基于引力搜索算法的湍流相位屏生成方法

Generation of turbulence phase screen based on gravitational search algorithm

本文提出了一种全新的相位屏生成方法,结合了经典快速傅里叶变换(FFT)模型与稀疏谱模型.经典的FFT模型由于低频成分的严重缺失,限制了其在高精度相位屏生成方面的应用,为此,本文将相位屏的低频部分单独提取出来,应用稀疏谱模型生成相应的低频补偿屏,将二者相加后得到最终的精确相位屏.结果表明,补偿屏的模拟精度与低频采样点的分布有关,且存在一种最优分布使得最终的相位屏结构函数与理论结构函数的误差最小.为兼顾相位屏生成速度,本文选取了16个低频采样点,采样点位置由两个待定参数确定,并应用引力搜索算法对参数进行优化得到最终的低频采样点分布.仿真结果表明,该方法与传统低频补偿方法相比精度提高了1-2个数量级,且运算速度优于传统方法.

The new techniques in adaptive optics,free space optical(FSO)communication rely on the use of numerical simulations for atmospheric turbulence to evaluate the performance of the system.The simulation of turbulence phase screen is the heart of numerical simulations which produces random wavefront phase perturbations with the correct statistical properties corresponding to models of optical propagation through atmospheric turbulence.The phase-screen simulation techniques can be roughly divided into fast Fourier transform(FFT)method and matrix-based method.Because of a better performance in computation time,the FFT method is generally used for modeling the performance of a real system.But the classical FFT method has a main deficiency of oversample in low frequency region,which leads to the lost of accuracy.To overcome this deficiency,many methods have been proposed for compensating for the oversample of low frequency components,in the last decades.Essentially,these methods achieve a higher accuracy at the expense of computation time.A good compensation method should take into consideration both accuracy and computation time.To achieve higher accurcy and lower computational cost simultaneously,we develop a hybrid method to generate turbulence phase screen,i.e.the classical FFT model is mixed with the sparse spectrum model.We first extract the low frequency region from the frequency grid of FFT model,and resample this region with 16 samples.It is found that the accuracy of phase screen is related to the distribution of these samples,and there must be an optimum distribution that can minimize the relative error between expected structure function and theoretical structure function in the low frequency region.So it permits one to use optimization algorithm to find the optimized distribution of low frequency samples.Here an improved gravity search algorithm is adopted in which the memory of each particle is taken into consideration.The optimization parameters are determined after a lot of tests,and the robustness testing shows that the algorithm is effective.To compare with existing subharmonic method,we choose the same parameters of phase screen as those used in the expanded subharmonic method,generate 1000 phase screens for each method,compute the phase structure function,and we also compare our results with those from the theoretical structure function.The comparison result shows that the curve of phase structure function generated by our method is nearly consistent with the theoretical one,the maximum relative error in low frequency region is about 0.063%which is much better than that from the expanded subharmonic method 5%.Finally in this paper,the computational cost is analyzed,showing that the generation speed for our method is at least 4.5 times as fast as that for the Johansson’s method.