Uniqueness in inverse scattering problems with phaseless near-field data generated by superpositions of two incident plane waves at a fixed frequency

Xiaoxu Xu

doi:10.3934/ipi.2023052

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2024, Volume 18, Issue 3: 730-750. Doi: 10.3934/ipi.2023052

This issue Previous Article Direct sampling method via Landweber iteration for an absorbing scatterer with a conductive boundary Next Article

Uniqueness in inverse scattering problems with phaseless near-field data generated by superpositions of two incident plane waves at a fixed frequency

Xiaoxu Xu^,

Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, China

^* Corresponding author: Xiaoxu Xu
^* Corresponding author: Xiaoxu Xu

Received: July 2023

Revised: November 2023

Early access: December 7, 2023

Published online: December 7, 2023

This work is supported by the National Natural Science Foundation of China (No. 12201489), the Young Talent Support Plan of Xi'an Jiaotong University, the Fundamental Research Funds for the Central Universities (No. xzy012022009).

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Abstract

This paper is concerned with the uniqueness in inverse acoustic and electromagnetic scattering problems with phaseless near-field data generated by superpositions of two incident plane waves at a fixed frequency. It can be proved that the unknown scatterer can be uniquely determined by the phaseless near-field data. The proof is based on the analysis of the phase information and the application of Rellich's lemma together with the Green's formula for the radiating solutions to the Helmholtz equation or the Stratton–Chu formula for the radiating solutions to the Maxwell equations.

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Mathematics Subject Classification: Primary: 78A46; Secondary: 35P25.

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Figure 1. Geometry of the problem in Theorem 3.1

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Figure 2. Geometry of the problem in Theorem 3.2

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Figure 3. Geometry of the problem in Theorem 3.6

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Figure 4. Geometry of the problem in Theorem 4.1

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