饶长辉
论文题目：非Kolmogorov湍流情况下低阶校正自适应光学系统的性能研究
作者简介：饶长辉，男，1971年09月出生，1998年03月师从于中国科学院光电技术研究所凌宁教授和姜文汉教授，于2001年07月获博士学位。
摘 要
本文在国家自然科学重点基金和国家高技术计划863-308的支持下，深入系统地研究了非Kolmogorov湍流情况下低阶校正自适应光学系统的性能。本文的主要研究内容和结果如下：
1. 本文首次比较全面地研究了光波在非Kolmogorov湍流中传播时相位扰动的时空特性，推导了相位空间和时间结构函数、时间功率谱以及几个表征大气湍流特性的几个参数——规格化大气相干长度、特征时间和特征频率的表达式。结果表明：在惯性区域内，相位空间结构函数与空间位移的（β-2）成正比（β为大气湍流功率指数），相位时间结构函数与时间的（β-2）成正比；在惯性区域内，相位时间功率谱的指数下降因子为（β-1）；规格化大气相干长度ρ0、特征时间τR和特征频率fR均是β的函数。
2. 本文首次系统地研究了应用Shack-Hartmann波前传感器测量大气湍流参数的方法和结果。文中结合Shack-Hartmann波前传感器所测量的斜率数据的时空相关，通过建立差分到达角起伏因子、斜率结构-相关因子、斜率归一化相关系数、到达角起伏方差、斜率结构函数以及斜率结构-相关函数等变量，用来测量大气湍流功率指数β和大气湍流强度ρ0。研究结果表明：差分到达角起伏因子、斜率结构-相关因子和斜率归一化相关系数均只与大气参数β有关，而与ρ0无关；波前到达角起伏方差、斜率结构函数和斜率结构-相关函数是大气参数β和ρ0的函数；斜率结构-相关因子和斜率结构-相关函数消除了相加噪声的影响；差分到达角起伏因子和斜率结构函数可以消除望远镜的抖动，但测量噪声对其有影响。
3. 本文首次系统地研究了非Kolmogorov湍流情况下大气湍流相位扰动低阶模式的时空特性。文中通过大气湍流相位畸变的Zernike多项式分解分析了非Kolmogorov湍流情况下大气湍流相位扰动低阶模式的空间特性，包括模式系数方差及其模式之间的相关性，结果表明：随着湍流功率指数β的增大，低阶模式在大气湍流相位扰动中所占比重逐渐增加，模式之间的耦合相对逐渐减小。文中还详细推导了非Kolmogorov湍流情况下大气湍流相位扰动低阶模式的时间功率谱的理论表达式，并进行了数值计算。研究结果表明：倾斜（包括Z倾斜和G倾斜）功率谱曲线的低频段的指数下降因子为4/3-6β/11，离焦、象散和彗差等高阶项的功率谱低频段指数下降因子为0； Zernike多项式各展开项系数的时间功率谱的高频段随频率的-(β+2)次方下降，G倾斜功率谱的高频段随频率的-β次方下降；大气湍流外尺度对Zernike多项式各展开项系数功率谱曲线的低频段影响显著，而对高频段几乎没有影响；大气湍流外尺度越小，低频段下降更快。
4. 通过引入时域模式校正因子和模式非等晕因子，本文比较完整地研究了低阶校正自适应光学系统的波前校正残余误差。在国际上首次报导了自适应光学系统对扩展目标进行校正时各阶模式的非等晕误差的研究结果，并给出了偏轴点源信标和在轴圆状均匀分布信标情况下的数值计算结果。研究结果表明：自适应光学系统对大气湍流波前扰动的时域校正效果与湍流功率指数β、系统测量信噪比snr以及系统闭环带宽f3dB等因素有关；在一定的系统闭环带宽f3dB情况下，湍流功率指数β越大，系统测量信噪比snr越大，系统时域校正效果越好；在一定的湍流功率指数β和系统测量信噪比snr的情况下，系统存在一个最佳闭环工作带宽，此时系统补偿效果最好。扩展目标情况下低阶模式校正自适应光学系统的模式校正有效性与湍流功率指数β、信标光强分布B(b)、观测系统孔径D以及传输距离L有关。与点源信标相比，圆状均匀分布信标所对应的模式非等晕因子明显减小。对同一信标而言，模式阶数越高，模式校正效果越差。对于同一信标和模式阶数而言，湍流功率指数β越大，光波传输距离L越小，观测系统孔径D越大，模式非等晕因子都越小，模式校正越有效。
5. 本文通过建立低阶校正自适应光学系统成像补偿效果与波前校正残余误差的关系，首次系统地研究了非Kolmogorov湍流情况下低阶模式校正自适应光学系统的成像补偿效果，并给出了计算结果。研究结果表明：与系统开环相比，低阶模式校正后能明显提高系统成像性能；在一定的条件下，湍流功率指数β越大，湍流强度越弱，系统测量信噪比越大，信标扩展度越小，系统补偿效果越好。在不考虑系统低阶校正残余误差及相同湍流强度ρ0和功率指数β情况下，系统被校正模式数越多，系统Strehl比越大，FWHM越小，系统补偿效果越明显。在观测系统口径不是很大且大气条件比较好的情况下，自适应光学系统只要校正大气湍流低阶模式误差，就可以取得接近系统衍射极限的补偿效果。对于各校正模式而言，各阶模式都存在一最佳闭环带宽，且最佳闭环带宽是其测量信噪比snr和湍流功率指数β的函数。其它条件一定，系统测量信噪比snr越大，最佳闭环带宽越大；湍流功率指数β越大，最佳闭环带宽越小。在相同校正模式阶数和相同湍流功率指数β情况下，随着目标扩展度的增加，系统补偿效果逐渐变差。对于扩展目标而言，在一定的目标扩展度情况下，偏轴点源信标比在轴均匀圆状信标的系统补偿效果要差得多。在对扩展目标进行校正时，并非系统校正模式阶数越多越好。对于一定的信标扩展度，系统存在一个最佳校正模式阶数。信标扩展度越大，最佳校正模式阶数越少。
