We propose a scheme for imaging periodic surfaces using a superlens. By employing an inverse scattering model and the transformed field expansion method, we derive an approximate reconstruction formula for the surface profile, assuming small amplitude. This formula suggests that unlimited resolution can be achieved for the linearized inverse problem with perfectly matched parameters. Our method requires only a single incident wave at a fixed frequency and can be efficiently implemented using fast Fourier transform. Through numerical experiments, we demonstrate that our method achieves resolution significantly surpassing the resolution limit for both smooth and non-smooth surface profiles with either perfect or marginally imperfect parameters.

翻译：我们提出了一种利用超透镜对周期表面进行成像的方案。通过采用逆散射模型和变换场展开方法，在小振幅假设下推导出表面轮廓的近似重建公式。该公式表明，在参数完美匹配的情况下，线性化逆问题可实现无限制分辨率。本方法仅需单一固定频率的入射波，并可通过快速傅里叶变换高效实现。数值实验表明，无论针对光滑或非光滑表面轮廓，以及完美或轻微不完美参数条件，该方法均能显著超越分辨率极限。