# Method for Accuracy Assessment of the Length Measurement Unit of Laser Tracking Systems
## 2 Materials and Methods  
The subject of the research is the Leica Laser Tracker LTD 840 laser tracking system. It is a device that utilizes both a laser interferometer (IF) and absolute distance meter (ADM) separately. In this particular model, the distance measurements are always carried out using IF, while ADM is used only for obtaining a start value for IF, for example, when the connection between the device and a target has been lost. The software used for control during the tests was the emScon program provided by the manufacturer. Due to the fact that it was not possible to access the length values and the values of the horizontal \(H\) and vertical \(V\) angles from the software level (alternative programs were also checked), and due to the need to automate the measurement process, a new program was created to acquire the values sent to the controller. The program was written using the libraries included in the Software Development Kit provided by the manufacturer. According to the latest calibration certificate, the maximum permissible errors of the tested system are defined by Equation (1) for the maximum permissible error (\(MPE\)):  
\[MPE_{\text{E}}=(25+35\,^{\star}\,L/1000)\ \upmu\text{m}, \tag{1}\]  
where:  
\(L\)--measured length in millimeters. The equation above determines the accuracy of the entire system, but the accuracy of the interferometer itself has not been determined--it has never been calibrated separately as a system component. The chosen parameters describing the system's accuracy are shown in Tables 1 and 2. Since the accuracy of the interferometer in the laser tracker system is unknown (it is known to be much better than the accuracy of the entire system), no condition can be formulated as to the requirements of the reference device. For this reason, one of the most accurate systems available on the market was used. The reference interferometer used in the study is the Renishaw XL-80 (after retrofitting the system from the ML10 Gold model), whose length measurement uncertainty is defined as 0.5 ppm, which can be represented by Equation (2):  
\[\text{U(L)}=0.5\ ^{\ast}\ L/1000\ \mu\text{m}, \tag{2}\]  
where:  
\(L\)--measured length in millimeters. The Renishaw interferometer was calibrated in Polish NMI both in terms of frequency and measured length. Due to the assumptions regarding a virtual machine for the laser tracking system, described in Section 1, the interferometer responsible for determining the distance had to be tested independently of the other systems included in the laser tracker system. Therefore, it is not enough to use a standard calibration method used for laser tracking systems such as the methodology described in tenth part of the ISO 10360 series [25] as they are focused on the accuracy of the entire system, and not separating specified components. All procedures described in this document involve angular movements of laser tracker components, so it was not suitable for conducting the research that is presented in this paper. To achieve the desired effect, it was necessary to ensure a fixed value of both angular encoders and the environmental conditions correction system. As the values of the horizontal \(H\) and vertical \(V\) angles are part of the set of parameters, based on which the coordinates of the measuring point are calculated, they cannot be excluded from the test; however, ensuring their fixed values allows the measurement result to be independent of errors coming from the angle measuring system. The fixed value of encoders was ensured by switching off the motors responsible for the rotation of the mirror directing the beam to the measuring point. The measurement setup used in the experiment is similar to the setup described in [17], in which the displacement of one retroreflector is measured by both reference and tested systems. The second experimental setup presented in [17] utilizes two retroreflectors, however, one of the objectives of the developed method was to eliminate the adverse effects of using two retroreflectors in the study.