Christoph Holst

Improved area-based deformation analysis of a radio telescope’s main reflector based on terrestrial laser scanning

Abstract The main reflectors of radio telescopes deform due to gravitation when changing their elevation angle. This can be analyzed by scanning the paraboloid surface with a terrestrial laser scanner and by determining focal length variations and local deformations from best-fit approximations. For the Effelsberg radio telescope, both groups of deformations are estimated from seven points clouds measured at different elevation angles of the telescope: the focal length decreases by 22.7 mm when tilting the telescope from 90 deg to 7.5 deg elevation angle. Variable deformations of ± 2 mm are detected as well at certain areas. Furthermore, a few surface panels seem to be misaligned. Apart from these results, the present study highlights the need for an appropriate measurement concept and for preprocessing stepswhen using laser scanners for area-based deformation analyses. Especially, data reduction, object segmentation and laser scanner calibration are discussed in more detail. An omission of these steps would significantly degrade the deformation analysis and the significance of its results. This holds for all sorts of laser scanner based analyses.

Challenges and Present Fields of Action at Laser Scanner Based Deformation Analyses

Abstract Due to improved laser scanning technology, laser scanner based deformation analyses are presently widespread. These deformation analyses are no longer based on individual points representing the deformation of an object at selected positions. Instead, they are based on a large number of scan points sampling the whole object. This fact either leads to challenges regarding metrological aspects as well as regarding modeling aspects: – Estimating and quantifying spatial correlations between scan points and incorporating them into the deformation analysis – Separating the laser scanners’ internal systematic errors from areal deformations – Minimizing the bias at areal deformation analyses due to a worse network configuration and limited object knowledge – Developing freeform parameterizations to reproduce arbitrary areal deformations of an object by individual parameters – Incorporating an extended uncertainty model considering also model errors due to imperfect knowledge and simplification of the sampled object. – Only when considering all of these aspects, laser scanner based deformation analyses can benefit from the potential of the areal object sampling. This study aims at naming and reasoning these aspects. Furthermore, it introduces first methodologies and approaches for dealing with them.

Aiming at self-calibration of terrestrial laser scanners using only one single object and one single scan

Abstract When using terrestrial laser scanners for high quality analyses, calibrating the laser scanner is crucial due to unavoidable misconstruction of the instrument leading to systematic errors. Consequently, the development of calibration fields for laser scanner self-calibration is widespread in the literature. However, these calibration fields altogether suffer from the fact that the calibration parameters are estimated by analyzing the parameter differences of a limited number of substitute objects (targets or planes) scanned from different stations. This study investigates the potential of self-calibrating a laser scanner by scanning one single object with one single scan. This concept is new since it uses the deviation of each sampling point to the scanned object for calibration. Its applicability rests upon the integration of model knowledge that is used to parameterize the scanned object. Results show that this calibration approach is feasible leading to improved surface approximations. However, it makes great demands on the functional model of the calibration parameters, the stochastic model of the adjustment, the scanned object and the scanning geometry. Hence, to gain constant and physically interpretable calibration parameters, further improvement especially regarding functional and stochastic model is demanded.

Biased and Unbiased Estimates Based on Laser Scans of Surfaces with Unknown Deformations

Abstract The estimates based on laser scans of surfaces with unknown deformations are biased and not reproducible when changing the scanning geometry. While the existence of a bias is only disadvantageous at some applications, non-reproducible estimates are never desired. Hence, this varying bias and its origin need to be investigated - since this situation has not been examined sufficiently in the literature. Analyzing this situation, the dependence of the estimation on the network configuration is highlighted: the network configuration - studied similarly to geodetic networks - rules about the impact of the deformation. As pointed out, this impact can be altered by manipulating the network configuration. Therefore, several strategies are proposed. These include manipulations of the leastsquares adjustment as well as robust estimation. It is revealed that the reproducibility of the estimates can indeed be significantly increased by some of the proposed leastsquares manipulations. However, the bias can only be significantly reduced by robust estimation.

Estimation of Focal Length Variations of a 100-m Radio Telescope’s Main Reflector by Laser Scanner Measurements

AbstractDue to gravitation, the main reflector of a radio telescope underlies a deformation that causes a change in focal length depending on the variations of the elevation angle of the telescope. To estimate these gravity dependent deformations of the main reflector of the 100-m radio telescope at Effelsberg, Germany, this study proposes a measurement concept based on a laser scanner being mounted upside down on the subreflector. The measurements that have been performed at seven different elevations between 90 and 7.5° are used to estimate the focal length variation of the main reflector parameterized by a rotational paraboloid. To guarantee reliability of the adjustment, this study uses an orthogonal distance regression (ODR) rather than a classical least squares adjustment in a Gauss-Helmert model and formulates the independence of the focal length estimation from the absolute position and orientation of the main reflector in space as a requirement for a reliable adjustment approach. This investigati...

