Calibration of a Terrestrial Laser Scanner - Institute of Geodesy and ...
Calibration of a Terrestrial Laser Scanner - Institute of Geodesy and ... Calibration of a Terrestrial Laser Scanner - Institute of Geodesy and ...
Inormal axis,intersectionpoint axis.leads collimationthisi.e. shouldbetween The torealisationideal errorstilting(virtual)condition17Laser verticalscanner Furthermore,and3000 horizontalof HDS Leica58 3. Calibration of Terrestrial Laser ScannerFor comparison, another laser scanner17 was investigated in the same way. The data acquired by the inclina¬tion data in the x-direction and y-direction as well as the sine curve defining the levelling error are shown inthe upper part of Figure 3.31. The parameters for the levelling error are identical concerning the frequencyand the amplitude, and the difference of the phase angle between the x-direction and the y-direction is 90 °.The remaining residuals between the acquired inclination data and the sine curve definingthe vertical axis can be seen in the lower part of Figure 3.31. These residuals show no systematicare small (< 0.03 mrad). Thus, this vertical axis has an ideal rotation and is free of a wobble.the wobble oftrends and-X,Y Directiono 0 0A /AV / V• data series Xdata series Ysine curve Y\'' \/ h / A>l/ A \ / /\\ / A \ j 1 \ *'1 \ \ / \ \ J I \/ 'r\ \1 ; \ \ 1 \ •W \ \ 1 ! \ \i f r 1'\ j \ \ '\ '/ï ! \ 'j i \ i \ y / \'**'' V/V \j\J \A/ \.500 1000azimuth [°]X.Y-Direction—•—residuals XA/h;1à/P—^ _,- 'lA /\i N/ \---residuals Y! W \ IÀ \ /\ r^v['p-J500 1000azimuth [°]Figure 3.31: Inclination values of a data series including the sine curve of the levelling error for the x-direction andthe y-direction (top). The residuals of the inclination data to the sine curve for the x-direction and the y-direction(bottom).In addition, a theodolite has a much smaller wobble of the vertical axis. According to [Matthias, 1961], theinvestigation of a theodolite results in a maximum error of 0.005 mrad that is caused bywobble. Finally, it should be mentioned that not only is the vertical axis affected byhorizontal axis can also be influenced.the vertical axisthe wobble, but the3.4.3 Error of Collimation AxisThe ideal construction of the collimation axis of a theodolite should beGeosystems
3.4 Instrumental Errors 59in the collimation axis. In detail, it can be distinguished between two different errors [Deumlich and Staiger,2002]:• collimation error and•eccentricity of the collimation axis.The investigated laser scanner has axes according to a theodolite, a collimation axis, defined bybeam, a horizontal axis and a vertical axis, cf. Figurethe laser3.25. Thus, the influence of the two errors of the colli¬mation axis can be investigated by performing measurements in two faces. For minimizing and separatingfurther instrumental errors, e.g.errors of the horizontal axis, the measurements were carried out ontargetsaligned in a horizontal line of sight, as defined by a zenith angle of « 90 °. The targets were spheres and po¬sitioned along the calibration track line. The range for positioning the spheres is limited to 20 m accordingto the quality and the quantity of the point cloud by scanning the spheres,cf. Section 3.2.2.The investigation procedure includes two spheres with two different diameters of 12 cm and 15 cm, whichwere scanned in two faces18 and twice by independent setups. The center points of the sphereslated by applying the 'fix' adjustment. Since the results from computing the center pointscoordinates, the spherical coordinates are derived bywere calcu¬are in Cartesianhz =arctan(-)xarccos(-)s(3.11)=\Jx2 + y2 + z1If the collimation axis shows errors, then the spherical coordinates, based on surveying in two faces, aredifferent. This is especially true for the horizontal angle hz and the vertical anglev. The deviations in theangles based on measurements in two faces are caused by the collimation error and the eccentricity of thecollimation axis.collimation axis errorideal collimation axis(laser beam)real collimation axis(laser beam)horizontal axisFigure 3.32: Collimation error applied to the laser scanner (top view). The real collimation axis, visualized by thelaser beam, shows a deviation from the ideal collimation axis (angle c) which hits the horizontal axis at a normal.A collimation error is present if the collimation axis is not normal to the horizontal axis. Figure 3.32 showsthe influence of the collimation error c on the horizontal direction. In addition, if the collimation errorhas corresponding deviation in the vertical direction, i.e.the collimation axis is not normal to the vertical18Due to the deflection principle, the rotating mirror of the laser scanner can be seen as the telescope of a theodolite
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Inormal axis,intersectionpoint axis.leads collimationthisi.e. shouldbetween The torealisationideal errorstilting(virtual)condition17<strong>Laser</strong> verticalscanner Furthermore,<strong>and</strong>3000 horizontal<strong>of</strong> HDS Leica58 3. <strong>Calibration</strong> <strong>of</strong> <strong>Terrestrial</strong> <strong>Laser</strong> <strong>Scanner</strong>For comparison, another laser scanner17 was investigated in the same way. The data acquired by the inclina¬tion data in the x-direction <strong>and</strong> y-direction as well as the sine curve defining the levelling error are shown inthe upper part <strong>of</strong> Figure 3.31. The parameters for the levelling error are identical concerning the frequency<strong>and</strong> the amplitude, <strong>and</strong> the difference <strong>of</strong> the phase angle between the x-direction <strong>and</strong> the y-direction is 90 °.The remaining residuals between the acquired inclination data <strong>and</strong> the sine curve definingthe vertical axis can be seen in the lower part <strong>of</strong> Figure 3.31. These residuals show no systematicare small (< 0.03 mrad). Thus, this vertical axis has an ideal rotation <strong>and</strong> is free <strong>of</strong> a wobble.the wobble <strong>of</strong>trends <strong>and</strong>-X,Y Directiono 0 0A /AV / V• data series Xdata series Ysine curve Y\'' \/ h / A>l/ A \ / /\\ / A \ j 1 \ *'1 \ \ / \ \ J I \/ 'r\ \1 ; \ \ 1 \ •W \ \ 1 ! \ \i f r 1'\ j \ \ '\ '/ï ! \ 'j i \ i \ y / \'**'' V/V \j\J \A/ \.500 1000azimuth [°]X.Y-Direction—•—residuals XA/h;1à/P—^ _,- 'lA /\i N/ \---residuals Y! W \ IÀ \ /\ r^v['p-J500 1000azimuth [°]Figure 3.31: Inclination values <strong>of</strong> a data series including the sine curve <strong>of</strong> the levelling error for the x-direction <strong>and</strong>the y-direction (top). The residuals <strong>of</strong> the inclination data to the sine curve for the x-direction <strong>and</strong> the y-direction(bottom).In addition, a theodolite has a much smaller wobble <strong>of</strong> the vertical axis. According to [Matthias, 1961], theinvestigation <strong>of</strong> a theodolite results in a maximum error <strong>of</strong> 0.005 mrad that is caused bywobble. Finally, it should be mentioned that not only is the vertical axis affected byhorizontal axis can also be influenced.the vertical axisthe wobble, but the3.4.3 Error <strong>of</strong> Collimation AxisThe ideal construction <strong>of</strong> the collimation axis <strong>of</strong> a theodolite should beGeosystems
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