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太阳望远镜在实际观测过程中的波前像差按其来源具体可分为三种类型:第一类为光学装调误差引起的静态位置失配波前像差,此类像差大多来源于主次镜位置失调;第二类为太阳辐射结构变形、指向相关结构弯沉、风载结构变形等引起的准静态位置失配波前像差,此类像差形式与静态位置失配波前像差相同,可以等效为主次镜位置失调所产生像差;第三类为低频加工误差、镜面热变形、环境温度变化等引起的非失配波前像差,此类像差往往表现为任意大小的像差组合。上述因素引起的波前像差主要以低阶像差(如倾斜、离焦、像散、彗差、球差)为主,且其时间频率较低,对于这些低阶低频的像差,将其定义为望远镜运行过程中的低时空频率像差。
夏克-哈特曼波前探测器能够实现对太阳望远镜运行过程中波前像差的实时探测,当太阳望远镜处于静态状态下时,太阳望远镜次镜的空间位置Х与夏克-哈特曼波前探测器的波前探测数据Ф存在如下关系:
$$ \varPhi = {{F}}(X) $$ (1) 太阳望远镜的次镜共有六个自由度的位移量,分别为X轴平移量Dx、Y轴平移量Dy、Z轴平移量Dz以及绕X轴旋转量Tx、绕Y轴旋转量Ty、绕Z轴旋转量Tz。由于次镜关于Z轴旋转对称,绕Z轴旋转量Tz不会对波前探测数据产生影响,故次镜共有五个方向上的位移对夏克-哈特曼波前探测器的波前探测数据Ф产生影响。利用次镜刚体位移对波前探测数据产生影响,实质上是影响系统像差的这一特性,可以达到使用次镜刚体位移对太阳望远镜系统像差进行校正的目的。
将望远镜次镜在某单一自由度方向上进行位移,如Tx,分别测量其在−0.05°、−0.04°、···、+0.05°处的夏克-哈特曼波前数据Ф,并分解为各项Zernike系数,文中采用的Zernike多项式的波前图样如图1所示,其中,Z1项为活塞像差,Z2项、Z3项分别为X和Y方向上的倾斜像差,Z4项为离焦像差,Z5项、Z6项分别为45°和0°像散,Z7项、Z8项分别为X方向和Y方向上的彗差,Z9项为球差。在五个自由度方向上均进行此操作,并代入灵敏度矩阵中进行拟合,得到次镜位移量与Zernike系数的数学关系如下:
$$ Z - {Z_0} = A\Delta {{X}}{.^2} + B\Delta {{X}} + \delta $$ (2) 式中:$ Z $为当前位置处的Zernike系数;$ {Z_0} $为起始位置处的Zernike系数;$ A $、$ B $分别为二次项系数矩阵和一次项系数矩阵;$\Delta {{X}}$表示次镜沿每个自由度方向上的位移量;$ \delta $为残差余项;$\Delta {{X}}{.^2}$表示次镜每个自由度方向上位移量的平方所形成的矩阵,如公式(3)所示:
$$ \Delta {{X}}{.^2} = [\begin{array}{*{20}{c}} {\Delta D{x^2}}&{\Delta D{{{y}}^2}}&{\Delta D{{\textit{z}}^2}}&{\Delta T{x^2}}&{\Delta T{y^2}} \end{array}]' $$ (3) 在望远镜实际运行中,对系统像差的校正转化为求解使得轴上视场像差的Zernike系数Z取最小值的次镜位移量,文中采用最小二乘法的方式进行求解。根据次镜位移量由位姿调整机构对次镜的位姿进行实时调整,最终实现对望远镜实际运行中低时空频率像差的实时闭环校正。
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格里高利系统是常见的太阳望远镜形式,文中对POST太阳望远镜系统[15-17]进行次镜刚体位移校正的数值仿真研究,望远镜光学布局和装置图如图2所示,系统参数如表1所示。
表 1 望远镜参数
Table 1. Telescope parameters
Surface Mechanical diameter d/mm Radius of curvature r/mm Interval D/mm Conic factor Primary mirror 600 −2 040 −1320 −1 Secondary mirror 180 504.812 - −0.466 为建立Zernike系数与次镜位置变化量的数学关系,保证系统像差次镜校正量的精确计算,对次镜进行五个自由度方向上的位置扰动,每个自由度方向上等间距选取11个采样点,受次镜位置影响的像差与次镜位置变化量的关系如图3所示。
分析可得,Dx和Ty对系统像差中的Z2项、Z8项有着相同程度的影响,但是其对Z4项、Z6项的影响不同,因此当系统像差中的Z2项、Z8项需要校正时,需要同时对Dx、Ty进行调整,在保证减小Z2项、Z8项的同时尽可能降低Z4项、Z6项。Dy和Tx对系统像差中Z3项、Z7项、Z4项、Z6项的校正,Dz对系统像差中Z4、Z9项的校正也遵循以上原则。通过对次镜在Dx、Dy、Dz、Tx、Ty五个自由度方向上的位置调整,达到最小化系统像差的目的。
