基于小波分析的大气湍流相位屏模拟

Simulation of Atmospheric Turbulence Phase Screen Based on Wavelet Analysis

大尺寸、高分辨率大气湍流相位屏的快速模拟对于在实验中验证自适应光学系统的性能及控制算法的稳定性至关重要。提出了一种基于小波分析模拟大气湍流相位屏的方案。根据离散小波变换的频段分割性质,对Von Karman型功率谱进行切割;基于能量守恒原理,生成不同尺度上对应频段的近似高频系数;利用小波层之间低频系数的递推关系,得到最高层低频系数的相关函数,并利用相关函数法来模拟低频系数;通过小波合成算法得到最终的大气湍流相位屏。模拟结果表明,基于小波分析产生的大气湍流相位屏与Von Karman模型较好地吻合;该方法的计算复杂度低,能快速模拟大尺寸、高分辨率大气湍流相位屏。

The fast simulation for atmospheric turbulence phase screen with large size and high resolution is essential to verify the performance and the control algorithm stability of the adaptive optical system in laboratory.A scheme of simulating atmospheric turbulence phase screen based on wavelet analysis is proposed.According to the frequency band segmentation of discrete wavelet transform,the Von Karman power spectrum is cut.The approximate high frequency coefficients of corresponding frequency bands at different scales are generated based on the energy conservation principle.The correlation function of low frequency coefficient of the top level is obtained when we use the recursive relations among the low frequency coefficients of wavelet layers,and the correlation function method is used to simulate low frequency coefficients.The final atmospheric turbulence phase screen is synthesized by the wavelet synthesis algorithm.Numerical simulation results show that the atmospheric turbulence phase screen generated based on wavelet analysis is consistent with the Von Karman model.The computational complexity of the proposed method is low,and it can quickly simulate atmospheric turbulence phase screen with large size and high resolution.