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

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40323 o.o; 50545 aT [jjs] 1.0().2 St[s] :1.20 :1.28 2.49 osi().02 ().06 0.02100 5. Kinematic Laser Scanningcomputer is derived as follows. A first time tag is stored, when the rotation is started. And a second timetag is stored, when the rotation is stopped. The difference of these two time pointsdefines the total time t.However, there is an uncertainty in this total time. A delay is obviously present, especially between startingthe rotation, defined by clicking a button 'start', and reaching the specified angular velocity, defined bycounting the number of vertical profiles. This time delay St is a specific constant for each angular velocityand can, therefore, be modeled mathematically.The modified relation is:T = t-St(5.11)Considering Equation (5.11), an adjustment problemcan be formulated. The observation is the total time tand the unknowns are the rotation time T as well as the time delay St. Based on the treatment of the numberof rotations n, a different adjustment problem is achieved: either (1) Gauss-Markov, i.e. n represents aconstant, or (2) Gauss-Helmert, i.e. nrepresents an observation. The resulting functional models are:f(t,CÜ,St)t = n-T + St(5.12)f(t,n,uj,6t)(t -St)-(n-T)=0(5.13)Both adjustment problems yieldthe same results. Theadvantageof Gauss-Markov is that no initial valuefor the unknown is required. In addition, Gauss-Helmert needs initial values. To determine the unknownrotation time T, several measurements were carried out. They cover a total time of one minute, ten minutesand one hour. Table 5.8 gives an overview of both the measurements and the results of the adjustments.Table 5.8: Results of both types of adjustment for deriving the rotation time T and the time offset St indirectly. Aprecision for the rotation time T 'of aT « 1 ms can be seen.12.5 rps 25 rps 33 rpsn t[s] n t[s] n t[s]730 59.012 1422 59.710 1909 58.343728 58.819 1426 59.854 1909 58.278lmin 728 58.874 1426 59.694 1909 58.311726 58.673 1426 59.837 1911 58.391727 58.722 1426 59.759 1913 58.4237433 599.433 14872 599.672 19619 599.3687435 599.552 14866 599.369 19616 599.18110min 7435 599.541 14879 599.934 19617 599.1807433 599.361 14868 599.523 19617 599.2127439 599.912 14947 602.704 19613 599.06844688 3603.738 89382 3603.859 117975 3603.51044693 3604.002 89391 3604.370 117973 3603.44760min 44691 3603.802 89382 3604.538 117971 3603.52644691 3603.980 89408 3605.488 119940 3663.51744691 3603.898 89382 3603.914 117973 3603.478T[s] 0.080638 0.0
of0.000001s5.2 Rotation Time of Rotating Mirror of Laser Scanner 1015.2.3 Discussion and ComparisonThe rotation time T of the rotating mirror were derived by two independentmethods. The direct methodrequires a more careful consideration of different influencing parameters caused by the use of two photodiodes.The autocollimation thereby defines the main problem, which is to achieve the claimed precisionfor the rotation time T. Comprehensive considerations regarding different parameters for carryingautocollimation yield acceptable results. On the contrary, the indirect method onlyout thedeals with the numberof full rotations and the total time. By using the tools of adjustment the rotation time T as well as the specifictime delay St for the three supported angular velocities can be derived indirectly. These time delaysfurther interest in performing kinematic applications.are ofTable 5.9 summarizes the results and derives a mean value for the rotation time T.It can be seen that amaximal difference of 5 /xs was achieved between the two methods. The claimed precision was not achievedcompletely,but the results are close.Table 5.9: Comparison of the results of both methods deriving the rotation time T. Homogeneousmaximum difference o/5/xsbetween the direct method and the indirect method can be seen.results with aRPSDirect MethodIndirect MethodMeanTifs]T2[s]T[s]12.5 0.080635 0.080639 0.08063725 0.040318 0.040323 0.04032033 0.030544 0.030544 0.030544Finally, a short discussion shall be presented to clarify the meaning of (1) a precision and (2) a systematicerror of 1 /xs for the rotation time T. If the rotation time has a precision of 1 /xs, then the 'true' value isoscillating around the derived value of 1 /xs. In addition, a systematic deviation of the derived value fromthe 'true' value means that with a growing measuring time, the error caused by the systematic1 /xs is increasing. Supposing a velocity—of v « 0.2deviation ofa test trolley on which the laser scanner is mounted,the observation time can be estimated at which an error in the position of the test trolley of 1 mm is achieved.In this example, each rotation generates an error of As = v At = 0.2 .= 0.0002 mm. Thismeans 5000 rotations yield the supposed position error of 1 mm. ConsideringT the observation time covers a time period of 2.5 min upthe different rotation timesto 6.7min. In terms of a file size for a laser scanof 2.5 min, depending on the scan resolution, several hundreds of Megabytes up to some Gigabytes areobtained.In summary, three rotation times T are derived with high precision. Based on the desired spacing betweentwo adjacent vertical profiles an appropriate velocity of the test trolley has to be chosen. Additionally, thespacing can also be influenced by selectinganother rotation time T. On the contrary, the scan resolutionwithin each vertical profile is only correlated to the sampling interval and cannot be changed by the velocityof the test trolley or by the rotation time. Considering a mean velocity of 0.2—, two adjacent vertical profileshave a spacing of• 1.6cm (for ui k, 0.08s),• 0.8 cm (for ui k, 0.04 s), and• 0.6cm (for ui k, 0.03s).In general, there are three different parameters to achieve the most appropriate point densitylaser scanning: the rotation time, the velocity of the test trolleyprofile.for kinematicand the scan resolution within each vertical
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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
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1.2 Motivation 3Precision [m10~1 "1
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6 1. Introduction
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8 2. Components of Terrestrial Lase
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10 2. Components of Terrestrial Las
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24 3. Calibration of Terrestrial La
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'28 3. Calibration of Terrestrial L
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"[m] of system 90%) 3540 distance b
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!36 3. Calibration of Terrestrial L
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138 3. Calibration of Terrestrial L
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Page 60 and 61: 50 3. Calibration of Terrestrial La
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
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Page 112 and 113: 102 5. Kinematic Laser Scanning5.3
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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 136 and 137: acquisitiondescribingFinally, thatM
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
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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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