We consider the problem of imaging a periodic surface by acoustic or electromagnetic waves. A slab of double negative metamaterial is placed above the surface and the scattered field is measured on the top boundary of the slab. The imaged surface is assumed to be a small perturbation of the flat surface so that we can make a transformed field expansion to linearize the problem and obtain a simple reconstruction formula. We show by analysis of the formula and numerical experiments that the resolution of the reconstruction can be greatly enhanced due to the double negative slab.
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