Objective  Accurate determination of camera-to-reference frame parameters is crucial. Traditional systems are limited by camera field of view, constraining object size measurability. Omnidirectional cameras offer wide view and high imaging quality by using rotation systems or combining with LiDAR for scene modeling. This paper proposes a calibration method for omnidirectional camera and rotation axis. It uses omnidirectional cameras to capture rotation of QR code chessboards. A reliable mathematical model and nonlinear fitting optimize initial results for accurate parameter estimation. This method has low equipment requirements, considering board placement within the camera's view. The experimental results indicate that the average optimized reprojection error of this method can be controlled below 0.15 pixel, satisfying the requirements of experimental measurements and demonstrating promising application performance in various scenarios.

  Methods  A reliable system is proposed to calibrate the extrinsic parameters between the camera and the rotation axis. A omnidirectional camera with a resolution of 4 000 pixel×3 000 pixel is utilized to capture the dual ChArUco calibration boards (Fig.2). For the extrinsic calibration, an algorithm is designed to fit the rotation plane and different methods for establishing the axis coordinate system are introduced (Fig.5). The accuracy of the system is evaluated using the distance from the optical center to the origin of the axis coordinate system (Fig.9) and the reprojection errors under different conditions (Fig.11).

  Results and Discussions   In this method, the Perspective-n-Point algorithm is employed to determine the camera's optical center coordinates. Subsequently, a nonlinear least squares fitting technique is applied to fit the rotation plane and sphere of the optical center (Fig.8). The circularity fitting standard deviation for the intersection between the plane and the sphere is measured to be 0.021 8 mm, while the flatness fitting standard deviation is 0.030 1 mm. The range of distances from the camera's optical center to the axis is found to be 0.085 mm, with a standard deviation of 0.021 mm (Fig.9). Additionally, the maximum reprojection error between the experimental reference group and the other two control groups is 0.141 6 pixel (Fig.12), thereby validating the accuracy of the proposed method.

  Conclusions  To address the issue of pose uncertainty between the camera and the rotation axis, this paper proposes a calibration method based on a omnidirectional camera and dual ChArUco calibration boards. The method captures multiple sets of images containing the dual targets to obtain the position information of the camera's optical center at each shooting position. By establishing a mathematical model for coordinate system transformation, the pose relationship between the camera and the rotation axis is computed and optimized, effectively suppressing the influence of random errors in the experiments. Experimental results demonstrate that the proposed method achieves sub-millimeter-level accuracy in the distance between the camera and the rotation axis, with an average optimized reprojection error controlled below 0.15 pixel. Compared to other methods, the method presented in this paper has lower system complexity, improved accuracy by use of two calibration boards, and effectively mitigates random errors caused by placement variations. The results indicate that this method exhibits good robustness and convenience, making it reliably applicable to shooting tasks in diverse scenarios.