# Effect of Optical Aberrations on Laser Transmission Performance in Maritime Atmosphere Turbulence
## 1 Introduction  
Aberration refers to the deviation between real and ideal image points within a practical optical system [1, 2]. Typically, due to the non-ideal characteristics of the optical imaging system, the paths of light rays are altered during transmission through the system's various surfaces, leading to various types of aberrations. These aberrations can result in image blur, size variations, and morphological distortions, among other defects. When a laser propagates through the maritime atmosphere, it inevitably encounters both static aberrations caused by optical system imperfections and dynamic aberrations due to marine atmospheric turbulence. This results in intensity scintillation [3, 4], beam wandering [5, 6], and beam spreading [7, 8], all of which degrade the quality of the laser beamreaching the target [9; 10]. Additionally, molecules and particles in the atmosphere cause energy attenuation of the laser beam, further exacerbating these problems and severely limiting the application of lasers in marine environments, particularly in critical fields such as laser communication, LiDAR, and laser weapons [11; 12]. Therefore, it is important to conduct research on the propagation behavior of lasers in the marine atmosphere. In recent years, research on the propagation characteristics of ideal laser beams in maritime atmospheric turbulence has become quite mature [13; 14; 15; 16; 17; 18; 19; 20]. However, to better align with the practical applications in optical engineering, scholars have increasingly focused on the atmospheric transmission characteristics of non-ideal lasers that incorporate system aberrations. [PERSON] [21] simulated dynamic wavefront errors caused by atmospheric turbulence based on [PERSON]'s [22] Zernike aberration decomposition method, which is suitable for adaptive optical correction dominated by low-order Zernike aberrations. [PERSON] et al. [23] simulated the wave aberrations of the annular pupil using a Zernike polynomial expansion within the ring domain, obtaining the statistical distribution of the wavefront aberration decomposition coefficients under different turbulence statistical models. Furthermore, [PERSON] et al. [24] equated the actual wavefront aberrations to the combination of dynamic aberrations introduced by atmospheric turbulence and static aberrations introduced by the system, concluding that Zernike spherical aberration has a significant impact on the beam quality factor. [PERSON] et al. [25] used two numerical methods and found that for focused Gaussian beams in specific conditions, correcting each new Zernike mode does not diminish gains uniformly, with certain modes, notably coma, showing increased importance, impacting adaptive optics system design. Additionally, [PERSON] et al. [26] studied the impact of aberrations in the emitting optical system on the on-axis gain in the far field, offering guidance for optimizing optical system design. [PERSON] et al. [27] employed the Fourier transform method to simulate the far-field spot distribution in the presence of aberrations and analyzed the impact of key parameters such as angular displacement, divergence angle, and gain on the light field distribution. Recently, [PERSON] et al. [28] further investigated how aberrations affect Laguerre-Gaussian beam quality, deriving analytical expressions for astigmatism and spherical aberration, and validating their validity through numerical simulations. In summary, Zernike polynomials have been extensively utilized in simulating and analyzing systematic aberrations in the propagation characteristics of non-ideal laser beams within atmospheric turbulence. Despite significant advancements, further in-depth research is necessary to fully comprehend the combined impacts of diverse aberration types and varying turbulence intensities on laser beam propagation.