Application of the bifocusing method in microwave imaging without background information

. In this study, we consider the application of the bifocusing method (BFM) for identifying the locations and shapes of small anomalies from scattering parameter data when the exact values of background permittivity and conductivity are unknown. To this end, an imaging function using numerical focusing operator is introduced and its mathematical structure is revealed by establishing a relationship with an infinite series of Bessel functions, antenna arrangements, and anomaly properties. On the basis of the revealed structure, we demonstrate why inaccurate location and size of anomalies were retrieved via the BFM. Some simulation results are illustrated using synthetic data polluted by random noise to support the theoretical result.