This paper is concerned with the inverse problem of determining the shape of penetrable periodic scatterers from scattered field data. We propose a sampling method with a novel indicator function for solving this inverse problem. This indicator functionl is very simple to implement and robust against noise in the data. The resolution and stability analysis of the indicator function is analyzed. Our numerical study shows that the proposed sampling method is more stable than the factorization method and more efficient than the direct or orthogonality sampling method in reconstructing periodic scatterers.

翻译：本文关注从分散的实地数据中确定可穿透周期散射器形状的反面问题。 我们提出了一个具有新指标功能的抽样方法,以解决这一反向问题。 这个指标函数非常简单,可以执行,而且对数据中的噪音非常有力。 对指标函数的分辨率和稳定性分析进行了分析。 我们的数字研究表明,在重建周期散射器方面,拟议的取样方法比系数化方法更稳定,比直接或正数抽样方法更有效。