Calibration of a Terrestrial Laser Scanner - Institute of Geodesy and ...

52 3. Calibration of Terrestrial Laser Scannernersystem, a coordinate transformation can be applied using the coordinates of the control pointsTheresiduals of the local scannerorigin define the eccentricity of the scan centerThe results of several independent and different setups show that there is no significant eccentricityin thescan center The residuals of the transformed local origin, defining the scan center, to the coordinate systemof the control points are less than 1 mm for the horizontal positionThus, the eccentricityis below the accu¬racy of the distance measurement system and the angle measurement system, respectively Furthermore, avertical offset was identified with a value of 0 222 m ± 1 mm depending on the screws of the tnbrachs3.4.2 Wobble of Vertical axisThe wobble of an axis is an instrumental error, which is caused by variations in the axis during rotationTheideal case is that the axis remains at a constant orientation during rotation, but inpractice, motion of the axisleads to deviations from the ideal positionCauses for the wobble are either manufacturing imperfectionsresulting from mechanical deficiencies, eg defective mould of the bearing, or the mechanical componentsof the axisThe bearing can especially cause systematic effects and result in changesin the orientation ofthe axis, cf [Matthias, 1961] and [Gerstbach, 1976]Variations in the vertical axis are investigated by measuring the inclination of the vertical axis Developingvalues for the orientation, l e the inclination of the vertical axis, allows conclusions to be drawn regardingthe behaviour of the vertical axisThe raw data provided by the inclination sensor have to be pre-processedbecause these data include somesystematic effects First, possible systematic effects caused by the inclina¬tion sensor itself have to be identified [Loffier et al, 2002] additive constant, linearity error14, long-termstability, temperature influences etc Second, systematic effects caused by the rotation of the laser scannerare of importance the influence of the levelling error, properties of the bearing, etcThe inclination sensor used is the Nivel 20 of Leica GeosystemsThe mam characteristics of this sensor are[Leica Geosystems, 1988]• inclination resolution 0 001 mrad (measuring range ±2 mrad)• linearity error ± [0 005 mrad + 0 5% of inclination value]For acquiring the inclination data during rotation, the Nivel 20 is mounted ontop of the laser scanner, nearlycentrallyin the vertical axismeasuring range during the rotation AThe laser scanner has to be levelled so that the inclination sensor is within thebe performed due to imperfectness in the levelling procedurebe eliminated mathematicallyor LRViewer15levelling error is present because absolute precise levelling cannotHowever, the levelling error produced canThe laser scanner is then controlled via the operating software LRCServerWithin this software, the laser scanner can be rotated to discrete horizontal directions basedon the local scanner orientationThe inclination of the actual vertical axis, in two perpendicular directionsx and y, can be read by the inclination sensor, as controlled by NivelPlane16The goal of the wobble analysis of the vertical axis is to analyze whether there are systematiceffects thatcan describe the wobble mathematically or whether there are no systematic effects and consequently, thevertical axis has no wobble The assumption is that the wobble results in harmonic oscillations, which canbe approximated by sine terms Therefore, a Fourier analysis is appliedon the inclination data to derivethe frequency, or period, the amplitude, and the phase angle of a possible significant frequency causing thewobble of the vertical axisThe sampling theorem has to be taken into account when the Fourier analysis14 An inclination displayed by the inclination sensor should be proportional to the real inclination The deviation between displayedand real inclination is defined as a linearityerror of the sensor15LRCServer and LRViewer are software for operating and controlling the laser scanner, both provided by Zoller+Frohlich GmbH16NivelPlane is a software tool for controlling the Nivel20 provided by Leica Geosystems