物理学报Issue(22)：1-8,8.DOI:10.7498/aps.64.224217
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
摘要
Abstract
The generation of atmosphere turbulence wave-front is important for studying the light propagation and imaging through the atmosphere, and correcting the atmosphere turbulence, such as the adaptive optics system. The power spectral 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.关键词
大气湍流/相位屏/功率谱反演/非均匀快速傅里叶变换Key words
atmospheric turbulence/phase screen/power spectrum inversion/nonequispaced fast Fourier transform引用本文复制引用
蔡冬梅,遆培培,贾鹏,王东,刘建霞..非均匀采样的功率谱反演大气湍流相位屏的快速模拟∗[J].物理学报,2015,(22):1-8,8.基金项目
山西省自然科学基金(批准号:2013011006-4)、中国科学院自适应光学重点实验室基金(批准号：LAOF201301)和微细加工光学国家重点实验室(批准号：KFS4)资助的课题.* Project supported by the Natural Science Foundation of Shanxi Province, China (Grant No.2013011006-4), the Foundation of Key Laboratory of Adaptive Optics, Chinese Academy of Sciences (Grant No. LAOF201301), and the State Key Laboratory of Optical Technologies for Micro-fabrication, China (Grant No. KFS4) （批准号:2013011006-4）
