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 ...
62 3. Calibration of Terrestrial Laser ScannerTable 3.13:Results of the adjusting hyperbola concerning the error of the collimation axis in horizontal direction.Parameter a defines for the gradient and parameter b defines the limit.Data Series a[°/m] b[°] aa[°/m] *fe[°]sphere 12 cm (1) 0.064 -0.016 0.0025 0.0007sphere 12 cm (2) 0.049 -0.016 0.0022 0.0006sphere 15 cm (1) 0.046 -0.014 0.0007 0.0002sphere 15 cm (2) 0.038 -0.014 0.0034 0.0010with the ranges and the difference tp of the horizontal directions in two faces corrected by the twofoldcollimation error. The resulting values for the eccentricity are summarized in Figure 3.35. The eccentricitye can be described by a mean value of 0.9 mm and a precision of 0.1 mm. The mean value is based on dataup to 15 m because the influence of the eccentricity decreases and then reaches the same degree of precisionas the precision of the angle measurement system, cf. Table 3.12.2.0eccentricity (horizontal component)>| 0.0co>uo4> -10— 12cm (1)—15cm (1)—12cm (2)—15cm (2)"200 2 4 6 8 10 12 14 16 18 20range [m]Figure 3.35: Eccentricity of the collimation axis in horizontal direction. The eccentricity of the collimation axis inthe horizontal direction is derived by using spheres with the diameters of'12 cm and 15 cm based on two independentsetups (1) and (2).In summary, the error budget of the collimation axis, consisting of the collimation error and the eccentricity,was derived. Considering the influence of both errors shown in Figure 3.34, it can be seen that the adjustinghyperbolaeintersect the abscissa. This means at the intersection point, about 3 m to 4 m), the error of thecollimation axis has no influence on the horizontal direction. The interpretationis the collimation error andthe eccentricity have opposite signs and they compensate each other. However, the most important aspectis that the influence of the error of the collimation axis is not constant for close ranges. The correction of thehorizontal angle data has to be completed separately according to the range and its error budget.Vertical ComponentSecond, the component in vertical direction is discussed. The results obtained by the two independentsetups are shown in Figure 3.36. It can be seen that the results of each setup obtained by the two sphereswith different diameters match each other.However, the results of the two independent setupseach other. With the exception of the first two meters, no systematic effects, depending on the range,do not fitcan beseen. The lines approximately describe a constant line. Thus, a significant influence of an eccentricity of thecollimation axis in the vertical direction cannot be seen. The constant line defines a collimation error in thevertical direction, which can be interpreted as an index error in the vertical encoder. Further assumptionsof the factors that influence the orientation of the laser beam concern an offset between the outgoing laserbeam and the encoder readings,variations on the rotation time and wobble effects of the horizontal axis.
-associated'tan(v).the3.4 Instrumental Errors 63Nevertheless, the index errorappears to be constant within each setup and is therefore, repeatable. How¬ever, in an independent setupwith a restart of the laser scanner-the collimation axis is different and is therefore, not reproducible.influence of the error ofsetup (1) and setup (2)—12cm (1)—15cm (1),,,,,,12cm (2)"15cm (2)10 12 \Arange [m]20Figure 3.36: Influence of the errors of the collimation axis in vertical direction. Thedifferences of the vertical direc¬tions in two faces derived by using spheres with diameters of 12 cm and 15 cm are shown for two independent setups(1) and (2).3.4.4 Error of Horizontal AxisThe error of the horizontal axis has to be discussed in a similar manner to the error of the collimation axis.The error budget consists of an eccentricity in the horizontal axis and a horizontal axis error. The horizontalaxis error is defined as the horizontal axis not being normal to the vertical axis. The steeper the line of sightthe greater is the influence of the horizontal axis error in the horizontal direction. The determination of theerror of the horizontal axis iby [Deumlich and Staiger, 2002]:is described in the literature. The formula for the calculation can be expressedAhzsin(v)(3.14)Therefore, the collimation error c, the difference of the horizontal directions Ahz, derived by measurementsin two faces, and the vertical angle, corrected by the index error, have to be known. The formula describedis an approximation that is sufficient with the exception of very steep lines of sight (< 1 ° ). A comprehensivediscussion of the axis errors of theodolites including a derivation of exact formulas, especially for the tiltingaxis error, can be found in [Stahlberg, 1997].The experimental setups for the determination of the error of the horizontal axis were performed