40 3. <strong>Calibration</strong> <strong>of</strong> <strong>Terrestrial</strong> <strong>Laser</strong> <strong>Scanner</strong>The results <strong>of</strong> the derived distances as well as the precision are shown in Figure 3.19.The settings<strong>of</strong> thedistance measurement match the settings chosen for the investigation <strong>of</strong> the distance measurement in the'static mode'. The results can be interpretedas follows:• Reflectivity values influence the distance detected bythe laser scanner.• Distances are not constant within the observation period <strong>and</strong> vary within the range<strong>of</strong> millimeters.• St<strong>and</strong>ard deviations show a constant precision within the observation period. The less the reflectivity,the worse the precision, accordingto SNR.In summary, the long-term stability showed no systematic effects <strong>and</strong> no correlations due to thermal heatingeffects. The amplitude <strong>of</strong> the distance variation is about 2 mm for each reflectivity. Surprisingly,the <strong>of</strong>fsets<strong>of</strong> the distances for the different reflectivity values are <strong>of</strong> several millimeters. However, the investigation <strong>of</strong>the 'static mode' concluded that a variation <strong>of</strong> several millimeters may be present, cf. Figure 3.12.3.0503.048-90% (white)-60% (grey)20% (dark grey)É 3.046.2 3.0443.0423.04020 40 60 80 100time [min]120 140 160 180302.590% (white)60% (grey)20% (dark grey)E_| 2.0en1 5AJ'AAA^^A AT^Ä' runnwv wvuw1.020 40 60 80 100time [min]120 140 160 180Figure 3.19: Development <strong>of</strong> the distance measurement system over a time period <strong>of</strong> 3 h. The variations <strong>of</strong> thedistances (top) <strong>and</strong> the variations <strong>of</strong> the precision (bottom) are shown.3.2.4 Frequency StabilityThe determination <strong>of</strong> distances is based on the modulation <strong>of</strong> carrier frequencies,cf. Section 3.2. A variationin the frequency directly influences the distance measurement. The variation can be <strong>of</strong> two different types:a long-term constant deviation <strong>of</strong> the real frequency to its nominal frequency<strong>and</strong> a short term variation.
3.2 Distance Measurement System 41The first one has to be proven by making periodic distance calibrations, called scale factor, <strong>and</strong> are causedbythe oscillator. Thesecond one can have different reasons that are caused by the environment such astemperature changes inside <strong>and</strong>/or outside the laser scanner.Variations in frequency results in variations in the distance measurements. However, it is not possible todistinguish between variations in distances <strong>and</strong> variations in the frequency because several parametersinterfere with each other <strong>and</strong> lead to distance variations, e.g.conditions, properties <strong>of</strong> the target (such as colour, material, roughness), angleadditive constant, scale factor, atmospheric<strong>of</strong> incidence.Thus, thedetermination <strong>of</strong> frequency variations has to be done directly by using an electronic unit for frequencymeasurements, cf. Section 3.1.4.The important frequency for the resolution <strong>of</strong> the distance measurement system is the modulated frequency<strong>of</strong> the fine channel component, i.e. high frequency signal 'hfs'. Thus, the investigationis focused on thismodulation frequency. In the experimental setup, the laser beam is aligned towards the diode, the signal <strong>of</strong>the frequency is detected <strong>and</strong> the real frequency is derived, cf. Figure 3.6. The investigation was performedwithin an observation period <strong>of</strong> nearly three hours with a samplinginterval <strong>of</strong> one minute. One assumesa time-dependent <strong>and</strong> temperature-dependent behaviour. Thus, the temperatureinside the laser scanneris recorded additionally. The temperature <strong>of</strong> the environment is constant because the investigation wascarried out in an air-conditioned laboratory.transmitter temperaturedifference to nominal frequency (« 45 MHz)Figure 3.20:Development <strong>of</strong> the frequency <strong>of</strong> high frequency signal 'hfs' <strong>and</strong> the internal temperature <strong>of</strong> the laserscanner.Figure 3.20 shows the time variations in both the modulation frequency 'hfs' <strong>and</strong> the internal temperature<strong>of</strong> the laser scanner, i.e. transmitter temperature. First, the deviations <strong>of</strong> the 'hfs' to the reference frequencycan be seen. Second, the 'hfs' reaches a constant frequency after nearly two hours in operation <strong>and</strong> showsa deviation to the nominal frequency <strong>of</strong> nearly 50 Hz. Third, the behaviour <strong>of</strong> the internal temperature <strong>of</strong>the laser scanner correlates to the frequency behaviour: an increasing temperature leads to a decreasingdeviation between real <strong>and</strong> nominal frequency, that means the real frequency is also increasing becausethe difference to the nominal frequency is calculated by subtracting the real frequencyfrom the nominalfrequency, <strong>and</strong> vice versa. The nominal frequency is defined by /hfs=44.781250 MHz.Based on the given nominal frequency /hfs <strong>and</strong> the real frequency / a scale factor rrif for the correction <strong>of</strong>a distance measurement caused by the difference <strong>of</strong> the real frequency to the nominal frequencycan bederived with [Joeckel <strong>and</strong> Stober, 1991]-/hfs /rrif 1 = '(3.6)/Applying this formula to all acquired real frequencies <strong>of</strong> the modulation frequency'hfs' one can achieve amaximum scale factor <strong>of</strong> 3.2 ppm. The constant frequency after two hours shows a value <strong>of</strong> —1.2 ppm. Con¬sidering the working range <strong>of</strong> the laser scanner <strong>of</strong> 50 m, the differences <strong>of</strong> the modulation frequency result