Uniqueness to inverse acoustic and electromagnetic scattering from locally perturbed rough surfaces. Issue 2 (25th January 2021)

• Record Type: Journal Article
• Authors: Zhao, Yu; Hu, Guanghui; Yan, Baoqiang
• Is Part Of: Applicable analysis. Volume 100:Issue 2(2021)
• Page Start: 361
• Page End: 382
• Publication Date: 2021-01-25
• Subjects: J. Sun; Inverse scattering -- uniqueness -- Helmholtz equation -- Maxwell equation -- local perturbation; 35R30; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1603371
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we consider inverse time-harmonic acoustic and electromagnetic scattering from locally perturbed rough surfaces in three dimensions. The scattering interface is supposed to be the graph of a Lipschitz continuous function with compact support. It is proved that an acoustically sound-soft or sound-hard surface can be uniquely determined by the far-field pattern of infinite number of incident plane waves with distinct directions. Moreover, a single point source or plane wave can be used to uniquely determine a scattering surface of polyhedral type. These uniqueness results apply to Maxwell equations with the perfectly conducting boundary condition. Our arguments rely on the mixed reciprocity relation in a half space and the reflection principle for Helmholtz and Maxwell equations.