Real-time detection of small objects in transverse electric polarization: Evaluations on synthetic and experimental datasets

Junyong Eom; Won-Kwang Park; Junyong Eom; Won-Kwang Park

doi:10.3934/math.20241104

AIMS Mathematics

2024, Volume 9, Issue 8: 22665-22679. doi: 10.3934/math.20241104

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Real-time detection of small objects in transverse electric polarization: Evaluations on synthetic and experimental datasets

Junyong Eom ¹,
Won-Kwang Park ^{2
,
,}

1.
Research Institute for Electronic Science, Hokkaido University, Sapporo, 001-0020, Japan
2.
Department of Information Security, Cryptography, and Mathematics, Kookmin University, Seoul, 02707, Korea

Received: 07 May 2024 Revised: 08 July 2024 Accepted: 10 July 2024 Published: 22 July 2024
MSC : 78A46

It is well-known that if one applies Kirchhoff migration (KM) to identify small objects when their values of magnetic permeabilities differ from those of the background (or transverse electric polarization), their location and outline shape cannot be satisfactorily retrieved because rings of large magnitudes centered at the location of objects appear in the imaging results. Fortunately, it is possible to recognize the existence and approximated location of objects in the 2D Fresnel dataset through the traditional KM, but no theoretical explanation for this phenomenon has been verified. Here we show that the imaging function of KM when tested on the Fresnel dataset can be expressed as squared zero-order and first-order Bessel functions and as an infinite series of Bessel functions of integer order greater than two. We also explain why the existence and approximate location of objects can be identified. This theoretical result is supported by numerical simulations on synthetic and experimental data.
- Bessel function,
- Kirchhoff migration,
- numerical simulations,
- transverse electric polarization
Citation: Junyong Eom, Won-Kwang Park. Real-time detection of small objects in transverse electric polarization: Evaluations on synthetic and experimental datasets[J]. AIMS Mathematics, 2024, 9(8): 22665-22679. doi: 10.3934/math.20241104

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Abstract

It is well-known that if one applies Kirchhoff migration (KM) to identify small objects when their values of magnetic permeabilities differ from those of the background (or transverse electric polarization), their location and outline shape cannot be satisfactorily retrieved because rings of large magnitudes centered at the location of objects appear in the imaging results. Fortunately, it is possible to recognize the existence and approximated location of objects in the 2D Fresnel dataset through the traditional KM, but no theoretical explanation for this phenomenon has been verified. Here we show that the imaging function of KM when tested on the Fresnel dataset can be expressed as squared zero-order and first-order Bessel functions and as an infinite series of Bessel functions of integer order greater than two. We also explain why the existence and approximate location of objects can be identified. This theoretical result is supported by numerical simulations on synthetic and experimental data.

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