## 4 Experiments  
The beams emitted by the multi-beam array system developed in our lab have a wavelength of 632.8 nm and a beam size of 50 mm in diameter. The interval of adjacent beams in the multi-beam array system is 80 mm. Guided by the Shack-Hartmann wavefront sensor in the setup as shown in Figure 8, we achieved a wavefront error of less than 0.02 \(\lambda\) RMS for each collimator beam in the multi-beam array system. The laser is a single-mode fiber-coupled laser with a fiber output power exceeding 10 mW. Some characteristics of the Shack-Hartmann sensor are presented in Table 2. Note that the beam size, with a diameter of 50 mm, emitted by the multi-beam array, is reduced through a reducer to match the field of view of the Shack-Hartmann wavefront sensor. Figure 8: The setup for the wavefront calibration of the beams in the multi-beam array system. Figure 7: Comparison of the Zernike coefficients of aberrations with the iterative method and the averaging method, which are presented for different scanning steps, (**a**) referencing Figure 4a, (**b**) referencing Figure 4b, and (**c**) referencing Figure 4c. Next, a Cassegrain-type collimating tube with a focal length of 20 m is employed to align the nine beams in the same direction, as shown in Figure 9. Each beam of the multi-beam array system is sequentially focused on the CCD using the collimating tube. We adjust the nine focal spots to align as closely as possible at the same position. However, due to the limitations of mechanism, the centroids of the spots did not exactly coincide at the same coordinates. Afterward, the setup for aberration measurement of the optical system is established, as shown in Figure 10b. The optical system has a focal length of 8 m with an aperture diameter of 560 mm. The testing procedure is outlined as follows:  
1. Align the central beam (No. 5) of the multi-beam array with the optical system's aperture center, which is used as the coordinate system origin. Determine coordinates for all measurement positions based on the optical system's aperture size and the array scanning step size. 2. Drive the multi-beam array along a two-dimensional guide to the positions determined in Step 1. Sequentially illuminate the beams according to their numerical order. Illuminate each beam for one second to stabilize spot images. Subsequently, the detector captures the image. After completing measurements at the current position, move the multi-beam array system to the next measurement position. Repeat Steps 1 and 2 until all positions within the optical system's aperture are covered. In summary of the above experiments, firstly, we accomplished the integrated installation of a multi-beam array that utilizes Hartmann wavefront sensors for real-time wavefront detection, guiding the coupling of fiber lasers. Next, we employed a long-focal-length collimating tube for the calibration and testing of the alignment consistency of a multi-beam array. Finally, we tested the wavefront of the optical system using the MASTS. The test results of the experimental measurement are illustrated in Figure 11. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Size of a Micro Lens** & **Micro Lens Focal** & **Micro Lens Array** & **CCD Pixel Size** & **Measurement Frame** \\  & **Length** & **Resolution** & **Rate** & **Rate** \\ \hline
0.3 \(\times\) 0.3 mm & 15 mm & 45 \(\times\) 60 & 5.5 μm & 15 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The characteristics of Shack–Hartmann sensor. Figure 9: The setup for the alignment of multiple beams. As shown in Figure 11, it can be seen that the root mean square (RMS) value obtained through the iterative method differs by less than 0.0001 \(\lambda\) from the RMS value of the interferometer data, which indicates the accuracy and correctness of the iterative approach. The RMS values of the reconstruction with a 20 mm step size are closer to the interferometer test results compared with the 40 mm step size.