The paper is concerned with the inverse scattering problem for Maxwell's equations in three dimensional anisotropic periodic media. We study a new imaging functional for fast and stable reconstruction of the shape of anisotropic periodic scatterers from boundary measurements of the scattered field for a number of incident fields. This imaging functional is simple to implement and very robust against noise in the data. Its implementation is non-iterative, computationally cheap, and does not involve solving any ill-posed problems. The resolution and stability analysis of the imaging functional is investigated. Our numerical study shows that this imaging functional is more stable than that of the factorization method and more efficient than that of the orthogonality sampling method in reconstructing periodic scatterers.

翻译：本文研究三维各向异性周期介质中麦克斯韦方程的逆散射问题。针对多个入射场下由散射场边界测量值快速稳定重构各向异性周期散射体形状的需求，我们提出一种新型成像泛函。该成像泛函实现简单，对数据噪声具有强鲁棒性，且无需迭代计算、计算成本低，无需求解任何不适定问题。文中分析了该成像泛函的分辨率与稳定性，数值研究表明：在周期散射体重构中，该泛函相比因子分解法具有更优的稳定性，相比正交采样法具有更高的效率。