Alignment Method of an Axis Based on Camera Calibration in a Rotating Optical Measurement System

Abstract

The alignment problem of a rotating optical measurement system composed of a charge-coupled device (CCD) camera and a turntable is discussed. The motion trajectory model of the optical center (or projection center in the computer vision) of a camera rotating with the rotating device is established. A method based on camera calibration with a two-dimensional target is proposed to calculate the positions of the optical center when the camera is rotated by the turntable. An auxiliary coordinate system is introduced to adjust the external parameter matrix of the camera to map the optical centers on a special fictitious plane. The center of the turntable and the distance between the optical center and the rotation center can be accurately calculated by the least square planar circle fitting method. Lastly, the coordinates of the rotation center and the optical centers are used to provide guidance for the installation of a camera in a rotation measurement system. Simulations and experiments verify the feasibility of the proposed method.

Comparison of Camera Calibration and Measurement Accuracy Techniques for Phase Measuring Deflectometry

“…The rotation matrix R and translation vector T are the external parameters. In Hou's method [17], assuming the coordinates of a point are M c in the camera coordinate system and M w in the world coordinate system, the relationship between M c and M w is expressed by the following equation:…”

“…Optically, the chief rays reflected off the SUT will certainly converge at the entrance pupil center of the camera lens [18][19][20][21]. The role of the projection center in the PMD system, as is mentioned in the references [13][14][15][16][17], is equivalent to this center. For the sake of distinction, we named it the entrance pupil center in our method, but it is still called the projection center in other methods.…”

“…Based on Zhang's technique, Xiao et al proposed a calibration method with a flat mirror to obtain the position of the projection center of the camera [15,16]. Additionally, Hou et al proposed a method to calculate the position of the projection center in a unified world coordinate system from the external parameters (including the translation vector and rotation matrix) of the camera [16,17]. Zhang's technique requires taking several images from different orientations and different poses, but it is not always accessible in deflectometry, especially for a machine-integrated system.…”

Tool-free axis calibration method for self-rotating three-dimensional vision systems

“…Zhao et al 15 captured multiple sets of planar object point clouds from diverse positions and completed the calibration of rotation axis by plane constraint method. Zhu et al 16 and Hou et al 17 captured images of the calibration plate from varying angles by rotating the turntable. They subsequently computed the optical center's position for each angle and employed arc fitting techniques to derive the rotation axis' position.…”

“…Zhu et al 16 . and Hou et al 17 . captured images of the calibration plate from varying angles by rotating the turntable.…”