# Method for Accuracy Assessment of the Length Measurement Unit of Laser Tracking Systems
## 3 Results  
The results of both experiments (motors inactive and motors active) are presented in the diagrams below. The results shown in Figures 3-5 show that the individual error values of the laser interferometer used in the tested laser tracker system range from \(-1\)\(\upmu\)m to \(1\)\(\upmu\)m. Additionally, the vast majority of the range values presented are smaller than \(1.5\)\(\upmu\)m or slightly higher than that value. It should also be noted that the distribution of errors for all measurement series is similar. A distribution of the measurement errors together with the spread values can be used to simulate the measurement of a point in a virtual machine model for a laser tracking system. Figure 3: Averaged error values during measurement: (**a**) increasing direction, inactive motors; (**b**) decreasing direction, inactive motors; (**c**) increasing direction, active motors; (**d**) decreasing direction, active motors. Error bars show the standard deviation value. As can be seen in Figure 3, similar characteristics were obtained for both measurement directions as well as for both tested states of the motors. In all cases, the dispersion of obtained results increased with an increase in the tested length, however, bigger dispersion values can be observed for the active state of the motors. It can be observed in Figure 4 that the hysteresis practically does not exceed more than 1 \(\upmu\)m and generally bigger values can be obtained in an inactive state of the motors. Analyzing the results shown in Figure 5, it can be concluded that range values grow with increasing length and, again, generally, they are bigger for the active state of motors. Therefore, it can be assumed that switching off the motors during the tests may increase the stability of the obtained results. Based on the above model and the data obtained in the described research, which will serve as input data for the Monte Carlo method simulations, it is possible to simulate the distance measurement of the laser tracker interferometer. Multiple sampling from the obtained distributions allows the determination of the uncertainty of a single measurement based on the standard deviation from the simulated series of measurements. Monte Carlo method simulations use as an input the experimentally determined parameters of probability density function. For lengths in which the interferometer error was not determined directly, the data from the nearest length that was used during experiments will be taken (for example, if the simulation is carried out for L = 523 mm, the input data obtained experimentally for L = 500 mm will be used). The scaled and shifted t-distributions can be used as probability functions due to the small amount of input data. Figure 4: Hysteresis error for measurements with motors turned off and on. Figure 5: The values of the intervals between cycles in both directions: (**a**) inactive motors; (**b**) active motors. Simulated uncertainty values attributed to laser interferometer may be used as one of the uncertainty contributors in a virtual model of the laser tracker system. The method of simulating the uncertainty of laser interferometer measurements with the Monte Carlo method and the results obtained with its application are presented below. For this purpose, a reconfigurable ball-bar was used. One of its main features is the possibility of using laser tracking systems equipped with a spherical retroreflector (SMR) for research. For this purpose, special sockets were designed that are mounted on a thermally non-expandable base pin. Each socket consists of three fixed centering balls and a central sphere that can be detached from the socket (Figure 6). The size of the central sphere corresponds to the size of the retroreflector used in the test (1.5 inches). Central spheres mounted on sockets along the bar allow the performance of calibration on a standard high-accuracy CMM.