  We consider an inverse scattering problem to identify the locations or shapes
of unknown anomalies from scattering parameter data collected by a small number
of dipole antennas. Most of researches does not considered the influence of
dipole antennas but in the experimental simulation, they are significantly
affect to the identification of anomalies. Moreover, opposite to the
theoretical results, it is impossible to handle scattering parameter data when
the locations of the transducer and receiver are the same in real-world
application. Motivated by this, we design an imaging function with and without
diagonal elements of the so-called scattering matrix. This concept is based on
the Born approximation and the physical interpretation of the measurement data
when the locations of the transducer and receiver are the same and different.
We carefully explore the mathematical structures of traditional and proposed
imaging functions by finding relationships with the infinite series of Bessel
functions of integer order. The explored structures reveal certain properties
of imaging functions and show why the proposed method is better than the
traditional approach. We present the experimental results for small and
extended anomalies using synthetic and real data at several angular frequencies
to demonstrate the effectiveness of our technique.
