基于广义惠更斯菲涅尔原理,通过将拉盖尔高斯光束场方程转化为厄米多项式的形式,计算得到了在非Kolmogorov湍流中传输的平均光强和均方根束宽表达式.数值结果表明,光束阶数越大,波长越长,传输距离越短,则归一化平均光强曲线转变为高斯形式越慢,同时,湍流幂律指数和内尺度越大,基模高斯束宽和湍流外尺度越小,非Kolmogorov湍流对标准拉盖尔高斯光束的作用越小.

Based on extended Huygens -Fresnel principle,the average intensity and the beam width of Standard Laguerre Gaussian beams propagating in non-Kolmogorov turbulence were derived,making use of the Hermite polynomials.Numerical results show that the average intensity profile converts into Gaussian form more slower with larger beam orders and wavelength,or shorter propagating distance.Moreover,the beam width of Standard Laguerre Gauss beams is less affected by non Kolmogorov turbulence with larger turbulent power law exponent and inner scale, or smaller beam width of the fundamental Gaussian mode and outer scale of turbulence.

从产生大气湍流随机相位屏的功率谱反演法原理出发,分析了均匀采样造成的随机相位屏大量低频信息泄漏的不足,提出利用非均匀采样方法对功率谱进行滤波产生随机相位屏.建立了非均匀采样模型,并分析比较了两种采样方法覆盖的采样频率范围和单边采样频率区域的湍流功率,理论证明了非均匀采样功率谱反演产生大气湍流随机相位屏的可行性和有效性.针对大气湍流的Kolmogorov谱,分别仿真计算了两种采样模型下功率谱反演生成的大气湍流随机相位屏.仿真结果表明,在不增加采样点和计算量条件下,非均匀采样方法生成的大气湍流随机相位屏具有丰富的低频和高频信息,有效改善了传统功率谱反演大气湍流随机相位屏时低频信息严重不足的缺陷.

Based on power spectral density method, the uniform sampling leading to the leakage of low frequency in atmosphere phase screens is analyzed. A new method – non-uniform sampling is proposed. The non-uniform sampling is modeled. The covered sampling frequency regions and the powers of single sampling region by the two sampling methods are dis-cussed and compared. The new method proves to be effective and feasible. For the Kolmogorov spectrum of atmospheric turbulence, the numerical simulation phase screens are generated by the two sampling methods. The simulation results show that the random phase screens generated by the non-uniform sampling method under the condition of increasing neither sampling number nor computation burden, possesses rich high and low frequency information.

为了提高涡粘性假设的湍流模型对于非稳态流动的求解精度,同时兼顾其对于稳态流动的求解性能,将雷诺应力项与连续变换方程（CSSE）结合而形成新的应力项,使其根据流场尺度、网格尺度及Kolmogorov尺度来自动调节当地的应力雷诺应力模化水平,避免网格因素在流场模拟中产生不利影响,改正了混合RANS/LES方法的速度型偏离对数率问题;同时,该方法并未引入显式亚格子模型（SGS）,因此回避了亚格子系数确定对于流场模拟精度产生的影响,改善了湍流模型对于流动不稳定性的辨识精度。在湍流平板算例中,CSSE方法计算的边界层速度型精度与雷诺平均方法（RANS）相当,而对于圆柱尾迹的模拟则证明了CSSE方法具有混合RANS/LES方法的优点,即能够准确模拟流动的不稳定性特征。

In order to get the higher precision of the unsteady flow predicted by using liner turbulence model as well as keep the capability of solving the steady flow,the Reynolds-stress term is combined with continuous scale switch equation(CSSE)to form one new stress term which can automatically adjust the local Reynolds-stress level according to the flow field scale,grid scale and Kolmogorov scale.The CSSE method eliminates the disadvantage of grid scale on the flow simulation,the problem of disagreement between the velocity profile obtained by the method of hybrid RANS/LES and the law of the wall is solved.Meanwhile, this method do not use the explicit sub-grid stress(SGS)model which can avoid the disadvantaged impact on the flow simulation caused by SGS coefficient,so the flow instability can be controlled more accurately .The simulations of the boundary flow of the plate and the flow over the cylinder both prove that CSSE method is robust.In the testcase of a turbulent flat-plat

基于实际自适应光学系统倾斜校正回路最常使用的比例积分控制器,分析了最优闭环带宽与大气湍流、测量噪声之间的关系.利用满足Kolmogorov湍流整体倾斜功率谱密度的时间序列进行了相关的数值仿真.结果表明,根据不同湍流强度及测量噪声选择合适的闭环带宽,可以充分发挥自适应光学系统倾斜校正回路的闭环校正能力,减小闭环残差.

Based on the most widely used proportional-integrator controller of the tip-tilt correction loop in an adaptive optical system, the relationship between the optimal closed-loop bandwidth and the atmosphere turbulence as well as the sensor noise is analyzed. Numerical simulation is also performed by using the time serial signals that follow the power spectrum density of the global tilt of Kolmogorov turbulence. Results show that with different atmosphere turbulences and sensor noises, the correction capability of the tip-tilt correction loop can be brought into full play by choosing appropriate closed-loop bandwidth and the residual variance can be reduced.

受大气湍流影响，空间光通信系统中接收光至单模光纤耦合效率降低，根据弱湍流理论，推导了Kolmogorov湍流信道情况下准直高斯光束至单模光纤平均耦合效率表达式，仿真了1 km传输距离下不同接收孔径下平均耦合效率与湍流强度的关系，结果表明：当大气折射率结构常数达到10-12时，耦合效率降到0.1以下，且耦合效率随接收孔径增大而降低。采用37单元自适应光学系统(AO)进行补偿实验，对畸变波前进行重构再利用反射变形镜进行修正的方法，对比不同AO状态下波面图质量及远场长曝光成像及质心位置漂移，发现AO进行低阶像差校正后，波面峰-谷值及标准差减小、斯特列尔比(SR)及耦合效率增加，进行高阶校正后情况进一步改善。

The coupling efficiency of received optical power into a single-mode fiber is degraded by atmospheric turbulence in a free space optical communication system. The expression of average coupling efficiency of a collimated Gaussian beam into a single-mode fiber was derived under Kolmogorov turbulence channel, according to the theory of weak turbulence statistics. The relations between average coupling efficiency and turbulence intensity under different received aperture in 1 km propagation path were also simulated. The results show that coupling efficiency decreases below 0.1 when refractive-index structure constant rises to 10-12, and coupling efficiency degrades when the received aperture increases. A 37-element adaptive optics system with H-S wavefront sensor was adopted to compensate the efficiency. Compared with long exposure imaging and centroid position offset in different status of AO system, it was found that the P-V value and standard deviation decreased, Strehl ratio and coupl