  This paper is concerned with the inverse problem of reconstructing small and
local perturbations of a planar surface using the field interaction between a
known plasmonic particle and the planar surface. The aim is to perform a
super-resolved reconstruction of these perturbations from shifts in the
plasmonic frequencies of the particle-surface system. In order to analyze the
interaction between the plasmonic particle and the planar surface, a well
chosen conformal mapping, which transforms the particle-surface system into a
coated structure, is used. Then the even Fourier coefficients of the
transformed domain are related to the shifts in the plasmonic resonances of the
particle-surface system. A direct reconstruction of the perturbations of the
planar surface is proposed. Its viability and limitations are documented by
numerical examples.