6. 本文还对太阳表面米粒结构图象探测对比度、模式耦合对扩展目标倾斜校正自适应光学系统性能的影响进行了分析，并根据所采集的实际太阳表面米粒图象采用事后处理的方法研究了自适应光学系统对太阳表面米粒结构倾斜校正时的补偿效果，验证了互相关因子和绝对差分这两种低对比度扩展目标跟踪算法的可行性。研究结果表明：探测器所探测到的太阳表面米粒结构图象对比度是观测系统口径、大气湍流功率指数、规格化大气相干长度以及探测器象素灵敏度的函数。相同系统口径情况下，随着湍流相干长度的增大，对比度逐渐增大。探测器所探测到的太阳表面米粒结构图象对比度与探测灵敏度有关，探测灵敏度越高，其对比度越大。与不存在模式耦合相比，高阶模式和倾斜模式之间的耦合使得系统倾斜校正波前残余误差有所增大。目标扩展度越大，湍流功率指数β越小，则系统倾斜校正波前残余误差也越大，模式耦合对倾斜校正自适应光学系统波前校正残余误差的影响也越大。对于如太阳表面米粒结构和太阳黑子这类低对比度扩展目标，采用互相关因子和绝对差分算法进行相关跟踪可以有效提取波前整体倾斜误差信号。相对于太阳米粒结构开环长曝光象，去除倾斜后能有效改善长曝光象的图象对比度。倾斜校正太阳米粒结构长曝光象的对比度改善程度与观测目标的视场、参考图象的扩展度以及观测目标区域与参考区域之间的角间距有关。观测目标视场越大，参考目标的扩展度越大，观测目标区域与参考区域之间的角间距越大，对比度改善就越小。
本文建立了一套比较完整的自适应光学低阶部分校正理论，对于自适应光学系统设计和性能评判等具有重要的指导意义和参考价值。
关键词：自适应光学，非Kolmogorov湍流，部分校正，性能分析。
Performance analysis of low-order correction adaptive optical system
for
non-Kolmogorov turbulence
Abstract
Under the support of the National Natural Sciences foundation and Hi-Tech Project, the performance of low-order correction adaptive optical system for non-Kolmogorov turbulence is studied systematically in this dissertation.
Firstly, This paper presents a theoretical approach of analysing the spatial and temporal characterizations of phase fluctuations in non-Kolmogorov turbulence. The spatial structure function, the temporal structure function and the temporal power spectrum of phase fluctuations are derived. The results show the spatial and temporal structure function of phase fluctuations are proportional to the β-2 power of spatial and temporal displacements respectively (β is the power-law exponent of the turbulence). The generalized coherence length ρ0, the characteristic frequency fR and the characteristic timeτR are expressed as functions of the index structure constant along the propagation path and the wind velocity.
