## 4 Experimental Results and Discussion  
### Wavefront Compensation without the Main Amplifiers in Operation  
Before wavefront shaping, the DM surface is set so that the beam can pass through the pinhole of spatial filter. Firstly, without the operation of the main amplifiers, the wavefront distortion of the entire laser system is observed when the DM is not working. At this condition, a plane 0\({}^{\circ}\) reflection mirror is placed at the DM position as the cavity mirror of the two-pass \(\Phi\)20 Nd/glass rod amplifier. Here, the wavefront refers to the output wavefront measured by the wavefront sensor in the diagnostic system when a pulse seed passes through the entire laser system without the main amplifiers working. Figure 3a shows the output wavefront distribution without the DM work. The saddle-shaped wavefront distribution indicates that the astigmatism aberration is very distinct in the laser system. The calculated wavefront peak-to-valley (PV) value is 3.34 \(\lambda\) (\(\lambda\) = 1053 nm) and the RMS value (i.e., root mean square) is 0.65 \(\lambda\). Obviously, it is necessary to do wavefront shaping to compensate the wavefront distortion without the main amplifiers in operation in the laser system. Figure 2: Overview of the wavefront shaping system in the laser system. The complex laser system consists of an all-fiber front end, a preamplifier, a transmission and amplifier, a frequency converter, and beam control and measurement. The blue two-direction arrow real lines refer to the relay image plane. P1 to P7: polarizers; FR1 to FR3: Faraday rotators; DM: deformable mirror; HWP: half-wave plate; CSF: cavity spatial filter in the main amplifier system; TSF: transport spatial filter; \(\Phi\)20, \(\Phi\)40, and \(\Phi\)70 rod Amp: 20, 40, and 70-mm-diameter Nd/phosphate glass rod amplifiers; the bidirectional blue arrow: the image relay plane. After the DM is installed in the beamline instead of the cavity mirror of the two-pass \(\Phi\)20 rod amplifier, the output wavefront without the main amplifiers in operation can be shaped actively. An off-line well-corrected DM surface is set to observe the initial output wavefront distribution with a PV value of 2.29 \(\lambda\) and an RMS value of 0.51 \(\lambda\). It is also the saddle-shaped distribution in the whole beam. According to the wavefront shaping method introduced in Section 2, the output wavefront distribution tends to flatten after the first compensation. After several iterations of compensation, the wavefront distribution gradually tends to flatten more; the final output wavefront PV value is 0.36 \(\lambda\), and the RMS value is 0.06 \(\lambda\) (see Figure 3b). The wavefront shaping algorithm is effective in realizing the wavefront shaping without the main amplifiers in operation in the laser system. Figure 4 indicates that both the PV and RMS values of the output wavefront decrease obviously in the entire shaping process. During the first three shots, the output wavefront changes greatly and then changes relatively slowly against the laser shot number as well as the increasing iteration times. After wavefront compensation without the main amplifiers in operation, the PV value of the output wavefront is less than 0.5 \(\lambda\), and the beam passes through the laser system successfully. The wavefront distortions without the main amplifiers in operation here mainly result from the original beam distortion of the pulse seed and the imperfections in a series of optical components in the laser system. These distortions have been compensated by the DM. Because the anisotropic thermal dissipation in the amplification media caused by the main amplifiers involves a deterioration of the wavefront profile as the laser system operates at a high energy level, a further wavefront shaping with the main amplifiers in operation is needed based on this work. Figure 4: The wavefront variety during the process of wavefront compensation without the main amplifiers in operation.