Modeling the Beam Deflection of a Gantry Crane under Load

AbstractGantry cranes load and unload containers from container ships. To ensure safety and operation, the deflection of their main beams under load should be analyzed. This deflection depends on the weight of the loaded container as well as on the position of the trolley that moves the container. For this study, a bivariate polynomial model is built to estimate the deflection based on these two inputs. This two-dimensional load-dependent model is developed in four steps in order to determine the shape of the deflection (dependent on the trolley position) as well as its magnitude (dependent on the container weight). A specific gantry crane was monitored with several sensors where five are inclinometer sensors that observe the tilt along the crane’s main beam and two are tacheometers that observe the trolley position and the absolute deflection. By collecting data from 18 loading operations, the parameters of the deflection model are estimated. Based on this data, the deflection under load is processed dep...

Automatic optimization of height network configurations for detection of surface deformations

Abstract Levellings are performed to observe height changes of different epochs at discrete surveying points. A reliable estimation of surface deformations by a bivariate polynomial needs a sufficient configuration of the underlying network. Because the spacial distribution of the surveying points is not homogeneous in the discussed regions, the network configuration has to be optimized. This study proposes an optimization procedure that estimates the optimal number and position of the surveying points considered for a reliable analysis. Furthermore, the already existing observations are accepted or rejected due to the network’s geometry. Therefore, two different approaches are combined. First, the sampling theorem from time series analysis is used to estimate the number and position of the surveying points. Second, the partial redundancies from statistics take the reliability into account. Applying the optimization procedure to several test regions, the benefit of the optimized network configurations is discussed.

Towards System Calibration of Panoramic Laser Scanners from a Single Station

Terrestrial laser scanner measurements suffer from systematic errors due to internal misalignments. The magnitude of the resulting errors in the point cloud in many cases exceeds the magnitude of random errors. Hence, the task of calibrating a laser scanner is important for applications with high accuracy demands. This paper primarily addresses the case of panoramic terrestrial laser scanners. Herein, it is proven that most of the calibration parameters can be estimated from a single scanner station without a need for any reference information. This hypothesis is confirmed through an empirical experiment, which was conducted in a large machine hall using a Leica Scan Station P20 panoramic laser scanner. The calibration approach is based on the widely used target-based self-calibration approach, with small modifications. A new angular parameterization is used in order to implicitly introduce measurements in two faces of the instrument and for the implementation of calibration parameters describing genuine mechanical misalignments. Additionally, a computationally preferable calibration algorithm based on the two-face measurements is introduced. In the end, the calibration results are discussed, highlighting all necessary prerequisites for the scanner calibration from a single scanner station.

Terrestrial Laser Scanner Two-Face Measurements for Analyzing the Elevation-Dependent Deformation of the Onsala Space Observatory 20-m Radio Telescope’s Main Reflector in a Bundle Adjustment

For accurate astronomic and geodetic observations based on radio telescopes, the elevation-dependent deformation of the radio telescopes’ main reflectors should be known. Terrestrial laser scanning has been used for determining the corresponding changes of focal lengths and areal reflector deformations at several occasions before. New in this publication is the situation in which we minimize systematic measurement errors by an improved measurement and data-processing concept: Sampling the main reflector in both faces of the laser scanner and calibrating the laser scanner in situ in a bundle adjustment. This concept is applied to the Onsala Space Observatory 20-m radio telescope: The focal length of the main reflector decreases by 9.6 mm from 85∘ to 5∘ elevation angle. Further local deformations of the main reflector are not detected.

Impact of spatial correlations on the surface estimation based on terrestrial laser scanning

Abstract In terms of high precision requested deformation analyses, evaluating laser scan data requires the exact knowledge of the functional and stochastic model. If this is not given, a parameter estimation leads to insufficient results. Simulating a laser scanning scene provides the knowledge of the exact functional model of the surface. Thus, it is possible to investigate the impact of neglecting spatial correlations in the stochastic model. Here, this impact is quantified through statistical analysis. The correlation function, the number of scanning points and the ratio of colored noise in the measurements determine the covariances in the simulated observations. It is shown that even for short correlation lengths of less than 10 cm and a low ratio of colored noise the global test as well as the parameter test are rejected. This indicates a bias and inconsistency in the parameter estimation. These results are transferable to similar tasks of laser scanner based surface approximation.