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In this letter, we address the problem of reconstructing the shape of a perfectly conducting object illuminated by a set of plane waves at a fixed frequency. The proposed method is made up of two parts. In the first one, for each incident wave, the field in the vicinity of a scatterer is reconstructed by means of a regularized single-layer potential approach. In the second part, the reconstructed fields are simultaneously exploited to build a system of polynomial equations whose solution yields to the unknown contour. As shown by numerical examples, the method is effective, robust against noise on data, and provides satisfactory reconstructions for star-shaped scatterers.