Multi-range joint calibration of a compact dual-camera visual measurement system under constrained two-axis motion

Large-workspace visual measurement requires local observations acquired from different viewpoints to be fused into a common reference frame. Compact camera-on-rotary-stage architectures can enlarge the observation range with fewer imaging sensors, but accurate calibration is difficult under two-axis-limited excitation when the rotary stage is used only for viewpoint adjustment rather than as a kinematic reference. This paper proposes a multi-range joint calibration method for a compact dual-camera visual measurement system composed of a fixed reference camera, a tracking camera mounted on a two-degree-of-freedom rotary stage, and a positioning board rigidly attached to the moving camera assembly. Calibration data acquired at multiple working distances are organized into local groups. A hierarchical joint optimization model is formulated with a global shared transformation, group-wise target poses, and frame-wise positioning-board poses. The tracking-camera reprojection branch provides the principal constraint on the shared transformation, while the reference-camera reprojection branch anchors the frame-wise board poses. To moderate range- and view-dependent reliability variations, group-wise weights derived from ellipse-center localization covariance are applied to the tracking-camera reprojection branch. An effective-information-based covariance analysis is further used to evaluate the stability of the estimated transformation under constrained motion. Monte Carlo simulations with prescribed ground truth show that the Track-Base joint formulations substantially improve robustness to image-coordinate noise, while the proposed reliability weighting provides an additional translational benefit and the separated pose-perturbation tests reveal estimator sensitivity. Experiments over a 2000–5000 mm workspace demonstrate that the proposed method improves cross-group image-domain consistency and chain-closure consistency, while yielding a more balanced covariance distribution. In calibrated-bar validation, it achieves an overall MAE of 0.188 mm and an overall RMSE of 0.241 mm, corresponding to a relative RMSE of 0.0267%.