Two single-measurement uniqueness results for inverse scattering problems within polyhedral geometries

We consider the unique determinations of impenetrable obstacles or diffraction grating profiles in \begin{document}$ \mathbb{R}^3 $\end{document} by a single far-field measurement within polyhedral geometries. We are particularly interested case that scattering objects impedance type. derive two new identifiability results for inverse problem aforementioned challenging setups. The main technical idea is to exploit certain quantitative geometric properties Laplacian eigenfunctions which were initiated our recent works [12,13]. In this paper, we novel generalize and extend related rid="b13">13], further enable us establish results. It pointed out addition shape obstacle profile, can simultaneously recover boundary parameters.