## 4 Experiment
### High-Weight Error Measurement and Compensation
The accuracies of the surface shapes of the standard flat rulers are shown in Figure 15.  
The measurement framework utilizes a quDIS and a high-precision ruler to compensate for the positioning accuracy and straightness of the linear axis. The theoretical positioning accuracy of the quDIS reaches 0.2 nm/mm and the working distance is 20-400 mm. During the Y-axis movement, the workbench produces a positioning error in the Y-direction and a straightness motion error in the Z-direction, resulting in micro-displacements. The Y-axis position is continuously read in real time by the quDIS sensor head in the Y-direction, and the value displayed by the quDIS is taken as the actual position of the Y-axis. The quDIS provides high-precision positioning and can accurately obtain the motion position of the Y-axis, thereby compensating for the error caused by inaccurate positioning on the straight axis. It also detects and compensates for Y-axis straightness errors in the Z-direction with a Z-direction sensor probe. Similarly, the error caused by the Z-axis movement was read and compensated by the measurement system in real time. The straightness error data were measured using the quDIS, and the data were fitted using the least-squares method,  
Figure 14: Jump test of air-bearing rotary table. Figure 13: Repeated positioning accuracy of rotary table A (**a**) and rotary table C (**b**). as shown in Figure 16. The Y-axis \(Z\)-direction straightness is reduced from 2.3 \(\upmu\)m per 300 mm to 0.48 \(\upmu\)m per 300 mm, and the \(Z\)-axis Y-direction straightness is reduced from 1.5 \(\upmu\)m per 80 mm to 0.40 \(\upmu\)m per 80 mm. In order to verify the accuracy of the measuring system, a high-precision flat mirror with a diameter of 82 mm was measured. Figure 17a shows the original measurement result of the measuring instrument. After compensating for geometric errors of high weights, the results obtained are shown in Figure 17b. As the result of compensation, the compensation effect is obvious. However, the result of the compensated pattern shows an eddy current pattern. It may be due to a small displacement in the measurement process, or poor alignment, inaccurate system calibration, or other reasons, which need to be further explored. The accuracy of each high-weighting error of the measuring instrument is presented in Tables 4 and 5. The results of the preliminary experiments proved that, by controlling the high-weighting errors, the measuring platform can effectively realize high-precision positioning and real-time compensation of straightness, and the designed high-precision large-diameter measuring machine has high accuracy and effectiveness. Figure 9:0 Straightness error on the Y-axis (**a**) and \(Z\)-axis (**b**) after compensation. Figure 9:1 Accuracy of the surface shape of standard flat rulers: (**a**) Standard flat rulers in the Y-direction, (**b**) Standard flat rulers in the Z-direction. the weights of the critical error components, making it challenging to improve the accuracy of the measuring machine. The results of the geometric error weight analysis are effectively used in the precision design and manufacture of large-aperture coordinate precision measurement instruments. The preliminary experiment of high-weight error measurement and compensation proves the effectiveness of the real-time compensation of the measurement framework and the high precision and effectiveness of the designed large-aperture coordinate precision measurement instrument, The measures taken to compensate for the different errors are shown in Figure 9:2  
In future work, we will use the measuring instrument to perform measurement experiments, and the coupling between different errors of different axes of the measuring machine will be further studied to improve the method of compensating only for the high-weight errors, improving the measurement accuracy of the measuring machine. Conceptualization, S.L., H.K., T.L. and J.L. ; methodology, S.L., T.L. and J.L. ; validation, S.L., T.L. and J.L. ; formal analysis, S.L., T.L. and J.L.