## 3 Study Method
The image coordinates used for the orientation were specified as the same points as the conjugate point used for the 3D coordinate calculation, to omit the process of acquiring the image coordinates for the conjugate point by performing the image coordinate acquisition process in the developed program. That is, the image coordinates used to calculate the initial orientation results were used as the conjugate point to calculate the 3D coordinates, which improved the efficiency of the image coordinate acquisition process. Simultaneous with the acquisition of the ground control point coordinates for the feature points on the VLBI antenna surface, the stereo image shown in Figure 6 was acquired from the two CCD cameras located on the \(y\)-axis of the local coordinate system for the fixed VLBI antenna shown in Figure 4.  
To acquire the image coordinates for the feature points using our software package for VLBI antenna static displacement monitoring, the user stores the captured images of the VLBI antenna surface and displays the stored images on the screen. The user then acquires the image coordinates used for calculating the orientation parameters by directly specifying the labeled feature points in Figure 5. This process is completed for the same points in both images in the stereo pair for later determining the 3D coordinates. Figure 7 shows the process of collecting image coordinates for the conjugate point of the stereo images in the developed program. The image zoom-in feature was implemented in this program to facilitate the user's acquisition of the image coordinates. When the position of a labeled feature point in Figure 5 is selected in the enlarged image, the image coordinates of the feature points and the results from the ground control point survey are displayed at the bottom of the program screen. Attaching separate targets to automate the acquisition of the image coordinates for the feature points on the VLBI antenna surface can degrade the positioning accuracy of the VLBI antenna due to radio wave interference. For example, it provides scattering centers for radio frequency interference to reach the receiver, or it degrades the surface accuracy for the wavefront from the source and leads to a slightly reduced forward gain. Therefore, the image enlargement feature was included in the program to allow users to directly acquire image coordinates. The use of an open or commercial library for automatic matching of the feature points was not considered in this study because its accuracy has not been sufficiently verified. Figure 6: Stereo images of the main reflector of VLBI antenna taken by the Charge Coupled Device (CCD) cameras. (**a**) the first image; (**b**) the second image. The initial values for bundle adjustment were calculated with the Direct Linear Transformation (DLT) algorithm, using the coordinates from the stereo images and ground control point survey results. To determine the final interior and exterior orientation parameters for the stereo images, an iterative adjustment was performed with bundle adjustment, using the initial orientation results calculated from the DLT algorithm. Finally, the 3D position coordinates were calculated using the acquired image coordinates for the conjugate point of the stereo images and the results of the interior and exterior orientation parameters. The process for calculating the interior and exterior orientation results is summarized in Figure 8.  
The interior orientation parameters are the primary factors influencing the light ray path from the perspective center point in the camera to a point in the picture. The interior orientation parameters include the position of the principal point in the picture coordinate system, camera focal length, and lens distortion quantity. The general lens distortion factors include radial distortion and tangential distortion. Radial distortion is the larger of the two [20].