# Assessment of Laser Galvanometer Scanning System Accuracy Using Ball-Bar Standard
## 3 Results and Discussion
Therefore, the following presentation of the accuracy of the system was accepted:  
\[\text{MPE(E0)}=\pm 0.5\text{ mm} \tag{3}\]  
For the X-axis, the minimal average error of 0.02 mm was obtained for the 2300 mm nominal. Below this length, the error was up to 0.2 mm. The range of results remained between 0.03 mm and 0.04 mm. Error increases significantly to 0.4 mm, also the range nearly triples to 0.09 mm for the 3000 mm nominal. The characteristic of the X-axis measurement errors is shown in Figure 7.  
The minimal average error of 0.1 mm was obtained for the Z-axis for 1600 mm and 3000 mm lengths. The range of the results remained at 0.04 mm and 0.03 mm, respectively. For the other checked lengths, the average range was 0.07 mm. The characteristic of the Z-axis measurement errors is shown in Figure 8.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Nominal [mm]** & **Error [mm]** & **R [mm]** & **MPE [mm]** \\ \hline  & 0.076 & & \\
199.833 & 0.070 & 0.029 & \\  & 0.099 & & \\ \hline  & 0.162 & & \\
899.812 & 0.122 & 0.040 & \\  & 0.127 & & \\ \hline  & 0.033 & & \\
1599.690 & 0.050 & 0.040 & 0.500 \\  & 0.073 & & \\ \hline  & 0.040 & & \\
2299.351 & 0.010 &Figure 3:0 \(Z-\)axis measurement error characteristic. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Nominal [mm]** & **Error [mm]** & **R [mm]** & **MPE [mm]** \\ \hline  & 0.256 & & \\
199.833 & 0.268 & 0.064 & \\  & 0.319 & & \\ \hline  & 0.262 & & \\
899.812 & 0.294 & 0.075 & \\  & 0.337 & & \\ \hline  & 0.125 & & \\
1599.690 & 0.085 & 0.041 & 0.500 \\  & 0.109 & & \\ \hline  & 0.299 & & \\
2299.351 & 0.393 & 0.094 & \\  & 0.334 & & \\ \hline  & 0.100 & & \\
2999.249 & 0.116 & 0.025 & \\  & 0.091 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Measurement errors of the Z-axis (vertical direction). Figure 7: X\(-\)axis measurement error characteristic. For the diagonal XZ1, the error characteristics oscillated between 0.1 mm and 0.2 mm. The minimal average error of 0.06 mm was obtained at the end of the standard. The range of results remained at the level of 0.03 mm. For the lengths 900 mm and 3000 mm, the value increased to 0.08 mm and 0.1 mm, respectively. The obtained characteristic (Figure 9) has the most stable form in relation to the other axes characteristics. The results for the XZ2 diagonal showed the most significant error values for the 200 mm nominal, averaging 0.4 mm. The error decreased to 0.1 mm as the center of the measurement space neared. Further into the measuring range, the average error remained at 0.2 mm. The range of values was between 0.04 mm and 0.06 mm. The measurement error characteristic of the XZ2 axis is shown in Figure 10. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Nominal [mm]** & **Error [mm]** & **R [mm]** & **MPE [mm]** \\ \hline  & 0.158 & & \\
199.833 & 0.177 & 0.033 & \\  & 0.191 & & \\ \hline  & 0.068 & & \\
899.812 & 0.143 & 0.075 & \\  & 0.112 & & \\ \hline  & 0.124 & & \\
1599.690 & 0.106 & 0.032 & 0.500 \\  & 0.092 & & \\ \hline  & 0.168 & & \\
2299.351 & 0.140 & 0.028 & \\  & 0.156 & & \\ \hline  & 0.050 & & \\
2999.249 & 0.006 & 0.117 & \\  & 0.123 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Measurement errors of the XZ1 axis. Figure 9: XZ1 –axis measurement error characteristic. The system obtained the best accuracy in the center of the working space, where the error reached an average value of 0.1 mm. The measurement error increased near the field of view edge. The error results at the edge of the verified range are almost four times higher than those in the middle. For the XZ1 and XZ2 axes, which are diagonals of the analyzed space, the obtained error values composite the vertical and horizontal axis errors. Figure 11 shows the combined characteristics of the indication errors. The average range of results for all the axes remained at 0.05 mm.