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The determination of a fully populated variance-covariance matrix (VCM) of a point cloud acquired with a terrestrial laser scanner (TLS) is not straightforward as physical correlations between TLS observations are not sufficiently known. Ignoring correlations leads to biased estimates, wrong modeling of surfaces, or the misinterpretation of geometric changes. For this reason, this study aims at progressing the empirical determination of correlations in TLS range observations by investigating short-scale correlations (mm to cm) of TLS rangefinders. Therefore, two methods are proposed to determine spatial correlations between TLS range observations. Both methods are evaluated for simulated laser scans, and then applied to empirical data of four different terrestrial laser scanners. The results demonstrate that short-scale correlations exist, and it is possible to quantify the relevant parameters to fill the VCM. It also shows that the correlation differs between the scanners and with the distance. Furthermore, we analyze the change of the correlation length with changing scanning configurations such as distance, incidence angle, and reflectivity with the result that this must be considered while applying the aforementioned methods to point clouds of large objects. All in all, this study trustfully quantifies physical short-scale correlations yielding from the rangefinder and suggests a guideline to apply this to point clouds of large objects.

The resolution capability of terrestrial laser scanners does not necessarily equal the scanning resolution. Laser scanners can acquire the surrounding with a point distance of less than a millimeter on ten meters but the footprint size amounts to at least a few millimeters. Hence, neighboring laser spots overlap and they are correlated as they do not provide individual information about the object. This study provides a new methodology to determine the spatial expansion of the resolution capability of terrestrial laser scanners in the angular direction for distances up to 80 m. It is demonstrated that the Leica ScanStation P20 better resolves objects in the horizontal direction than in the vertical direction. Furthermore, the correlation of neighbored range measurements is empirically derived from the resolution capability and the effective number of measurements is determined. This provides a more realistic measure of the number of uncorrelated points in a scan. It is demonstrated that the resolution capability has a big impact on the correlation of the scan points as the number of uncorrelated points is reduced by up to 93% depending on the scanner settings.

In geodetic very long baseline interferometry, pairs of radio telescopes simultaneously observe signals from quasi stellar objects to estimate the baseline between their reference points. Gravity-dependent variations of the radio telescopes’ reference points deteriorate the estimated baseline's accuracy since they lead to signal path variations in the radio telescopes. This study investigates a new concept for determining the stability of a radio telescope's reference point. Differing to previously used strategies, this concept is able to reveal instabilities due to an elevation-dependent tumbling of the telescope independent from the part of the axis offset that is constant for all elevation angles. The new concept is exclusively based on terrestrial laser scanning that at the same time is used for analyzing the main reflector's shape deformation. We applied this concept to the Onsala Space Observatory (OSO) 20-m radio telescope: The results show that we cannot disprove the reference point's stability. In general, our new strategy can be transferred to also investigate the stability of other radio telescopes’ reference points. A prerequisite for this strategy is that the laser scanner – that moves between the elevation angles – observes identical objects from different stations. These objects need to be stable during all measurements. In the case of the OSO 20-m radio telescope, the radome is used for this purpose.

Portable coordinate measuring arms (CMA) represent a special class of coordinate measuring machines providing high accuracy combined with high flexibility. To obtain high accurate and reliable 3D coordinates, the kinematic model has to represent precisely the mechanical construction of the CMA. Thus, a reliable and accurate calibration is essential to preserve the CMA's accuracy. However, due to its redundant characteristics, estimating the kinematic parameters has to deal with linear dependencies and, therefore, with rank deficiencies. A profound statistical analysis of the existing calibration approaches has not yet been performed. For this reason, this paper introduces an innovative and replicable least-squares calibration approach based on the general case of adjustment (Gaus–Helmert model). This rigorous optimization procedure integrates the original observations and enables a statistical evaluation of the estimated parameters as well as of each observation, based on the configuration analysis. The applicability of the approach is proofed using simulated and real measuring data. Thanks to the configuration analysis and supported by experimental results, it is shown that an accurate solution of the calibration can be obtained using measurements only located in a small part of the workspace.