A novel study on the bifocusing method for imaging unknown objects in two-dimensional inverse scattering problem

Sangwoo Kang; Won-Kwang Park; Sangwoo Kang; Won-Kwang Park

doi:10.3934/math.20231386

AIMS Mathematics

2023, Volume 8, Issue 11: 27080-27112. doi: 10.3934/math.20231386

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A novel study on the bifocusing method for imaging unknown objects in two-dimensional inverse scattering problem

Sangwoo Kang ¹,
Won-Kwang Park ^{2
,
,}

1.
Advanced Defense Science & Technology Research Institute, Agency for Defense Development, Daejeon 34186, Korea
2.
Department of Information Security, Cryptology, and Mathematics, Kookmin University, Seoul 02707, Korea

Received: 14 July 2023 Revised: 19 September 2023 Accepted: 19 September 2023 Published: 25 September 2023
MSC : 78A46

In this paper, we consider the application of the bifocusing method (BFM) for a fast identification of two-dimensional circle-like small inhomogeneities from measured scattered field data. Based on the asymptotic expansion formula for the scattered field in the presence of small inhomogeneities, we introduce the imaging functions of the BFM for both dielectric permittivity and magnetic permeability contrast cases. To examine the applicability and the various properties of the BFM, we show that the imaging functions can be expressed by the Bessel function of orders zero and one, as well as the characteristics (size, permittivity, and permeability) of the inhomogeneities. To support the theoretical results, various numerical results with synthetic and experimental data are presented.
- bifocusing method,
- inverse scattering problem,
- Bessel functions,
- numerical results
Citation: Sangwoo Kang, Won-Kwang Park. A novel study on the bifocusing method for imaging unknown objects in two-dimensional inverse scattering problem[J]. AIMS Mathematics, 2023, 8(11): 27080-27112. doi: 10.3934/math.20231386

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Abstract

In this paper, we consider the application of the bifocusing method (BFM) for a fast identification of two-dimensional circle-like small inhomogeneities from measured scattered field data. Based on the asymptotic expansion formula for the scattered field in the presence of small inhomogeneities, we introduce the imaging functions of the BFM for both dielectric permittivity and magnetic permeability contrast cases. To examine the applicability and the various properties of the BFM, we show that the imaging functions can be expressed by the Bessel function of orders zero and one, as well as the characteristics (size, permittivity, and permeability) of the inhomogeneities. To support the theoretical results, various numerical results with synthetic and experimental data are presented.

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