# Accurate Phase Calibration of Multistatic Imaging System for Medical and Industrial Applications
## 5 Imaging Result  
The differences in reconstructed images with and without phase calibration were compared using the simple back-projection method of waves. The simple back-projection method of waves reconstructs the object from the amplitude and phase of the scattered waves measured at the Rx antenna. Microwaves emitted from a Tx antenna are scattered by objects, and the scattered waves spread with the objects as the wave source. The scattered electric field is measured with the Rx antenna so that the space containing the wave source is surrounded by a closed surface. Calculating the time reversal of this measured scattered electric field converges to the wave source. In this way, the object that is the wave source is back-projected. This method is based on the Cauchy problem [27], and back-projection by time reversal using pulses has been used in many studies [28; 29; 30]. The reconstructed image of the object is obtained by subtracting the reconstructed images calculated for the presence and absence of the object, respectively. Figure 8 shows the reconstructed image of a metal rod placed in the cylindrical cavity in the center of the antenna array by the simple back-projection method of waves. The diameter of the metal rod is 12 mm. This diameter is less than 1/4 of the wavelength at  
Figure 7: The phase of transmission coefficients measured at ten pairs of opposing Tx and Rx antennas in the antenna array: (**a**) without phase calibration, measured between calibration planes; (**b**) with phase calibration, measured between measurement reference planes. the 6.5 GHz frequency used for reconstruction and is beyond the diffraction limit. The frequency used for the reconstructed images was 6.5 GHz and the tomograms were taken at a height of 37.5 mm from the bottom of the antenna array. This height of 37.5 mm corresponds to the midpoint of the antenna array. Figure 8a,b are calculated from data without phase calibration, and Figure 8c,d are calculated from data with phase calibration. Figure 8a,c show the amplitude distributions, while Figure 8b,d show the phase distributions. The horizontal axis of the reconstructed image shows the x-axis, and the vertical axis shows the y-axis. The white solid circles in the reconstructed image show the shape of the antenna array. The outer circle is the outer edge of the antenna array, and the inner circle is the inner edge of the array. The color bar in the reconstructed image of amplitude is proportional to the amplitude of the scattered wave, with higher values indicating greater scatter. The color bar in the reconstructed image of the phase shows the phase. The color bars of the amplitude distribution are set about the reconstructed image in the presence of the object. The phase calibration enabled the identification of the object from the reconstructed image using the simple inverse projection method of the wave motion. Initially, the differences in amplitude distribution with and without the phase calibration are compared. Figure 8: Reconstructed image of a 12 mm diameter metal column by simple back-projection of waves using a frequency of 6.5 GHz. Tomographic image at 37.5 mm from the base of the antenna array: (**a**) amplitude distribution without phase calibration; (**b**) phase distribution without phase calibration; (**c**) amplitude distribution with phase calibration; and (**d**) phase distribution with phase calibration. In the absence of the object, the object could not be identified from the reconstructed image. In contrast, the object could be seen in the reconstructed image with phase calibration. The areas with large values appeared at the position where the object was placed. The diameter and shape of the object in the reconstructed image were almost identical to the actual object. Artifacts appeared around the object in a circular area centered on the object. These artifacts were due to multiple reflections in the metal and on the inner surface of the antenna array. In the region where \(y>0\), artifacts appeared on the body of the antenna array.