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

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