## 1 Introduction  
High-power laser is of great interest for inertial confinement fusion [1; 2; 3], industrial processing [4; 5], optoelectronic countermeasures [6], strong-field physics [7; 8], and scientific research [9; 10; 11; 12]. As an important factor related to the beam quality, a uniform wavefront is conducive to maintaining the high quality spatial distribution in propagation. The wavefront is directly related to the far-field distribution of the output laser that influences the focused intensity as well as the alignment of the beam path in a high-power laser system (like spatial filter) [13]. Additionally, in a frequency conversion module, the frequency conversion efficiency decreases sharply with the increase of the wavefront error [14; 15], due to the angle matching of conversion cannot be achieved perfectly in the full aperture range. Therefore, it is necessary to control the wavefront in high-power laser systems, which can satisfy the basic requirements for laser transmission, focusing, and frequency conversion [16; 17]. However, the factors causing wavefront distortion are various such as heat dissipation in gain medium and machining error of optical elements that are difficult to be suppressed, especially in a complex high-power laser system. At present, the wavefront compensation technique is an effective approach to improve the output beam quality. Some devices have recently been employed for wavefront correction in high-power laser systems, and include stimulated Brillouin scattering phase conjugation mirrors (SBS-PCMs) [18; 19; 20; 21; 22], a liquid-crystal spatial light modulator (SLM) [23], and a deformable mirror (DM) [24; 25; 26]. Using SBS-PCMs is a passive method for wavefront shaping, and they are used as cavity end mirrorsthat can only compensate the wavefront aberration of the elements in a double-pass structure. Unlike SBS-PCMs, SLMs and DMs are active devices for wavefront shaping. However, the maximum wavefront correction provided by an SLM is limited in \(2\pi\), which cannot correct the large wavefront error in complex high-power lasers. Compared with SLMs, commercially available DMs are capable of wavefront correction with an adjustment range of up to several or even tens of micrometers [27; 28]. Therefore, DMs are considered to be promising for correcting the low-frequency and large-area spatial wavefront distortion in a complex high-power laser system. To date, large-aperture DMs have been applied to wavefront shaping in many large solid-state laser systems, such as the National Ignition Facility in the Lawrence Livermore National Lab [29; 30], the OMEGA EP Laser Facility at the University of Rochester [31; 32], the LMJ Facility in France [33], and the SG-III Laser Facility in China [34; 35]. Photo-controlled DMs are used in the HiLASE system at the Institute of Physics ASCR in Czech Republic [9; 10; 36; 37; 38]. These large-aperture DMs are placed in the end-stage of the laser systems to realize the wavefront compensation, which requires high-level machining technology and high cost. In addition, a higher risk of laser-induced damage may be introduced when a DM is exposed at the end of the high-power laser system with high fluence. To address this challenge, we propose low-cost active wavefront shaping by placing a small-aperture DM at the front end of a high-power laser system. Different from the output-stage wavefront compensation by directly correcting the final output, our method realizes output wavefront optimization by pre-compensating the wavefront distortion by inserting an actively adjusting small-aperture reflecting DM in the front stage of the laser system. Through the feedback of iterative calculation, a high-quality flattening output wavefront can be effectively obtained.