Uniqueness to inverse acoustic and electromagnetic scattering from locally perturbed rough surfaces

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.

COMMUNICATED BY:

• J. Sun

Keywords:

• Inverse scattering
• uniqueness
• Helmholtz equation
• Maxwell equation
• local perturbation

2010 Mathematics Subject Classification:

• 35R30

Acknowledgements

The authors would like to thank Xiaodong Liu (CAS, China) for reading through the original version of this manuscript and for his comments and generous discussions which help improve the presentation.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of G. Hu is supported by the NSFC grant (no. 11671028) and NSAF grant (no. U1530401). The work of B. Yan is supported by the National Natural Science Foundation of China (no. 61603226) and the Fund of Natural Science of Shandong Province (no. ZR2018MA022).