optimum weighting coefficient so that we can reconstruct the surface shape of a scatterer at various distances of the observation points.