by scan¬ning spheres in two faces. The spheres were distributed in a vertical plane to generate varying lines of sightregarding the vertical direction. The slope distances differ between 1.5 m and 5 m. The lines of sight covera field of view between 15° and 164° in the vertical direction. The calculations were carried out usingEquation (3.14).Since within close ranges, up to 15 m, the influence of the error of the collimation axis isnot constant, cf. Section 3.4.3, the values for the parameter c are varying. The corresponding influence ofthe error of the collimation axis then has to be applied.The results for two different experimental setups in Table 3.14 show an error in the horizontal axis of up toan absolute value of 0.08 °, but the values differ substantially and the signs change. Building an average ofthe values, an error of approximately 0.045 °is derived.Since the setups for the investigation procedure were not optimal, the results have to be interpreted in acritical manner. Short ranges did not allow for the assessment of the error budget of the horizontal axis, es-
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-associated'tan(v).the3.4 Instrumental Errors 63Nevertheless, the index errorappears to be constant within each setup <strong>and</strong> is therefore, repeatable. How¬ever, in an independent setupwith a restart <strong>of</strong> the laser scanner-the collimation axis is different <strong>and</strong> is therefore, not reproducible.influence <strong>of</strong> the error <strong>of</strong>setup (1) <strong>and</strong> setup (2)—12cm (1)—15cm (1),,,,,,12cm (2)"15cm (2)10 12 \Arange [m]20Figure 3.36: Influence <strong>of</strong> the errors <strong>of</strong> the collimation axis in vertical direction. Thedifferences <strong>of</strong> the vertical direc¬tions in two faces derived by using spheres with diameters <strong>of</strong> 12 cm <strong>and</strong> 15 cm are shown for two independent setups(1) <strong>and</strong> (2).3.4.4 Error <strong>of</strong> Horizontal AxisThe error <strong>of</strong> the horizontal axis has to be discussed in a similar manner to the error <strong>of</strong> the collimation axis.The error budget consists <strong>of</strong> an eccentricity in the horizontal axis <strong>and</strong> a horizontal axis error. The horizontalaxis error is defined as the horizontal axis not being normal to the vertical axis. The steeper the line <strong>of</strong> sightthe greater is the influence <strong>of</strong> the horizontal axis error in the horizontal direction. The determination <strong>of</strong> theerror <strong>of</strong> the horizontal axis iby [Deumlich <strong>and</strong> Staiger, 2002]:is described in the literature. The formula for the calculation can be expressedAhzsin(v)(3.14)Therefore, the collimation error c, the difference <strong>of</strong> the horizontal directions Ahz, derived by measurementsin two faces, <strong>and</strong> the vertical angle, corrected by the index error, have to be known. The formula describedis an approximation that is sufficient with the exception <strong>of</strong> very steep lines <strong>of</strong> sight (< 1 ° ). A comprehensivediscussion <strong>of</strong> the axis errors <strong>of</strong> theodolites including a derivation <strong>of</strong> exact formulas, especially for the tiltingaxis error, can be found in [Stahlberg, 1997].The experimental setups for the determination <strong>of</strong> the error <strong>of</strong> the horizontal axis were performed by scan¬ning spheres in two faces. The spheres were distributed in a vertical plane to generate varying lines <strong>of</strong> sightregarding the vertical direction. The slope distances differ between 1.5 m <strong>and</strong> 5 m. The lines <strong>of</strong> sight covera field <strong>of</strong> view between 15° <strong>and</strong> 164° in the vertical direction. The calculations were carried out usingEquation (3.14).Since within close ranges, up to 15 m, the influence <strong>of</strong> the error <strong>of</strong> the collimation axis isnot constant, cf. Section 3.4.3, the values for the parameter c are varying. The corresponding influence <strong>of</strong>the error <strong>of</strong> the collimation axis then has to be applied.The results for two different experimental setups in Table 3.14 show an error in the horizontal axis <strong>of</strong> up toan absolute value <strong>of</strong> 0.08 °, but the values differ substantially <strong>and</strong> the signs change. Building an average <strong>of</strong>the values, an error <strong>of</strong> approximately 0.045 °is derived.Since the setups for the investigation procedure were not optimal, the results have to be interpreted in acritical manner. Short ranges did not allow for the assessment <strong>of</strong> the error budget <strong>of</strong> the horizontal axis, es-
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