# Alignment Method of an Axis Based on Camera Calibration in a Rotating Optical Measurement System
## 1 Introduction  
In recent years, an optical measurement method based on the photogrammetry principle [1; 2; 3] has been developed rapidly because of its high speed, non-contact, high accuracy and flexibility. Optical measurement is one of the effective methods for coordinate measurement, trajectory measurement or surface reconstruction. It is widely used in different fields such as three-dimensional (3D) sensor measurement, panoramic image mosaic, aerospace, virtual reality (VR), augmented reality (AR), industrial manufacturing and so on [4; 5; 6; 7; 8; 9]. In the large-scale scene or 360-degree annular area measurement, due to the limitation of the field of view (FOV) of the camera, a single lens camera cannot cover the whole measurement range of the target. Therefore, scanning photography [10] is employed, in which a rotating mechanism rotating around a fixed point enables the camera to enlarge the measuring range by acquiring images from multiple angles. Theoretically, adjacent images taken by the camera rotating around its projection center can be matched by a purely projective transformation of their regions of overlap without requiring the three-dimensional shape of the scene [11; 12; 13]. In order to facilitate calculation and later data fusion, it is crucial to coincide the optical center of the camera with the rotation center of the rotating mechanism in practice for the creation of panoramic images. Here, the optical center of the camera is the origin of the camera coordinate system in the computer vision. It is also called the projection center in many references and corresponds to the first nodal point (or principle node) of the camera lens installed in the same medium. For the close-range applications, the misalignment of the two centers will be introduced into the final results and the images may not be spliced well. For simplicity, in the rest of this article, the \"optical center of the camera\" is abbreviated as \"optical center\". The alignment of a rotating optical measurement system has always been a hot topic in many fields and has aroused the research interest of many researchers. [PERSON] et al. (2018) proposed a centering procedure, in which the rotation center was aligned by moving the camera via the translation platform with the help of the transition line of far and nearby targets, and the location accuracy can reach one tenth of a millimeter. [PERSON] et al. (2018) designed special calibration target \"cones\" to align the optical center with the rotation center to realize the adjustment of the digital camera to a spherical panoramic camera head. The achieved projection center uncertainty was approximated to be about 1 mm. [PERSON] et al. (2018) developed a method to find the rotation center based on the camera calibration method, in which a three-dimensional calibration target is employed. The X, Y and Z shifts for the correction of the camera location were obtained by a numerical method. The standard deviation between the projection center and the rotation center after calibration could reach 0.161 mm. On the contrary, in some studies, the relationship between the camera and the rotation mechanism is calculated by the system calibration in advance, and then it is substituted into the final image mosaic ([PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2018). For instance, [PERSON] et al. (2018, 2019) designed a measuring system named Photo Total Station System (PTSS), within which a metric camera with known internal parameters was rigidly installed on the telescope of the total station to extend the FOV and improve the accuracy. [PERSON] et al. (2019) designed a theodolite-camera (TC) measurement system consisting of a theodolite and a camera for precise measurement at large viewing angles. The total station or theodolite can provide the spatial coordinates of the control points, which can be used to establish the relationship of the camera while rotating.