# Accurate Phase Calibration of Multistatic Imaging System for Medical and Industrial Applications
## 2 Phase Calibration Method  
In this study, phase calibration was performed using the difference in electrical length. The difference in electrical length was determined by the reflection coefficients from the measurement reference plane of the antenna element. The measurement reference plane is the position where the signal is reflected, such as at the conversion section of a transmission line. If there is a signal reflection, the position can be defined as a measurement reference plane for phase calibration. This calibration method was designed for a system like the one shown in Figure 1. The system consists of a VNA, RF switches, an ECal module,and antenna elements. ECal is an automated calibration module for VNA that simplifies traditional manual calibration procedures and improves accuracy and efficiency [20]. While traditional calibration requires multiple references (e.g., open, short, loaded, through, etc.) to be prepared and performed manually, ECal allows these references to be switched electronically within the module for a quicker calibration. The RF switches require one port to be connected to the ECal module, in addition to the ports used for measurements. This port is called the reference port. RF switches and coaxial cables have different electrical lengths for each channel. In Figure 1, the electrical length difference with the reference port is indicated by \(l_{\mathrm{tx}}(\omega,\ n_{\mathrm{tx}})\) and \(l_{\mathrm{rx}}(\omega,\ n_{\mathrm{rx}})\), while \(\omega\) represents the angular frequency, and \(n_{\mathrm{tx}}\) and \(n_{\mathrm{rx}}\) denote the numbers of the Tx and Rx ports. If the electrical length of the port is longer than the electrical length of the reference port, \(l_{\mathrm{tx}}(\omega,\ n_{\mathrm{tx}})\) and \(l_{\mathrm{rx}}(\omega,n_{\mathrm{rx}})\) are represented by a positive number. The green dotted line shows the calibration plane of the Ecal module; if only the ECal module is used for calibration, the VNA calibration plane is the green dotted line. The orange dotted line indicates the measurement reference plane of each channel. The calibration plane and the measurement reference plane are not the same for each channel, even if the reference port is configured with the ECal module. The phase calibration is performed by determining the electrical length deviation from the reflection coefficient in such a system. The electrical length is calculated by taking dispersion into account.  
The calibration procedure is shown in Figure 2. The phase calibration is performed in three steps. First, the reference port connected to the ECal module is calibrated using ECal. The ECal module is connected only to the reference port for its calibration, and the reflection coefficients of other ports are measured by VNA in the frequency domain. In the second step, the reflection signal at the measurement reference plane is extracted from the measured reflection coefficients. The phase change is then obtained, considering the variance of each port. In the third step, phase calibration is performed using the phase change due to the difference in electrical length.  
Figure 1: Systems where phase calibration is expected to be applied in this study.