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

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54 3. Calibration of Terrestrial Laser Scannerby an imperfect levelling procedure, can be eliminated in two ways. First, the levellingerror results in asine curve during a full rotation about 360 °.This sine curve has to be calculated and the inclination datahave to be reduced according to this sine curve. Second, the levelling error is derived by averaging thecorresponding inclination data in the two faces. This means the data at position x and position x +180 °averaged and result in a new inclination value that represents the levelling error. The absolute lengthoriginal data is reduced byareof the180 °. Both methods yield new inclination values that should be zero via the firstmethod or a constant value, which defines the absolute levelling error, via the second method. However,if the data are different to these ideal cases, other errors in the vertical axis influencing the inclination arepresent, such as wobble of the vertical axis.Before discussing the wobble of the vertical axis with one data series as an example, a summaryof severaldifferent and independent data series will be examined with respect to the repeatability of the levellingerror acquired by the inclination sensor.Therefore, the sine curve representing the levelling errors of thesetups are calculated by using the Curve Fitting Tool Box provided by Matlab®. The results of three inde¬pendent data series including three to four repeatedmeasurements within each data series are discussed.The derived levelling error is based on the mathematical model of a sine oscillation [Matthias, 1961] andcan be expressed mathematically [Bronstein and Semendjajew, 1999] byf(x)=a sin(f x + ip). (3.10)Table 3.10: Results of the calculation of the levelling error based on the data of the inclination sensor in the x-directionand in the y-direction for different setups (A, B, C) and repeated data series (1, 2, 3) within each setup.Setup Data Series Amplitude a [mrad]Frequency fPhase Angle ip [°]xyxyxy10.401 0.4321.029 1.025305 218A20.414 0.4571.021 1.014312 22730.414 0.4441.012 1.014317 22910.476 0.4901.028 1.022123 37B20.469 0.4961.015 1.012137 4930.462 0.5061.010 1.007140 5310.271 0.2090.989 1.005344 256C20.282 0.2190.980 0.991349 26630.286 0.2120.978 0.990352 267Table 3.10 gives an overview of the calculated levellingthe x-direction and in the y-direction. The setups are independenterrors based on the data of the inclination sensor infrom each other and the inclination datawere acquired with different setups of the laser scanner, i.e. the laser scanner was set upwith and without atribrach on an observation pillar and a granite table. The homogeneity in the data series within each setupcan be seen and the levelling error appears to be repeatable because(1) the amplitudes a are nearly constant in the x-direction and y-direction within each setup,(2) the phase angles y are nearly constant in the x-direction and y-direction within each setup,(3) the frequency of the levelling error corresponds with each other and is nearly 1.000, which means aperiod of 2 tt, and(4) the angle differences of the phase angles y match up to 90° between the x-direction and the y-direction, according to the Cartesian coordinate system of the inclination sensor.
3.4 Instrumental Errors 55The inclination sensor produces reasonable data and the levelling error can be derived reliably.However,the question is whether a wobble of the vertical axis is present and whether this error is both repeatableand reproducible. Therefore, the analysis of one data series is described as an example. In this example, thelaser scanner was mounted directly on a granite table without using a tribrach, cf. Figure 3.28.This setuprepresents an ideal setup because the granite table shows no deformations or vibrations during the rotationas tripods or tribrachs normally do.Figure 3.28: Laser scanner mounted on a granite table directly without using a tribrach.On top of the laser scannerthe inclination sensor Leica Nivel 20 can be seen.Figure 3.29 shows the inclination data acquired bythe inclination sensor Nivel 20. Thelevellingerror isalready eliminated from the inclination data and the left error shows a harmonic oscillation caused by thewobble of the vertical axis. The data for the x-direction and the y-direction show similar behaviour. First, itseems that the present harmonic oscillation is repeatable because the three data series for the x-direction andthe y-direction fit each other. Second, the amplitudes of the harmonic oscillations are identical consideringthe x-direction and the y-direction. Third, the data series acquiredin the x-direction of the inclination sensorare closer to each other than the data series acquired in the y-direction of the inclination sensor. Fourth, theamplitude of the first oscillation does not fit the amplitudeof the other oscillations both in the x-directionand in the y-direction. Nevertheless, the acquired data series suggest that there is a significant frequency inthe harmonic oscillation, which can be identified by a Fourier analysis.Table 3.11: Results from the Fourier analysis of the vertical axis wobble. The values for the dominant frequency aresummarizedfor both directions of the inclination sensor, x and y.Data Series Period [°]Amplitude a [mrad]Phase Angle ip [°]xyxyxy1180 1800.133 0.115176.2 60.52180 1800.119 0.113178.7 61.23180 1800.121 0.117182.1 61.2The Fourier analysis, cf. Figure 3.30, shows a dominant frequency, which is identical in each data series andfor both directions x and y of the inclination sensor. A more precise overview is given in Table 3.11, wherethe parameters of interest ,i.e. frequency (period), amplitude and phase angle of the three data series, aresummarized. It can be seen that also the parameters amplitude and phase angle fit relatively well with eachother considering the x-direction and the y-direction, separately. The amplitude of the wobble acquired inthe x-direction also corresponds to the amplitude of the wobble acquired in the y-direction. Unfortunately,the phase angle gives an indifferent impression: the phase angle derived by the x-direction should match to
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DISS. ETH NO. 17036Calibration of a
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ZusammenfassungSeit einigen Jahren
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ContentsAbstractiiiZusammenfassungv
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Contentsix6.1.3 Results Ill6.2 Stat
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1Introduction1.1 Terrestrial Laser
Page 13: 1.2 Motivation 3Precision [m10~1 "1
Page 16 and 17: 6 1. Introduction
Page 18 and 19: 8 2. Components of Terrestrial Lase
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—1.104 5. Kinematic Laser Scannin
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propagationresults series Taylorter
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108 5. Kinematic Laser Scanningonly
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cf.aroundframe regardingsetupusinga
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112 6. Applications of Terrestrial
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acquisitiondescribingFinally, thatM
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132 7. Summaryrange, achievable by
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134 7. Summary
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136 A. Imaging System of Imager 500
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138 B. Technical Data of Imager 500
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u140 C. Adjustment of SphereA =dfi,
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142 C. Adjustment of Sphere
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144 D. Electronic Circuit for Deter
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aMulti-SensorPlatform,PhDGeodesy Sw
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Accuracy-AeinTPS1200 AG, -Version 1
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-GenauigkeitsbetrachtungenInvestiga
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152 BibliographyWunderlich, T. A. [
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List of Figures3.22 Residuals of th
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156 List of Figures
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158 List of Tables
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200220072002Curriculum VitaePersona
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