Secondly, the spatial and temporal characterization of the phase fluctuations in non-Kolmogorov turbulence and the methods of measuring the atmospheric parameters with Shack-Hartmann wave-front sensor are investigated. To our knowledge, the several major parameters that characterize the atmospheric turbulence, the generalized coherence length, the characteristic time and the characteristic frequency are first expressed as the functions of the index structure constant along the propagation path and the wind velocity. For G-tilt and Z-tilt, the variance of the angle-of-arrival fluctuations for non-Kolmogorov turbulence is first derived. Based on Shack-Hartmann wave-front sensor, The differential angle-of-arrival fluctuations coefficient, the slope structure-correlation coefficient, the normalized slope correlation coefficient and the slope structure-correlation function for non-Kolmogorov turbulence are developed to evaluate the atmospheric parameters, the power-law exponent of the turbulenceβand the generalized coherence lengthρ0. The developed methods are compared and are used to evaluate β in the atmospheric experiments for laser beam propagation through 1000m horizontal path.
Thirdly, the spatial and temporal characterization of the low order modes of the phase perturbation is analyzed. The Zernike-coefficient variance and the correlation of the Zernike modes are given for non-Kolmogorov turbulence. The temporal power spectrum of the low-order Zernike modes for non-Kolmogorov turbulence is first deduced in detail. The numerical results and the experimental results are presented. The results show in horizontal atmosphere, the temporal power spectra is proportional to the 4/3-11β/6 power of the frequencyν for tilts andν0 for defocus, astigmatism and coma for smallν values respectively. For largeν values, all the spectra have the same asymptotic behavior and decrease as the –β-2 power of ν except for G-tilt whose power spectra decrease as the –β power of νin horizontal atmosphere. The temporal power spectra is influenced by outer scale of atmospheric turbulence for small ν values and with the decrease of outer scale, the spectra becomes steeper and steeper.
Fourthly, The wavefront residual error of low-order correction adaptive optical system is analyzed by introducing the temporal modal correction coefficient and the modal anisoplanatic coefficient. The research of the anisoplanatic error of low-order correction adaptive optical system with the distributed beacons, to our knowledge, is first reported. With distributed beacons, the modal anisoplanatic coefficient is derived by using the wavefront expansion on the Zernike polynomials for non-Kolmogorov turbulence. Numerical results are presented for laser beam horizontal atmospheric propagation with offset point beacon and on-axis uniform circular beacon. The results show that the compensation for the on-axis uniform circular beacon is much more effective than that for the offset point beacon. The low-order modes are much more correlated than the higher-order modes. The larger the power-law exponent β, the smaller the propagation path length L and the larger the diameter D of the telescope aperture, the more effective the compensation is. For a specific beacon extended degree of beacon for which there are a maximum number of modes Nmax to be corrected, only low-order-correction systems are useful.
Fifthly, the imaging compensation effectiveness of low-order correction adaptive optical system is investigated in detail by constructing the relationship between the compensation effectiveness and the wavefront residual error. The computation results are presented. The results show the long-exposure image Strehl ratio and FWHM can be improved by closed-loop low-order correction markedly. With the increase of the generalized coherenceρ0, the long-exposure image Strehl ratio becomes larger and the image FWHM decreases gradually for the same power-law exponentβ. Under the condition of the same generalized coherenceρ0, the compensation effectiveness becomes worse with the increase of the power-law exponent β when β is relatively smaller. Whenβis very large, the compensation effectiveness improve gradually with the increase ofβ. The more the number of the corrected modes is, the compensation of adaptive optical system is more effective for the same power-law exponent β and the same generalized coherenceρ0. Under the better atmospheric condition, the low-order correction image FWHM is close to the diffraction limit resolution of the telescope.
Sixthly, The r.m.s. contrast in the solar granulation, the effect of modal coupling on the performance of low-order adaptive optical system for extended object, and the performance of the tip-tilt correction adaptive optical system for solar granulation by post-processing according to the calibrated solar granulation images are studied. The relationships between the r.m.s. contrast in the solar granulation and the diameter of the telescope, the atmospheric coherent length and the pixel sensitivity of the detector are analyzed respectively. The effect of the modal coupling on the performance of the tip-tilt correction adaptive optical system is investigated. The feasibility of the correlation algorithm for the low contrast and extended object, the cross-correlation coefficient and the absolute difference algorithm, is verified. The long exposure images are compared with and without the tip-tilt correction.
This dissertation set up a set of theory of low-order adaptive optical system comparative completely. It is very useful and beneficial for the design and performance evaluation of adaptive optical system.
Key words: adaptive optics, non-Kolmogorov turbulence, partial correction, and performance analysis.
