  This paper is dedicated to design a direct sampling method of inverse
electromagnetic scattering problems, which uses multi-frequency sparse
backscattering far field data for reconstructing the boundary of perfectly
conducting obstacles. We show that a smallest strip containing the unknown
object can be approximately determined by the multi-frequency backscattering
far field data at two opposite observation directions. The proof is based on
the Kirchhoff approximation and Fourier transform. Such a strip is then
reconstructed by an indicator, which is the absolute value of an integral of
the product of the data and some properly chosen function over the frequency
interval. With the increase of the number of the backscattering data, the
location and shape of the underlying object can be reconstructed. Numerical
examples are conducted to show the validity and robustness of the proposed
sampling method. The numerical examples also show that the concave part of the
underlying object can be well reconstructed, and the different connected
components of the underlying object can be well separated.
