Effective bi-static array factor for tomographic imaging

In many antenna array applications, the beam pattern is defined as a product of the individual element pattern and the array factor generated by the spacing, orientation and relative phasing and apodization of the elements. In this paper we explore the interaction between the two beam patterns of associated antennas in a circular tomographic imaging configuration and demonstrate that the effective zones of sensitivity are relatively narrow cigar-shaped swathes between the transmit and receive antennas in spite of the isotropic beam patterns of the individual monopole antennas. In this case, the rows of the Jacobian matrix used in the image reconstruction process provide the maps of the sensitivity within the propagation zone which become the bi-static array factor. This analysis further informs antenna design and the overall impact on signal-to-noise considerations.