## 2 Materials and Methods  
### Antenna Design and Characterization  
Designing a small and efficient antenna is very important in microwave tomography, as a smaller size can accommodate a greater number of antennas in the array. Employing multiple antennas in the system is helpful in acquiring sufficient data to deal with the ill-posedness of the inverse problem, but also poses a cross-coupling issue between the constituting antenna elements of the array. A lossy immersion medium can minimize cross-coupling and multipath signals [21; 27; 28], and at the same time broaden the antenna's operation bandwidth and improve impedance matching with human tissue, such as skin. There is, however, a trade-off between these benefits and the attenuation that a lossy immersion liquid will cause to the signals received by the imaging system. For these reasons, the choice and impact of immersion and coupling media on the design and performance of microwave tomography systems have been extensively studied in the literature [29; 30; 31; 32].  
Glycerine-water mixtures are attractive candidates, as they are easy to make and allow control of the mixture's dielectric constant and conductivity [27]. Corn syrup mixtures with water can produce the same range of permittivity values as glycerine-water mixtures, but with quite lower conductivity [32]. The dependence on frequency, however, is stronger, and the solution itself is too viscous and poses handling issues. Based on these considerations, we designed a compact antenna that can operate in the 1.0-3.0 GHz frequency range when immersed in coupling media commonly used in microwave tomography. Figure 0(a) shows a schematic of the front and rear views of the printed monopole antenna modelled in CST Microwave Studio. The dimensions of the antenna patch, substrate, transmission line, and the partial ground are included in the drawing. The printed monopole antenna has been realized on FR-4 substrate and is fed with an SMA connector. A fabricated prototype is shown in Figure 0(b).  
The antenna's measured reflection coefficient \(S_{11}\) is plotted in Figure 0(a) for three different immersion liquids. A value under \(-10\) dB for \(S_{11}\) suggests good operation in the whole range of interest, 1.0-3.0 GHz. Moreover, Figure 0(b) plots the voltage standing wave ratio (VSWR) inside 80% and 90% glycerine-water immersions, as calculated by CST simulations. The VSWR of the antenna stays below 2.0 in 1.0-3.0 GHz, thus demonstrating good impedance matching for the entire frequency range of interest. The dielectric properties of the three immersion liquids considered in Figure 2a were measured using Keysight's dielectric spectroscopy kit, and are plotted in Figure 3. In addition, we measured the properties of Triton X-100, which is a low-loss reference liquid that has been proposed and studied for microwave imaging [33]. We then imported the measured data into CST Microwave Studio, using second-order curve fitting to model frequency dispersion. Figure 3 plots the dielectric properties for the four materials after curve fitting the experimentally measured dataset.  
Figure 1: **(a)** Schematic of the proposed antenna modelled in CST Microwave Studio; **(b)** Photo of the fabricated antenna.  
Figure 3: Measured (**a**) relative permittivity and (**b**) conductivity for the immersion liquids considered in this study (material properties of Triton X-100 were measured at Politecnico di Torino).  
Figure 2: **(a)**\(S_{11}\) for the printed monopole of Figure 1 when immersed in the glycerine and corn syrup mixtures measured in Figure 3; **(b)** Calculated voltage standing wave ratio (VSWR) of the antenna immersed in 80% and 90% glycerine–water mixtures, using CST simulations.