非Kolmogorov大气湍流随机相位屏模拟

介绍了功率谱法、Zernike多项式法、分形法模拟生成非Kolmogorov湍流相位屏的过程，并利用这三种方法对符合非Kolmogorov统计特征的大气湍流相位屏进行了模拟。将不同方法得到的相位屏的相位结构函数与理论结构函数进行对比，分析了三种相位屏模拟方法的准确性和模拟速度。结果表明:添加次谐波和增加Zernike多项式阶数分别可以弥补功率谱法和Zernike多项式法生成的相位屏低频和高频不足的缺点，但导致模拟效率下降；分形法生成的湍流相位屏高频和低频都较为充足，且模拟效率较高；随着非Kolmogorov湍流谱幂率的增加，功率谱法所需要的次谐波级数增加，Zernike多项式法所需要的Zernike多项式的阶数减少，分形法生成的相位屏的精度更高。

Simulation of random phase screen of non-Kolmogorov atmospheric turbulence

The methods of power spectrum, Zernike polynomial and Fractal used to generate atmospheric phase screens with the non-Kolmogorov statistics were introduced. Based on the three methods, non-Kolmogorov turbulent phase screens were simulated. Phase structure functions were calculated and compared with the theoretical results. In addition, the accuracy and efficiency of different methods were also analyzed. It shows that phase screen created by FFT method has the drawback of lacking low frequency, by adding subharmonics the phase screen can be compensated which also leading to the decreasing of simulation efficiency; phase screen created by Zernike polynomial method has the drawback of lacking high frequency, by using much more orders of Zernike polynomials the phase screen can be compensated which also leading to the decreasing of simulation efficiency; phase screen created by Fractal method is relatively good at both low and high frequency and the simulation efficiency is also high. In addition, the number of subharmonics and the order of Zernike polynomials under same condition of accuracy are related to the power law of non-Kolmogorov turbulent spectrum. As the spectral power law increases, the number of subharmonics increase and the order of Zernike polynomials decrease, and phase screens created by fractal method are more accurate.