遗传算法在激光整形中的应用

Genetic algorithm used in laser shaping

同爬山算法相比,遗传算法具有全局优化能力,为了研究遗传算法的波前整形能力,利用32单元变形镜和12项Zernike多项式构成的畸变波前建立了激光波前整形系统仿真模型。基于Zernike多项式的单位正交性特点,得到了两个常数矩阵,简化了算法的运算过程,加快了算法运行时间。然后分别对遗传1000,10000和100000代后的斯特列尔比和整形效果进行了模拟仿真,仿真结果为:进行100000代遗传后,遗传算法可分别将初始畸变波前的斯特列尔比从0.3771整形到0.9049,波前峰谷值从0.8078λ整形到0.3758λ,均方根从0.1572λ整形到0.0503λ,并且随着遗传代数的增加,斯特列尔比逐渐和整形效果均逐渐趋于最优,进一步表明遗传算法是一种优化逼近控制算法,可以通过对变形镜驱动电压的优化控制来实现波前整形,为遗传算法应用于波前整形技术中提供了理论依据。

Comparing with hillclimbing algorithm, genetic algorithm can make global optimization. To investigate the wavefront shaping capability of genetic algorithm, the model of laser wavefront shaping system is constructed by dis tortion wavefront described by 12 Zeruike polynomials and 32unit deformable mirror. Two constant matrixes are ob tained with orthogonality of Zernike polynomials in unit circle,which can simplify computations and speed up the run ning time of algorithm. Then Strehl ratio and the shaping effect after 1000,10000 and 100000 generations are respec tively simulated. The results are that：after 100000 generations Strehl ratio, difference between peak and valley value, root mean square of initial wavefront distortion are respectively shaped from 0. 3771 to 0. 9049,0. 8078λ to 0.3758λ ,0. 1572λ to 0. 0503λ. And the Strehl ratio and the shaping effect all gradually approach to the optimization when generation accelerates. Furthermore, it shows that genetic algorithm is a kind of approaching optimization control algorithm and can achieve to shape laser wavefront by control the voltage of deformable mirror. It provide theoretic ba sis for wavefront shaping technology with genetic algorithm.