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.

中文翻译：

---

混合位置高精度测量仪器的 3D 自校准


使用传统校准方法校准高精度 3D 测量仪器具有挑战性，因为这些仪器需要使用更高精度的校准工件。自校准模型可以通过使用辅助工件将系统误差与总体测量误差分开，其精度在待校准对象的范围内；因此，此类模型在生产成本和实现条件方面都具有显着的优势。本文提出了一种基于最小二乘法的 3D 自校准模型，涉及工件的混合位置。在此模型中，校准工件从其初始位置旋转或平移到其他位置，然后用于执行测量。与现有的需要四个位置的3D自校准模型相比，所提出的模型涉及三个位置，包括通过旋转和平移获得的混合位置。因此，所提出的模型需要更少的步骤和更短的处理时间。通过仿真来评估 3D 自校准模型，仿真结果验证了其将系统误差与噪声产生的总体测量误差分开的能力。该模型还获得了<;1的误差传播率，表明该模型可以抑制噪声。使用计算机断层扫描仪进行的实验证实了该模型的有效性和可重复性；具体来说，3D自校准过程之后回到初始位置的工件之间的标准偏差小于校准过程之前观察到的标准偏差。