## 3 Study Method
The radial lens distortion model corrects the bias in the radial direction, \(\delta_{r}\), according to the distance from the lens center, and is expressed as follows [21]:  
\[\delta_{r}=K_{1}r^{3}+K_{2}r^{5}+K_{3}r^{7}, \tag{1}\]  
where \(r\) is the radial distance from the principal point, equal to \(r^{2}=(x-x_{0})^{2}+(y-y_{0})^{2}\). \(K_{1},\ K_{2},\ \text{and}\ K_{3}\) are the radial distortion coefficients, \(x\) and \(y\) are the image coordinates, and \(x_{0}\) and \(y_{0}\) are the coordinates of the principal point. Radial distortion has a symmetric radial shape in the optical center and is characterized by higher distortion as the distance from the center increases [22]. Therefore,  
Figure 3:0 Acquisition of image and ground control point coordinates for the conjugate point in the stereo images using the developed program. (**a**) acquisition of the image coordinates for the conjugate point in the left image; (**b**) acquisition of the image coordinates for the conjugate point in the right image; (**c**) the image coordinates for the conjugate point in the stereo images. the linear term was not considered in Equation (1). The radial distortion quantity \(\delta_{r}\) is converted into two elements for each picture coordinate direction, as follows:  
\[ \begin{array}{c}\delta_{rx}=\frac{\delta_{r}(x-x_{0})}{r},\\ \delta_{ry}=\frac{\delta_{r}(y-y_{0})}{r}.\end{array}  \tag{2}\]  
The tangential lens distortion model corrects the variations caused by the non-horizontal position of the lens and the sensor or by the incorrectness of the lens center during the camera manufacturing process. For the tangential lens distortion model, \(\delta_{x}\) and \(\delta_{y}\) are expressed by the following equations for the \(x\) and \(y\) directions of the picture coordinate axis:  
\[ \begin{array}{c}\delta_{x}=P_{1}\Big{[}r^{2}+2(x-x_{0})^{2}\Big{]}+2P_{2}(x -x_{0})(y-y_{0}),\\ \\ \delta_{y}=P_{2}\Big{[}r^{2}+2(y-y_{0})^{2}\Big{]}+2P_{1}(x-x_{0})(y-y_{0}), \end{array}  \tag{3}\]  
where \(P_{1}\) and \(P_{2}\) are the tangential distortion coefficients. In this study, the distortion was corrected using the radial and tangential lens distortion model, and the radial distortion coefficients \(K_{1},\ K_{2},\ \text{and}\ K_{3}\) and tangential distortion coefficients \(P_{1}\) and \(P_{2}\) were considered. In this study, the locations and orientations of the two cameras were fixed because they were installed on fixed pillars. This means that accurate orientation results for the cameras installed on a fixed structure did not have to be calculated repeatedly. Therefore, the initially accurately determined results of the interior and exterior orientation parameters for the two cameras can be used over the long term. Furthermore, the first total station measurement results can be used for the ground control point coordinates of the feature points on the VLBI antenna surface in the long term. The user can quickly  
Figure 8: Calculation process for interior and exterior orientation results. calculate the 3D coordinates of the conjugate point according to the time series by directly entering the positions of the labeled conjugate point in Figure 5 and loading the previous orientation results.