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

More documents

Recommendations

Info

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
Analysisvalueseffects, beforehandthroughTheseprocedureof the sensor, ThisNivel applicationFourier systematicareinclinatione.g. error,Data vertical 20 includes which analysis.abalance alevellingpart two-face-measurements.always Series havepresentaxiseliminatedlaseracquisitionusingscanner. producedapplied todata easily after acalibration3.4 Instrumental Errors 53is applied to a data series [Taubenheim, 1969]. The Nyquist frequency /nyq defines the maximum frequencybased on the sampling interval At, which can be detected byf=2At-(3'8)This means the real signal can only be detected if at least two samples fall within a full periodof thewavelength. All frequencies higher than the Nyquist frequency cannot be detected and lead to aliasingeffects thereby, defining the aliasing frequencies that superpose the frequency / [Taubenheim, 1969]:/, 2fnyq±f, 4fnyq±f,...(3.9)An example of aliasing is given in Figure 3.27. It can be seen that based on the samplesmore than onesine curve fits to the data. All frequencies higher than the Nyquist frequencyto aliasing effects.remain undetected and leadMore information concerning Fourier analysis, Nyquist frequency, aliasing,found in [Taubenheim, 1969] and [Welsch et al., 2000].etc. can ber«.jèX" i \iff \ l\ / \ / \1 \J'JlA f„1 10,I P p,IJ \I \j'J1I \ I \ / "\ f/- \ ( \1 \{ / \ dr",--f /"ft. 1uI\ i~^£.7Figure 3.27: Aliasing effects based on sampling: More than one sine curve fits to the samplings.The comprehensive investigations of the vertical axis wobble include several different experimental setups:(1) The laser scanner was mounted on a tribrach and then installed on a tripod and on an observationpillar.(2) The laser scanner was mounted on a granite table directly without using a tribrach.During the investigation a counter weight was attached on one side of the laser scanner to balance the massof the laser scanner (approx. 5 kg). The advantage is better symmetry in mass, but the disadvantage isthat the counter weight increases the mass of the laser scanner considerably. The assumptionis the balanceweight influences the wobble of the vertical axis in a positive way. All different data series have two thingsin common: the sampling interval At varies between 5 ° to 30 ° and the sampling rangethree to four full rotations according to 1080° and 1440°. Thus,a reasonable acquisitionvaries betweenof data series isguaranteed assuming that the wobble causes harmonic oscillations with periods of 720 ° or shorter. Themathematical description of a possible wobble of the vertical axis requires both repeatability and repro¬ducibility of the parameters characterizing the wobble: amplitude, frequency and phase angle. Comparingdata series acquired by the same setup, one also finds that the levelling errors correspondwith each other.
Page 1:
DISS. ETH NO. 17036Calibration of a
Page 5 and 6:
ZusammenfassungSeit einigen Jahren
Page 7 and 8:
ContentsAbstractiiiZusammenfassungv
Page 9 and 10:
Contentsix6.1.3 Results Ill6.2 Stat
Page 11 and 12: 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
Page 20 and 21: 10 2. Components of Terrestrial Las
Page 34 and 35: 24 3. Calibration of Terrestrial La
Page 38 and 39: '28 3. Calibration of Terrestrial L
Page 44 and 45: "[m] of system 90%) 3540 distance b
Page 46 and 47: !36 3. Calibration of Terrestrial L
Page 48 and 49: 138 3. Calibration of Terrestrial L
Page 68 and 69: Inormal axis,intersectionpoint axis
Page 76 and 77: j/-*'.-,•66 3. Calibration of Ter
Page 84 and 85: 74 4. Static Laser Scanning4.1.2 Mi
Page 86 and 87: 76 4. Static Laser ScanningOptical
Page 88 and 89: 78 4. Static Laser Scanningmaximum
Page 90 and 91: 80 4. Static Laser Scanningand gene
Page 92 and 93: 82 4. Static Laser Scanning• Ther
Page 94 and 95: 84 4. Static Laser Scanning4.3.3 NU
Page 96 and 97: 86 4. Static Laser Scanning
Page 98 and 99: 88 5. Kinematic Laser Scanningmirro
Page 100 and 101: 90 5. Kinematic Laser ScanningThe a
Page 102 and 103: 92 5. Kinematic Laser Scanninghas a
Page 104 and 105: '94 5. Kinematic Laser Scanningbeam
Page 106 and 107: —96 5. Kinematic Laser ScanningTa
Page 108 and 109: ''iI98 5. Kinematic Laser ScanningA
Page 110 and 111: 40323 o.o; 50545 aT [jjs] 1.0().2 S
Page 112 and 113:
102 5. Kinematic Laser Scanning5.3
Page 114 and 115:
—1.104 5. Kinematic Laser Scannin
Page 116 and 117:
propagationresults series Taylorter
Page 118 and 119:
108 5. Kinematic Laser Scanningonly
Page 120 and 121:
cf.aroundframe regardingsetupusinga
Page 122 and 123:
112 6. Applications of Terrestrial
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
Page 132 and 133:
Page 134 and 135:
Page 136 and 137:
acquisitiondescribingFinally, thatM
Page 138 and 139:
Page 140 and 141:
Page 142 and 143:
132 7. Summaryrange, achievable by
Page 144 and 145:
134 7. Summary
Page 146 and 147:
136 A. Imaging System of Imager 500
Page 148 and 149:
138 B. Technical Data of Imager 500
Page 150 and 151:
u140 C. Adjustment of SphereA =dfi,
Page 152 and 153:
142 C. Adjustment of Sphere
Page 154 and 155:
144 D. Electronic Circuit for Deter
Page 156 and 157:
aMulti-SensorPlatform,PhDGeodesy Sw
Page 158 and 159:
Accuracy-AeinTPS1200 AG, -Version 1
Page 160 and 161:
-GenauigkeitsbetrachtungenInvestiga
Page 162 and 163:
152 BibliographyWunderlich, T. A. [
Page 164 and 165:
List of Figures3.22 Residuals of th
Page 166 and 167:
156 List of Figures
Page 168 and 169:
158 List of Tables
Page 171:
200220072002Curriculum VitaePersona
show all

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

Create successful ePaper yourself

Delete template?

Save as template?