Comparison of 3-D Self-Calibration Methods for High-Precision Measurement Instruments

Abstract

Three-dimensional self-calibration for high-precision 3-D measurement instruments can separate the system errors using an auxiliary artifact, with accuracy comparable to that of the instrument to be calibrated, having significant advantages in terms of production costs and realization conditions. The auxiliary artifact is rotated and/or translated to different positions. From measurements of the artifact in various positions, the system errors of the measurement instrument are separated after the elimination of the artifact’s errors through the self-calibration model. In this study, an iterative optimization method in 2-D self-calibration was extended to 3-D and compared with an established 3-D self-calibration method, namely the equation method based on least squares. The optimization method involves an optimization of 3-D instrument to eliminate its system errors by a correction function during an iterative loop. The equation method is used to establish a 3-D self-calibration model and solve the overdetermined equation model by least squares. The uncertainties of these two methods were analyzed using different approaches. The two methods were compared by simulation with the separated system errors and the effect of calibration when the artifact position scheme changed. Experiments on a computed tomography (CT) instrument were conducted to confirm the effectiveness of the two methods of 3-D self-calibration, through the mutual verification of results.