  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.
