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This paper is dedicated to design a direct sampling method of inverseelectromagnetic scattering problems, which uses multi-frequency sparsebackscattering far field data for reconstructing the boundary of perfectlyconducting obstacles. We show that a smallest strip containing the unknownobject can be approximately determined by the multi-frequency backscatteringfar field data at two opposite observation directions. The proof is based onthe Kirchhoff approximation and Fourier transform. Such a strip is thenreconstructed by an indicator, which is the absolute value of an integral ofthe product of the data and some properly chosen function over the frequencyinterval. With the increase of the number of the backscattering data, thelocation and shape of the underlying object can be reconstructed. Numericalexamples are conducted to show the validity and robustness of the proposedsampling method. The numerical examples also show that the concave part of theunderlying object can be well reconstructed, and the different connectedcomponents of the underlying object can be well separated.

Inverse electromagnetic obstacle scattering problems with multi-frequency sparse backscattering far field data