非均匀采样的功率谱反演大气湍流相位屏的快速模拟

Fast simulation of atmospheric turbulence phase screen based on non-uniform sampling

对大气湍流功率谱非均匀采样可以有效改善传统功率谱反演法低频采样严重不足的缺陷,实现高精度的大气湍流相位屏的模拟.但采用的直接求和运算计算复杂度高,相位屏的模拟速度极慢.将非均匀快速傅里叶变换(NUFFT)引入到大气湍流相位屏的模拟,可以实现相位屏的快速模拟.从随机过程的谱分解出发,将大气湍流相位随机过程表示为有限谐波分量叠加和的均方极限.通过一个高斯核函数的卷积,将非均匀分布的谐波复振幅映射到均匀网格空间,进而利用快速傅里叶变换,降低计算复杂度,加快大气湍流相位屏的模拟速度.以大气湍流的Kolmogorov谱为例,利用NUFFT仿真得到大气湍流相位屏,并对相位屏的模拟精度、模拟速度和误差进行统计分析.结果表明,NUFFT的引入可以实现快速、高精度的大气湍流相位屏的模拟.

The generation of atmosphere turbulence wave-front is important for studying the light propaga^lon ann tm^m~ through the atmosphere, and correcting the atmosphere turbulence, such as the adaptive optics system. The power spectrM density method generates phase screens quickly for using the fast Fourier transform （FFT）. The main drawback to this approach is that lower order aberrations such as tilt are often under represented. The reason is that the low frequency is sampled inadequately. Since the low order aberrations include a major percentage of the atmospheric energy spectrum, the error of simulated phase screens makes this method less desirable to use. To overcome this shortcoming, a non-uniform sampling method is proposed to generate phase screens accurately. Unfortunately, when the sampling is nonuniform, the FFT does not apply directly. Generating such a phase screen is computation intensive which greatly reduces simulation speed. In this paper, we develop a fast, more accurate method to generate atmospheric turbulence phase screens, according to non-uniforming sampling. The nonequispaced fast Fourier transform （NUFFT） arises in a variety of application areas, ranging from medical imaging to radio astronomy to the numerical solution of partial differential equations. Speeding up the simulation of atmospheric turbulence phase screens is possible by using the non-uniform fast Fourier transform. In this paper, the atmospheric turbulence phase screen is decomposed into a series of harmonics. Then the non-uniform distributed har- monics are projected onto over-sampled uniform grid by using the Gaussian kernel function. Atmospheric turbulence phase screen will be generated using the standard fast Fourier transform on the over-sampled uniform grid. The at- mospheric turbulence phase screens can be generated quickly. Using Kolmogorov spectrum model in this paper, the phase screens can be generated quickly. The performances of generated phase screens are analyzed through their phase structure functions. The statistical results are in very good agreement with the theoretical values. The relative error curve of simulation phase screens is calculated and analyzed. The more the oversampling grid, the more the relative error is. Compared with the result from the direct harmonics summation method, the error here mainly concentrates in high-frequency region where the sampling frequency points are sparse. However, the atmosphere turbulence phase screen is simulated in high accuracy on the whole. Compared with the time cost of the harmonics summation, the time using NUFFT is decreased to about 800 times. The simulated phase screens indicate that non-uniform fast Fourier transform is able to generate atmospheric turbulence phase screen with high accuracy and fast speed.