# Large-Aperture Real-Time Compensated Collimating Wavefront Error Detection Method
## 3 Experiment and Analysis  
The pentaprism converted the initial transverse wavefront into a longitudinal wavefront. The centroid offset was only related to the offset of the measured spot. By referencing the centroid coordinates after calibration, the centroid offset of the coordinates of the sampling points was obtained. The ratio of the focal point to the focal length of the lens was the slope of each wavelet wavefront. The integral of each slope was taken. The values from the integrals and the positions of the scanned wavefront from the guide rail were used for polynomial curve fitting, and the fitting coefficients for the measured wavefront were obtained. The wavefronts, which had been corrected for tilting, were reconstructed by the obtained coefficients, and the original wavefront under measurement in the pentaprism scanning direction was obtained. The beam of the emergent light wave incident on the pentaprism was incomplete. In the wavefront fitting, the incomplete interference points on the spot edge had to be removed in order to reduce the influence of large errors on the wavefront detection results. The experimental system mainly included a light source, a collimated wavefront generating system, a high-precision electronically controlled translation stage, a pentaprism scanning system, and a right-angle prism error compensation system, as shown in Figure 3. The high-precision electronically controlled translation stage was a custom-made marble guide rail and a linear motor-driven micro-translation stage with a displacement resolution of 1 nm and a positioning repeatability of 0.5 \(\upmu\)m. For the size of the pentaprism, a smaller optical aperture was selected to improve the detection accuracy of the collimated wavefront with a large aperture. However, the size of the pentaprism was also constrained by the illumination intensity of the beam to be measured; if the size is too small, the optical intensity of the sampled beam is weak. Insufficient luminous flux makes it difficult for CCD cameras to detect valid signals and can lead to difficulties or failures in centroid determination. Therefore, a pentaprism with an optical aperture of 10 mm, \(k9\) material, and an anti-reflection coating on the surface was used in the experiment. The wavefront under measurement in the experiment was the collimated wavefront from an Image Science IS-200 transfer function source. The collimated wavefront was reflected from the off-axis parabolic mirror with a 200 mm aperture with a peak-to-valley (PV) value of standard accuracy of 50 nm, or 0.44 \(\lambda\). According to the sampling theorem, the signal spectrum will be extended periodically in the frequency domain according to the time domain sampling, and the change of the sampling interval is equivalent to the change of the extension period. If the sampling interval is increased, the signal spectral aliasing is abnormal after the expanding periods are reduced, and the final original signal cannot be reconstructed. In order to reconstruct the original signal, the sampling frequency under normal conditions must be greater than twice the signal frequency. If the sampling frequency is reduced to a certain extent, because the sampling interval and frequency have a reciprocal relationship, the sampling theorem is not satisfied. Therefore, the original signal and wavefront cannot be reconstructed. The actual sampling interval of 4 mm was determined according to the Nyquist sampling theorem [PERSON] (1948). As the stage moved, the spots were obtained by continuous sampling from 0 to 220 mm. The pixel centroid coordinates from the camera were obtained using the centroid algorithm. The data is shown in Figure 4. Figure 4a shows the coordinate data of spot centroids obtained by the scanning subsystem, and Figure 4b shows the coordinate data from the error compensation subsystem. The deviation of the data was large in the travel ranges of 0-10 mm and from 210 mm to 220 mm of the guide rail, which was due to the potential energy error inherent to the precision translation stage.