Analysis of the random measurement error of areal 3D coordinate measurements exclusively based on measurement repetitions

Abstract The measurement uncertainty characteristics of a measurement system are an important parameter when evaluating the suitability of a certain measurement system for a specific measurement task. The measurement uncertainty can be calculated from observed measurement errors, which consist of both systematic and random components. While the unfavourable influence of systematic components can be compensated by calibration, random components are inherently not correctable. There are various measurement principles which are affected by different measurement error characteristics depending on specific properties of the measurement task, e. g. the optical surface properties of the measurement object when using fringe projection or the material properties when using industrial X-ray computed tomography. Thus, it can be helpful in certain scenarios if the spatial distribution of the acquisition quality as well as uncertainty characteristics on the captured surface of a certain measurement task can be found out. This article demonstrates a methodology to determine the random measurement error solely from a series of measurement repetitions without the need of additional information, e. g. a reference measurement or the nominal geometry of the examined part.