3-D Self-Calibration for High-Precision Measurement Instruments With Hybrid Positions

Calibrating high-precision 3-D measuring instruments by using traditional calibration methods is challenging because these instruments require the use of higher-precision calibration artifacts. Self-calibration models can separate system errors from overall measurement errors by using auxiliary artifacts with accuracy within that of the object to be calibrated; therefore, such models have substantial advantages in terms of production costs and realization conditions. This article proposes a least-squares-based 3-D self-calibration model involving a hybrid position of the artifact. In this model, the calibration artifact is rotated or translated from its initial position to other positions and then used to execute measurements. Compared with existing 3-D self-calibration models, which require four positions, the proposed model involves three positions, including a hybrid position obtained through both rotation and translation. Thus, the proposed model requires fewer steps and a shorter processing time. Simulations were conducted to evaluate the 3-D self-calibration model, and the simulation results validated its ability to separate system errors from overall measurement errors generated by noise. An error propagation ratio of < 1 was also obtained for the model, indicating that the model can suppress noise. Experiments conducted using a computed tomography instrument confirmed the effectiveness and repeatability of this model; specifically, the standard deviation among the artifacts back to the initial position after the 3-D self-calibration process was less than that observed before the calibration process.