**4. Discussion**

One of the more interesting aspects of our imaging system revolves around the notion of why a 2D algorithm works in the first place. While there have been efforts by others exploring 2D imaging, most have reverted to 3D implementations when 2D efforts failed. Notably, Semenov et al. [61] concluded that the reason their 2D system did not work was because of the inherent mismatch between the actual 3D wave propagation and the assumed 2D propagation in their algorithm. However, we contend that there are scientifically valid reasons why our 2D algorithm works well. The most important is that by choosing the monopole antennas, we are able to position them on a quite small diameter circle surrounding the target. Given the vertical orientation of the antennas, in the limit of a decreasing array circle diameter, the aspect ratio of the antenna length to the diameter of the circle naturally increases. This can be theoretically extrapolated to the point where the domain closely mimics that of cylindrical geometry. For competing systems, the motivation has often centered about acquiring as much measurement data as possible. This often implies that the antenna array must be configured on a larger diameter circle for the simple reason relating to space limitations associated with the physical size and the increased number of radiating elements. In Semenov et al. [62], thousands of antennas (effective number based partially on mechanical motion) were positioned on a 60 cm diameter circle for a roughly 8 hour, 3D data acquisition, single frequency exam time, while the diameter for the Dartmouth system is only on a 15.2 cm diameter where the broadband data acquisition takes roughly 10 minutes. For the latter, the field patterns have simply not devolved into their spherical radiation behavior within the small zone while they are considerably further along that process for the larger diameter system.

In Meaney et al. [63], we compared the magnitude and phase values for the scattering from a simple phantom illuminated in our imaging chamber. It is noteworthy that there was very little difference between the phase calculations using both 2D and 3D models. There was some deviation for the magnitude, but the differences never exceeded 0.5 dB. It is worth examining the far field behavior of the 2D and 3D waves, in spite of the fact that it is a simple estimation in this situation. For the phase in the main beam, the phases propagate as a function of R (distance from the antenna) for both the 2D and 3D cases. This presumably accounts for the close match of the previous calculations. However, for the magnitude, they decay as a function of 1/R and 1/R<sup>2</sup> for the 2D and 3D cases. Likewise, this likely partially accounts for the previously mentioned differences. As hypothesized above, these differences are likely mitigated because we operate within such a physically constrained space. As a final note, the lossy coupling bath most likely assists for this comparison by substantially attenuating (and almost eliminating) signals that might propagate out of the plane of interest only to be reflected back into it during the propagation process. Regardless, our 2D configuration in conjunction with our 2D algorithm has provided good images in a variety of settings from simulations, phantom experiments, animal experiments and even clinical trials.
