基于改进型粒子群优化算法的畸变光斑校正仿真研究

Distortion Spot Correction Based on Improved Particle Swarm Optimization Algorithm

相干探测激光雷达作为一项重要的光学探测技术,在实际应用中面临着大气湍流的影响:大气湍流会导致光斑发生畸变,从而降低探测性能。为解决这一问题,笔者提出了基于改进型粒子群优化算法的畸变光斑校正方法。该方法通过引入Metropolis准则以一定的概率接受劣质解,达到了更高的收敛极限。另外,改进型粒子群优化算法对惯性参数的取值不敏感。对于不同的惯性参数,随着迭代次数增加,所提算法最终都能够达到相同的收敛极限,这说明改进型粒子群优化算法的鲁棒性较好。在中强湍流和强湍流下,对比分析了随机并行梯度下降(SPGD)算法、粒子群优化(PSO)算法和改进型PSO算法的校正结果。仿真结果表明:在收敛速度方面,SPGD算法用时最长,其次是PSO算法,改进型PSO算法用时最短。在收敛极限方面,对于中强湍流,三种算法都能够使斯特列尔比提高到0.8以上,可以认为畸变校正达到了理想效果;对于强湍流,SPGD、PSO和改进型PSO算法使斯特列尔比分别提高了1.2、2.6、3.2倍(与校正前相比)。综合来看,相比SPGD和PSO算法,改进型PSO算法更有利于提高相干探测激光雷达的性能,尤其是在强湍流条件下。

Objective Coherent detection lidar, a pivotal optical sensing technology, is widely used in various fields, including meteorological forecasting, wind energy generation, and other fields. However, the performance of coherent-detection lidar is significantly affected by atmospheric turbulence in practical applications. Turbulence induces random variations in the optical path, resulting in wavefront distortion that adversely affects the quality of the received beam. Wavefront distortion correction, achieved through adaptive optics technology, has been proved to be an effective solution. The core of this method involves the use of optimization algorithms to control a deformable mirror, generating a phase that is conjugate to the wavefront distortion, thereby compensating for wavefront aberrations.The stochastic parallel-gradient descent(SPGD) algorithm is widely used for this purpose. However, because of the introduction of random perturbations, it exhibits a slow convergence speed. The particle swarm optimization(PSO) algorithm, proposed by Kennedy and Eberhart, is favored owing to its rapid convergence, simplicity, independence from derivative information, and parallel computation capabilities. However, both algorithms are susceptible to becoming trapped in local optima, particularly when addressing large and complex problem spaces. To address this challenge, we propose an improved PSO algorithm for distortion spot correction.Methods The improved PSO algorithm introduces the Metropolis criterion to probabilistically accept solutions with relatively low performance, which aids in escaping local optima, thereby achieving a higher convergence limit. The application of this algorithm to wavefront distortion correction further enhances the correction capabilities. First, we simulated the laser transmission through atmospheric turbulence based on the multi-phase screen propagation principle, resulting in the generation of distorted spots.Subsequently, we optimized the inertial parameters in both the PSO and improved PSO algorithms as well as the gain coefficients and perturbation amplitudes in the SPGD algorithm. This is because different parameter values can significantly influence the optimization performance. Hence, these parameters were adjusted to ensure that the algorithms operated at their peak efficiencies. Finally, we conducted a comprehensive comparative analysis of the correction results achieved by the SPGD, PSO, and improved PSO algorithms under medium and strong turbulence conditions, using the Strehl ratio(SR) as the evaluation function.Results and Discussions The improved PSO algorithm exhibited remarkable insensitivity to the inertial parameters(Fig. 9),indicating its superior robustness. All three algorithms were employed to correct the distorted spots under medium and strong turbulence conditions(Figs. 10 and 11). Based on the correction results, the convergence speed and limit were analyzed. Table 2 lists the convergence iterations and the time required by each of the three algorithms to achieve convergence. Under similar conditions,SPGD converges the slowest, followed by PSO, and the improved PSO converges the fastest. The reason for this discrepancy is the pronounced stochasticity of the SPGD algorithm during the optimization process, resulting in a longer convergence time.Additionally, the improved PSO algorithm concentrated the energy of the corrected distorted spot and achieved a higher SR because it increased the probability of accepting bad solutions(Fig. 12). Under strong turbulence conditions, the SPGD, PSO, and improved PSO algorithms contributed to SR improvements of 1.2, 2.6, and 3.2 times, respectively. Strong turbulence can result in severe spot distortion. When local optima are present during optimization, the advantages of the improved PSO algorithm become particularly prominent, enabling it to attain a higher convergence limit. This is advantageous for enhancing the system coupling efficiency, thereby effectively improving the performance of coherent detection lidar.Conclusions Coherent detection lidar is affected by atmospheric turbulence. Turbulence results in spot distortion, which reduces the detection performance. AO technology is an effective method for mitigating this distortion, and the selection of an intelligent optimization algorithm is crucial in this process. The SPGD algorithm exhibits parallel processing capabilities;its incorporation of random voltage perturbations results in slow convergence, whereas the PSO algorithm not only offers parallel processing and simplicity but also achieves rapid convergence without the need for derivative information. Nonetheless, both algorithms easily fall into the local optima. To address this problem, this study proposes an improved PSO algorithm that introduces the Metropolis criterion to escape local optima and reach a higher convergence limit. This algorithm is insensitive to the inertial parameters and exhibits better robustness. In comparison with the SPGD and PSO algorithms, the improved PSO algorithm enhances the convergence speed and convergence limit. In summary, the improved PSO algorithm demonstrates a more advantageous capacity for improving the performance of coherent detection lidar, particularly for strong turbulence.