In this paper we consider the inverse electromagnetic scattering for a cavity surrounded by an inhomogeneous medium in three dimensions. The measurements are scattered wave fields measured on some surface inside the cavity, where such scattered wave fields are due to sources emitted on the same surface. We first prove that the measurements uniquely determine the shape of the cavity, where we make use of a boundary value problem called the exterior transmission problem. We then complete the inverse scattering problem by designing the linear sampling method to reconstruct the cavity. Numerical examples are further provided to illustrate the viability of our algorithm.

中文翻译：

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非均匀空腔的内部逆电磁散射

在本文中，我们考虑了在三个维度上被非均匀介质包围的腔的逆电磁散射。测量结果是在腔内的某个表面上测量的散射波场，其中这种散射波场是由于在同一表面上发射的源。我们首先证明测量唯一地确定了空腔的形状，我们利用了称为外部传输问题的边界值问题。然后我们通过设计线性采样方法来重建腔体来完成逆散射问题。进一步提供了数值例子来说明我们算法的可行性。