# Method for Accuracy Assessment of the Length Measurement Unit of Laser Tracking Systems
## 2 Materials and Methods
This solution introduces many errors to the study, related to, e.g., the movement of the platform the retroreflectors are mounted on, or the non-parallelism of the axis of movement of the two reflectors. Moreover, it should be noted that both systems cooperate with other retroreflectors. Even if they are of the same type, their accuracy may differ. The process of determining these errors is long and complicated and the results may have a significant impact on the test result, as described in [16]. In order to eliminate these effects, a method was developed in which both the tested and the reference system work with the same retroreflector. A precision guide with a mobile platform was used as the system implementing the retroreflector's movement, but in this case, there is no need to estimate errors related to the platform's movement, mainly caused \begin{table}
\begin{tabular}{c c} \hline \multicolumn{2}{c}{**Manufacturer Specifications of Length Unit**} \\ \hline wavelength & 633 nm \\ distance accuracy (\(\pm 1\ ^{\circ}\)C, \(\pm 3\) mmHg) & \(\pm 2.5\) pm \\ \hline \end{tabular}
\end{table} 
Table 1: The manufacturer specifications of length unit of laser tracker Leica LTD 840. \begin{table}
\begin{tabular}{c c} \hline \multicolumn{2}{c}{**Manufacturer Specifications of Angular Unit**} \\ \hline angular resolution & 0.14 arcsec \\ measurement accuracy (of a static target) & \(\pm 10\) μm/m \\ \hline \end{tabular}
\end{table} 
Table 2: The manufacturer specifications of angular unit of laser tracker Leica LTD 840.  
by geometric errors of the guide, since the effects resulting from the movement affect both the tested and the reference system in the same way. The use of a common retroreflector also required using a common beam splitter. To this end, a splitter was used, constituting the instrumentation of the reference interferometer with an attached reference beam retroreflector. The splitter was set at an angle to the measurement axis to facilitate establishing the base point in the laser tracker system. Due to the different method of guiding the beam to the retroreflector in both systems, there are no disturbances in the wave interference of these systems. The experimental setup diagram is shown in Figure 1 while the test station with the measuring track is shown in Figure 2a,b. The study was carried out in an air-conditioned room at small intervals during one day. During the tests, the values of environmental parameters were monitored using an external thermohygrometer and additional temperature sensors along the measurement path. The average values of the environmental parameters recorded during the test were as follows: temperature 21.11 \({}^{\circ}\)C, humidity 55%, pressure 993 hPa. The changes in humidity and pressure were negligible, and the temperature fluctuations did not exceed a value \(\pm\)0.3 \({}^{\circ}\)C from the average, while the temperature distribution was the same along the measurement path. The study range was 0 to 1500 mm with measuring points spaced every 50 mm. In order to test the hysteresis, the heading on the points was carried out successively until the end of the measuring range, and then the points were measured in the opposite direction. After the final point was measured in the \"increasing direction\", an auxiliary movement was carried out for 1550 mm (without measurement at this point), then the measuring reflector was moved by a distance of 1500 mm (the opposite way--decreasing direction)  
Figure 1: The simplified diagram of test station: red line—laser tracker beam, orange line—reference interferometer beam. Figure 2: Test station—retroreflector (1), beam splitter (2), tested system (3), reference system (4) and linear guide (5); (**a**) top view; (**b**) view from the reference system side. and the first measurement was made at this point concerning the \"decreasing direction\". This cycle was repeated ten times.