# Evaluation of the Large-Length Indoor Standard Installation Based on Single Point Scanning
## 4 Results and Analysis
### Comparative Analysis of Multiple Measurement Results
The results of ten measurements of the laser interferometer with a measurement interval of 5000 mm are shown in Figure 4. Compared with the results of the laser tracker, there was obvious oscillation in the constant speed stage. The reflector was rigidly fixed on the cylinder, and thus, has low oscillation resistance during motion. In addition, there were uncertainties in terms of the distance difference and time difference of the laser tracker and the laser interferometer. Since both methods were non-coaxial measurements, the Abbe error was introduced. Since the laser tracker method has small interference, it is more advantageous in the measurement of LLISI. The measurement interval and the nominal speed were 5000 mm and 150 mm/s, respectively. The measurement results of the laser interferometer are shown in Table 4. The mean value of the local average speed was stable within the distance range of 5000 mm, with all values between 150.0033 mm/s and 150.0052 mm/s. The number of measurement points that met the requirement was between 314 and 318. When the sampling frequency is the same, the three-dimensional measurement value is theoretically greater than that of one-dimensional measurement, and the increase in the instantaneous speed leads to an increase in the local average speed. Comparing the measurement results of the two methods, the mean value of the local speed of the laser interferometer (0.0056 mm/s) was higher than that of the laser tracker. During dynamic measurement, there were micron-level differences between the two methods, which verified the effectiveness of the laser tracker. Compared with the laser tracker method, the average time in the whole movement period  
Figure 4: Results of ten measurements with a measurement interval of 5000 mm. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Measurement** \\ **Interval (mm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Nominal Speed** \\ **(mm/s)** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Average Time of** \\ **Stage of Multiple** \\ **Measurements (s)** \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} **Average Time of** \\ **Measurements** \\ **(mm/s)** \\ \end{tabular} } & \multicolumn{2}{c}{\
\begin{tabular}{c} **Maximum Time of** \\ **Measurements** \\ **(mm/s)** \\ \end{tabular} } & \multicolumn{2}{c}{
\begin{tabular}{c} **Global** \\ **(the Movement** \\ **Period (s)** \\ \end{tabular} } \\ \hline
100 & 50 & 1.2 & 50.0124 & 3.4 & 3.4 & 29.4103 \\
100 & 100 & / & / & 2.7 & 2.7 & 32.9874 \\
100 & 150 & / & / & 3.2 & 3.5 & 31.5788 \\
300 & 50 & 5.4 & 50.0003 & 7.5 & 7.9 & 40.0002 \\
300 & 100 & 1.7 & 100.0028 & 5.8 & 6.5 & 52.0232 \\
300 & 150 & 0.2 & 150.0122 & 4.6 & 4.9 & 65.6937 \\
500 & 50 & 9.2 & 50.0000 & 11.2 & 11.3 & 44.7756 \\
500 & 100 & 3.7 & 100.0060 & 7.2 & 7.4 & 69.4442 \\
500 & 150 & 1.2 & 150.0150 & 5.6 & 6.0 & 88.7562 \\
1000 & 50 & 19.2 & 49.9992 & 21.9 & 22.2 & 45.7312 \\
1000 & 100 & 8.6 & 99.9989 & 11.8 & 11.9 & 84.7452 \\
1000 & 150 & 4.8 & 149.9967 & 9.2 & 9.6 & 108.3020 \\
5000 & 50 & 99.2 & 49.9995 & 101.4 & 101.7 & 49.2358 \\
5000 & 100 & 47.4 & 99.9987 & 52.5 & 53.4 & 95.2984 \\
5000 & 150 & 31.4 & 149.9983 & 35.7 & 35.9 & 140.2853 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Measurement results of the laser tracker at different measurement intervals and speeds. The calculation of the measurement uncertainty components are as follows: multiple measurements were carried out with a nominal speed of 150 mm/s, a collection time of 0.1 s, and a nominal range of 0.015 m. The standard deviation was calculated based on the Bessel equation \(\mathrm{u_{A}(s_{1})=\sqrt{\frac{\mathrm{\Sigma_{n=1}^{n}(D-\overline{D})^{2}}}{n -1}}}=11.45\)\(\mathrm{\SIUnitSymbolMicro m}\) The measurement uncertainty can be obtained from the calibration certificate, \(U\) = (0.80 + 0.11 L) mm, (L:m), (\(k\) = 2). Thus, the standard uncertainty component at 0.015 m was \(\mathrm{u_{B1}(s_{1})\approx 0.4\)\(\mathrm{\SIUnitSymbolMicro m}\).