大气湍流随机相屏模拟方法研究

对几种模拟随机湍流相位屏的方法进行了总结，利用结构函数对每种方法进行了分析，并从Zernike多项式分解的思路和激光大气传输的角度，通过焦斑扩展和焦斑质心漂移对几种方法进行了完整比较，最后对湍流低频倾斜信息的补偿方式进行了探讨。通过分析发现:傅里叶变换(FFT)法模拟的相屏体现的湍流高频信息较充分，但低频信息不足;Zernike法模拟的相屏体现的湍流低频信息较充分，但高频信息不足。随着采用的Zernike多项式阶数的增加，其体现的高频信息会得到改善，但这些高频信息主要集中在圆域的边缘区域。分形法模拟的相屏体现的湍流高低频信息均较好。针对焦斑扩展和焦斑质心漂移，除分形法外，其他算法均存在不同缺陷。采用FFT法与Zernike多项式展开法相结合的方式或FFT法与湍流自相似理论相结合的方式模拟大气湍流随机相屏，也不失为一种较有效的方式，但从激光大气传输的角度来说，采用分形法模拟湍流随机相屏最好。

Methods for simulating turbulent phase screen

Some methods for simulating turbulent phase screen are summarized, and their characteristics are analyzed by calculating the phase structure function, decomposing phase screens into Zernike polynomials, and simulating laser propagation in the atmosphere. Through analyzing, it is found that, the turbulent high-frequency components are well contained by those phase screens simulated by the FFT method, but the low-frequency components are little contained. The low-frequency components are well contained by screens simulated by Zernike method, but the high-frequency components are not contained enough. The high-frequency components contained will be improved by increasing the order of the Zernike polynomial, but they mainly lie in the edge-area. Compared with the two methods above, the fractal method is a better method to simulate turbulent phase screens. According to the radius of the focal spot and the variance of the focal spot jitter, there are limitations in the methods except the fractal method. Combining the FFT and Zernike method or combining the FFT method and self-similar theory to simulate turbulent phase screens is an effective and appropriate way. In general, the fractal method is probably the best way.