# Accurate Phase Calibration of Multistatic Imaging System for Medical and Industrial Applications
## 3 Experiment  
The microwave imaging system used in this study is illustrated in Figure 4. This device consists of a VNA, RF switches, an antenna array, and coaxial cables. The two ports of the VNA (Keysight P9371A, 300 kHz to 6.5 GHz) are connected to Tx and Rx switches. Each switch port is connected to antenna elements fixed on the antenna array and an ECal module (Keysight N7551A). The RF switches for Tx and Rx have 32 ports each. The Tx switch consists of an SP4T (Single-Pole Four-Throw, Mini-Circuit USB-SP4T-63) and four SP8T (Mini-Circuit USB-1 SP8T-63H) switches, and the Rx switch consists of an SP4T and two SP16T (Mini-Circuit USB-1 SP16T-83H) switches. The RF switch is connected to  
Figure 3: Consider the circuit in Figure 1 as three vertically connected circuits. antennas and the ECal module via 3 m coaxial cables (CRYSTEK CCCSMA18-MM-086F-120). The antenna array is cylindrical in shape, with antenna elements fixed along the circumference. The antenna array has an outer diameter of 150 mm and an inner diameter of 280 mm, with a height of 85 mm. This antenna array consists of three rows of antennas. Ten Tx antennas and ten Rx antennas are fixed per row. The Tx and Rx antennas are arranged alternately every 18 degrees. The Tx and Rx antennas used are balanced Vivaldi antennas (BVAs) [24; 25]. This type of antenna has a small error in phase measurement and is thus suitable for this study. A schematic of a BVA is shown in Figure 5. The BVA is a three-layer structure consisting of two ground layers and a feed line layer. A connector and the feed line are sandwiched and implemented between a two-layer Printed Circuit Board (PCB). The feed line of this antenna is the stlip line (SL) that is sandwiched between both ground layers. The microwave propagated through the SL is converted into a transmission line, propagating double-sided slotline, i.e., the bilateral slotline (BSL). By exponentially widening the width of the BSL, the microwave is irradiated. The BVA, by changing the SL into the BSL, offers the following advantages [25; 26]:  
* Using SL to BSL reduces the amount of radiation from the feed line. * BSL has less dispersion compared to the slotline. Figure 4: The microwave imaging system. The antenna array consists of three rows, with 20 Tx and Rx antennas per row. Figure 5: Balanced Vivaldi antenna (BVA): (**a**) exploded view of the BVA construction; (**b**) geometry and parameters of the BVA. In this study's phase calibration, we confirm the reflection coefficients of the BVA. Figure 6a shows the phase of the reflection coefficients of the BVA. The graph has frequency on the x-axis and phase on the y-axis. In the frequency sweep from 1.0 to 6.5 GHz, the phase decreases at a constant rate. Then, it is considered that the position of reflections in the BVA is constant regardless of frequency. Next, we examine the positions of reflections within the BVA. Since it was assumed that signals reflect at the transmission line transitions of the SL and BSL shown in Figure 3, we checked the reflection coefficients of five different BVAs with varying BSL widths, \(d\). Figure 6b illustrates the result of transforming the BVA's \(\mathrm{S}_{11}\) into the time domain using discrete inverse Fourier transform. The x-axis represents time, and the y-axis represents reflection intensity, with peaks appearing at the positions where signals reflect. The time at which the first peak appears is \(t_{1}\) and the time at which the second peak appears is \(t_{2}\). The reflection coefficients of the five antennas showed two peaks. The peak at \(t_{1}\) matched the delay time when a signal entered from the BSL connector and was reflected at the transmission line transition. Comparing the peak heights, the peak at \(t_{1}\) varied with the width of the BSL; the narrower the BSL, the higher the peak height. On the other hand, the peak at \(t_{2}\) remained the same height regardless of the BSL width.