Calibration of 3D scan trajectories for an industrial computed tomography setup with 6-DOF object manipulator system using a single sphere

In industrial x-ray computed tomography (CT), the application of more complex scan paths in comparison to the typical circular trajectory (${360}^{\circ}$ rotation of the measurement object) can extend the potential of CT. One way to enable such 3D scan trajectories is to use a 6-degrees-of-freedom (DOF) object manipulator system. In our case, a hexapod is mounted on top of the rotary table of a commercial CT scanner. This allows for adaptive tilting of the measurement object during the scan. For high accuracy, the geometry calibration of such setups is typically done using the x-ray projections of a calibrated multi-sphere object. Contrary to this, here, we demonstrate a procedure that is based on only a single sphere and can therefore experimentally be implemented with low effort. Using the intrinsic geometry parameters of the CT device as prior information, the hexapod coordinate system with respect to the CT machine coordinate system is determined by means of a one-step optimization approach. The resulting parameters are used to calculate projection matrices that enable the volume reconstruction for 3D scan trajectories. The method is validated using simulated x-ray images and experimental investigations including dimensional measurements. For the used setup, geometric measurement results for 3D scan trajectories that are calibrated with the presented method show in sum increased errors compared to the circular scans. A limited pose accuracy of the manipulator system is discussed as a potential cause. The results nevertheless indicate that the presented method is generally feasible for dimensional CT measurements provided that the pose accuracy is sufficient. The calibration procedure can therefore be a low-cost and easier to implement alternative compared to trajectory calibration methods based on multi-sphere objects, but with a tendency towards lower measurement accuracy. The methodology can in principle be transferred to different setups with 6-DOF manipulator systems, e.g. C-arm CT devices with a robot arm.