# Assessment of Laser Galvanometer Scanning System Accuracy Using Ball-Bar Standard
## 3 Results and Discussion  
Projector software provided the position error value of the reference spheres as vertical (dV) and horizontal (dH) deviations in the local coordinate system and their combination. Deviations were calculated as the difference between measured and nominal positions of  
Figure 4: Ball-bar positions in the projector workspace: 1—positions of the standard; 2—position of the device. Figure 3: Compared standards: (**a**) calibration board and (**b**) ball-bar standard. spheres and given as absolute values. Nominal positions were taken directly from the CAD and could not be modified. Thus, the CAD model of the reference object must be built based on the calibrated positions of references spheres in the local coordinate system. The view of the control window with the listed deviations and the geometric error representation is shown in Figure 5. The spatial deviation, defined as 2D in Figure 5, was used to assess the system's accuracy. Figure 6 represents the CAD model of the used ball-bar standard in the laser projector software. After uploading the model, it was necessary to define the ball-bar alignment in the projector's virtual space. It is done by linking the chosen features of the CAD model with the corresponding elements of the object. It is recommended by the manufacturer to choose at least six alignment points. The spheres 0, 9, 14, 15, 19, 30, and the outer sphere (off the axis of the others) were used for the coordinate system alignment. The alignment is performed by scanning specific spheres and fitting the object to the CAD model. By identifying the same features on the CAD model and the object, the system performs a least squares method to fit the object to the model. According to the CAD model, the projector software takes the directions and zero point of the local coordinate system. Further measurements are carried out in the local coordinate system. The research involved measuring a selected length standard following the recommendations of ISO 10360. The measuring station consisted of a Faro laser projector model TracerSl with BuildIT 2019 software, a 3000 mm ball-bar length standard, and a temperature data logger. First, the workspace of the system was defined and marked. The projector was mounted on a dedicated tripod which remained stationary throughout the experiment. Each time the ball-bar was repositioned so that the positioning requirements were met as closely as possible. Due to limitations in the operation of the image capturing head and limitations of the software used, not all the required standard positions were measured. Spheres numbered 0, 2, 9, 16, 23, and 30 were used to measure errors. The sequence and the method of determining the length follow the recommendations of the ISO 10360:1  
Figure 5: System deviations: (**a**) software output and (**b**) geometrical interpretation of the result. Figure 6: CAD model of ball-bar standard. 12 standard. In order to improve the optical properties, the scanning spray was used. This makes it possible to obtain a non-reflective surface while not affecting the measurement results' quality. The ambient temperature during the test was 24 \(\pm\) 2 \({}^{\circ}\)C. For each tested position, the standard was placed in the center of the projector's field of view at a distance of 4.6 m from the system (Figure 4). The results of the measurements are presented graphically (Figures 7-11) and in tabular form (Tables 2-5). An error measurement was performed on six reference spheres for each of the projector workspace axes tested. Three series of such measurements were made. The following values can be found in the tables:  
* Nominal--nominal value of the position of the test sphere (in line with the standard main direction)
* Error--measurement error
* R--range: \[\text{R}=\text{max(Ei)}-\text{min(Ei)};\] (1)
* MPE--Maximum Permissible Error: \[\text{MPE(E0)}=\pm\text{B}\] (2) where B--maximum error value. The analysis of the results has shown that the increase of the tested length does not cause the error increase.