基于二维随机场的地基大型光学望远镜风扰动时程模拟与性能预测

Wind disturbance simulation and optical performance prediction for large ground-based optical telescopes based on two-dimensional stochastic fields

随着地基光学望远镜口径的不断增大,风扰动已成为影响望远镜成像质量最为关键的因素之一。为了深入研究风扰动对望远镜系统性能的影响规律及作用机理,从时域角度对望远镜在风扰动作用下的响应进行时程模拟以及系统性能预测。首先,简要介绍了望远镜结构组成并采用有限元方法建立了结构动力学模型,通过模态变换方法将动力学模型转换到模态坐标系下,从而降低了模型维数、提高了计算效率。然后,提出了一种基于二维随机场的风速时程模拟方法,将望远镜圆顶内的风速场表达为随时间和空间位置变化的二维随机场,通过引入波数谱,克服了谱表达方法中各个离散采样点处互功率谱矩阵Cholesky分解出现数值不稳定的问题,从而可以表达空间和时间频率范围内几乎连续的随机场,并且在数值计算中引入了快速傅里叶变换FFT算法,进一步提高了模拟效率。最后,以2 m口径望远镜为例,对风速环境进行了时程模拟,并对外界平均风速为10 m/s及15 m/s的风扰动作用下,望远镜的性能进行了预测。仿真分析结果表明:作用在望远镜主镜上的风扰动分别造成主镜最大接近45 nm和70 nm的面形误差;作用在次镜及桁架上,主要造成低频的主次镜相对位置和角度偏差。

As the aperture of large ground-based optical telescopes increases,wind disturbance has be⁃come one of the most significant dynamic factors degrading the performance of telescopes.To investigate the influence and interaction principles of wind disturbance on the performance of telescopes,a time-history simulation of the wind disturbance response and performance prediction for telescopes were performed in the time domain.First,the structural parts of the telescope were simply introduced,and a dynamic model of the telescope was established using the finite element method.Using modal transformation,the dynam⁃ic model,expressed in nodal coordinates,was transformed into modal coordinates,thus greatly decreasing the model dimension and greatly improving the computational efficiency.Second,a time-history simula⁃tion method for wind speed was presented based on two-dimensional stochastic fields.The wind speed field in the doom was expressed as a two-dimensional stochastic field that varied according to the temporal and spatial frequencies.The numerical instability occurring in the Cholesky decomposition of the cross-power spectrum matrix in the spectral method was avoided by introducing the wave-number spectrum.The simulation efficiency was further improved by applying the fast Fourier transform(FFT)technique.Finally,using a ground-based telescope with a 2 m aperture as a case study,a time-history simulation of the wind speed,wind disturbance response,and system performance prediction for the telescope was per⁃formed.The simulation results showed that wind disturbances with a mean speed of 10 and 15 m/s would result in a maximum surface root mean square error of the primary mirror of approximately 45 and 70 nm,respectively.In addition,the wind disturbance acting on the secondary mirror and truss would mainly cause optical axis angle and position errors.