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

70 3. Calibration of Terrestrial Laser Scanner3.6.1 Single Point PrecisionThe precision of one single point is derived by two methods. The first one is based on the identified preci¬sion for the distance component (ss) and the encoder components for the horizontal direction (shz) and thevertical direction (sv). A theoretical error budget for one single point (sp) can be calculated by:sp = ^jsl+ s2y + s\ (3.15)withsxsyszO •ss= s tan{2> Shz) (3.16)= s tan{2> sv)For the precision of the x-component, the trifold precision,i.e. standard deviation, is used since it refersto 99.9% of measurements. For the y-component and the z-component,the distance s has to be takeninto account as well as the trifold precision of the angle measurement system.The second method usesthe acquired point cloud to derive a single point precision. Spheres were scanned and the center pointswere calculated by applying the adjustment algorithm, cf. Section 3.1.5. The resultingmean error of theunit weight (so) defines the precision of one single coordinate. Thus, the precision of one single pointcontaining three coordinates can be determined by:sp = a/3•s0. (3.17)The spheres were positioned along the calibration track line in varying ranges so that the development ofthe precision of one single point can be derived. Figure 3.45 shows the results obtained by the two differentmethods.Since the second method can only be applied up to ranges of approximately 20 m, the upperfigure is also limited up to this range. Reasons for the limited range are the quality and the quantity of theacquired point cloud decrease rapidly with the range, cf. Section 3.2.2. The precision obtained by the secondmethod is verified using two spheres with different diameters, i.e.12 cm and 15 cm. The values lie about5 mm and fit with each other. In addition, the theoretical precision based on the first method increases withthe range. The lower figure shows the development of the precision. The noise of one single point reachesvalues in the order of some centimeters in ranges of more than 30 m.In summary, it can be concluded that the two methods fit each other and show a precision for one singlepoint of less than 1 cm up to a range of 20 m. The development of the theoretical precision gives an impres¬sion of the resulting precision in ranges of more than 30 m, which increases up to 2 cm. The difference in thetwo methods is that the derived theoretical precision is based on an angle of incidence of 90 °, which meansthe laser beam hits the object normal. A variation of the angle of incidence leads to lower distance precisionand also results in lower single point precision, cf. Section 3.5.2. On the contrary, the method using thespheres takes the varying angle of incidence into account. Furthermore, the investigationcan be continuedfor different reflectivity values. The spheres used are white in colour, approximating a reflectivityAlso, the distance accuracy required for the first method refers to a reflectivityof 90 %.of 90 %.3.6.2 Accuracy of Modeled Objects (Spheres)The accuracy of modeled objects is shown exemplarily by considering the calculated center point of spheres.The spheres with two different diameters, i.e. 12 cm and 15 cm, were positioned along the calibration trackline and were scanned with three different scan resolutions.Based on the acquired data, the center point