# Effect of Optical Aberrations on Laser Transmission Performance in Maritime Atmosphere Turbulence
## 4 Discussion and Future Work  
This study systematically investigates the propagation characteristics of laser beams with four typical aberrations--defocus (\(Z_{4}\)), y-direction coma (\(Z_{7}\)), spherical aberration (\(Z_{11}\)), and secondary y-direction trefoil (\(Z_{25}\))--after they propagate through maritime atmospheric turbulence over 1.1 km. Using the Zernike aberration fitting method and multi-layer phase screen simulation, we calculate the scintillation index, intensity probability density distribution, beam wandering and beam expansion effects at the target plane in maritime atmospheric turbulence under varying turbulence strengths, weight coefficients, and receiver aperture radii. The results show the following:  
(1) Compared to the other three types of aberrations (i.e., defocus (\(Z_{4}\)), spherical aberration (\(Z_{11}\)), and secondary y-direction trefoil (\(Z_{25}\))), the range of fluctuations in the relative change rate of the scintillation index for the \(Z_{7}\) aberration is the largest relative to the no-aberration state. Thus, in practical system design, it may be necessary to pay particular attention to the correction of coma. This is similar to the result in reference [44], but what distinguishes our study is that we have added an analysis of the relative change rate compared to the no-aberration state, which provides a more comprehensive explanation of the trend regarding the influence of aberrations on the scintillation index. (2) Increasing the receiver aperture radius can partially mitigate the scintillation effects of intensity fluctuations, as also validated in [45]. Moreover, this study reveals that different aberrationsrespond differently to the aperture averaging effect. This observation provides a theoretical basis for targeted aberration correction strategies. (3) The on-axis log-intensity distribution of laser beams with different aberrations approximately follows a log-normal distribution, with skewness (S < 0) and kurtosis (K > 0) exhibiting a negative correlation. This is consistent with the empirical results in the land-based environment reported in Reference [29], indicating that the log-intensity distribution of laser beams under turbulent atmospheric conditions exhibits a universal log-normal characteristic. (4) It is important to note that in practical communication systems, the \(SNR\) typically operates within a limited range, making it challenging to achieve the extremely high values often assumed in theoretical analyses or simulations. To ensure efficient and stable communication in environments with complex turbulence, a multi-parameter optimization approach is necessary. This approach should consider factors such as aberration correction, aperture design, and turbulence mitigation to enhance system performance.  
All the findings in this paper apply to short-distance (1.1 km) laser atmospheric transmission over the sea. In practical applications, the laser communication distance often needs to exceed 1.1 km [46, 47], and the actual system involves complex combinations of aberrations as well as atmospheric non-uniformity patterns. By initially discussing the effects of various aberrations on short-distance laser atmospheric transmission over the sea, the next step is to comprehensively analyze their impact on long-distance laser transmission in a non-uniform atmospheric environment using the weighted summation approach provided in Reference [48]. Additionally, to enhance the reliability and practical value of our research results, we also plan to conduct relevant experimental validation. This aims to provide more theoretical and technical support for practical applications in free-space optical communications.