Inverse scattering of periodic surfaces with a superlens

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.