## 3 Results and Discussions
From there, since the dielectric permittivity of air is much smaller than that of the lung tissue, the wave could reach the receiver faster traveling through the air region than by simply remaining inside the lung tissue, producing some undesired signals. For all the antenna positions, the intensity of the second echo (circle in Figure 4) was comparable with the intensity of the first one (square). This was a consequence of the small difference in dielectric properties between the lung tissue and the target material. In fact, the conductivity of this material, which affects the attenuation, was only a factor of two higher than the surrounding. Figure 4: Calibrated waveforms \(B_{n}\) for a 3 cm deep target at 1 GHz central frequency and a \(3\times 3\) antenna grid. The black triangle, square, and circle represent, in order from left to right, the middle time of the pulse excitation and the return time for the first and second interface of the target. (**a**) Waveforms for the corner antennas. (**b**) Waveforms for the top and bottom central antennas. (**c**) Waveforms for the left and right central antennas. (**d**) Waveform for the central antenna. Passing to the confocal images, Figure 5 shows the confocal map for 0.6 GHz frequency, target depth of 6 cm, and an antenna distribution on top of the lung tissue following a \(3\times 3\) grid. To better visualize the results, the confocal map is sliced parallelly to the \(x\)-plane (Figure 5a) and to the \(z\)-plane (Figure 5b), respectively. The slices intersect each other at the center of the target which is represented by a red circle. Note that the confocal images are oriented as Figure 2 with the antennas positioned on the top. In general, a good localization of the target requires that most of the pixel intensity should cluster at one position. In Figure 5 although there are clear and intense signals at the expected position of the nodule (red circle), the cluster at the target is not a continuous spot, but presents some modulations. This was not a novel phenomenon in confocal imaging, see for example reference [29], and in our case it can be reconnected with the findings of Figure 4 where some signals intensity was not only present at the return time expected for the target echos. However, despite the clustering, the target position could clearly be inferred although not with high accuracy. Some reconstruction artifacts are visible in Figure 5 as rings extending from the lung surface into the lung. The other three types of artifacts and features were encountered in the set of simulations and are collected in Figure 6. The extend of these artifacts and features could completely ruin the localization of the pulmonary nodule. Beyond the ring artifacts visible in Figure 5, Figure 6 shows the appearance of a ghost-like artifacts, where the concentrations of pixel intensity are at a location deeper than the expected position of the target (Figure 6a) and the appearance of an undersized target at a lower depth than the expected target (Figure 6b). Furthermore, in Figure 6c there is a case where no pixel intensity is present in the proximity of the target. Some of these artifacts can potentially be decreased or eliminated by image analysis algorithms, based for example on Fuzzy logic [30,31]. These artifacts and features were common to all the antenna grids. Figure 7 shows in which range of frequencies and target depths the artifacts appeared. At the lowest frequencies, below circa 1 GHz, independently of the target depth, the main artifact was the appearance of rings in the confocal map as those of Figure 5. At higher frequencies this artifact appeared only when the target was in a shallow position up to 1-2 cm of depth. The appearance of a ghost target was visible at 1 GHz with deep targets and at higher frequencies at all depths. The maps that showed a too-small target or no target at all were those made at the highest frequencies and at the highest depths.