图 3 Zernike系数受次镜五个自由度方向位移影响曲线图。 (a) x方向平移;(b) y方向平移;(c) z方向平移;(d) x方向旋转;(e) y方向旋转
Figure 3. Curve of Zernike coefficients affected by the displacement in the direction of five degrees of freedom of secondary mirror. (a) Translation around x axis; (b) Translation around y axis; (c) Translation around z axis; (d) Rotation around x axis; (e) Rotation around y axis
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通过引入不同类型的像差,能够验证由建立起数学关系计算得到的次镜位移量对系统像差的校正能力。由指向相关结构弯沉、风载结构变形、太阳辐射结构变形等准静态位置失配误差引起的像差与静态位置失配像差形式相同,以倾斜、离焦、彗差为主,同时含有少量像散与球差。
位置失配误差引起像差的次镜刚体校正效果如图4所示,使用次镜刚体校正后,系统像差RMS值由1.331 μm降低至0.005 μm,次镜刚体位移校正效果良好,位置失配误差引起像差被完全校正。
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对于镜面热变形、环境温度变化、低频加工误差等因素引入的非失配误差,其具有低阶像差大小以任意比例组合的特点,与主次镜间位置失配引起的像差组合比例具有显著区别,但是从形式上看,依然以倾斜、离焦、彗差、像散、球差为主。对非失配误差进行反演与补偿的研究,次镜刚体位移校正结果如图5所示。
图 5 非失配误差引起像差的波前图和Zernike系数。(a) 校正前; (b) 校正后
Figure 5. Wavefront diagram and Zernike coefficients of aberration caused by non-mismatch error. (a) Before correction; (b) After correction
分析波前数据,波前像差RMS值由2.433 μm降低至0.276 μm,其中倾斜、离焦、彗差项被完全校正,Z6项0°像散由−0.197 μm降低至−0.150 μm,剩余像差以Z9项球差、Z6项0°像散为主(次镜对Z5项无校正能力),对其继续校正会产生更大量的倾斜、彗差、离焦,不满足整体像差RMS最小化的条件。据此可以得出结论,对于由非失配误差引入的像差,次镜刚体位移对倾斜、离焦、彗差校正效果好,对像散和球差也有一定的校正效果。
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太阳望远镜在实际运行过程中的像差来源总是多种的,对包含了位置失配误差和非失配误差的多源混合误差的校正反映了次镜刚体位移在太阳望远镜运行过程中实际的校正效果,如图6所示。次镜刚体校正后,系统像差RMS值由1.337 μm降低至0.279 μm,剩余像差主要以Z9项球差和Z6项0°像散为主,次镜刚体位移对望远镜运行过程中多源混合误差也具有较好的校正效果。
图 6 多源混合误差引起像差的的波前图和Zernike系数。 (a) 校正前; (b) 校正后
Figure 6. Wavefront diagram and Zernike coefficient of aberration caused by multi-source mixed error. (a) Before correction; (b) After correction
分析次镜刚体位移对位置失配误差、非失配误差、多源混合误差的校正情况,得到次镜刚体位移像差校正的总体原则:在校正某一像差时总会影响其他像差,这些像差也应被降低,或是其增大量小于那些被校正的像差,即校正后,系统像差的总RMS值降低。
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实验使用与主镜同焦点的光源代替主镜,同时使用Hexapod对次镜的位移量进行控制,使用哈特曼相机对环境光进行标定,消除环境光的影响后,对轴上视场出瞳面波前像差进行测量。光路图和实际布局如图7所示。
文中研究的望远镜系统属于同轴系统,经过穿轴处理,并通过物像关系调整各个光学元件的前后间距,完成粗装调,并使用灵敏度矩阵法精装调后,在该位置重新测量灵敏度矩阵,通过随机调整光学元件的位置、改变变形镜面型的方式引入不同误差来源的像差,分别对位置失配像差、非位置失配像差、多源混合像差各进行了五组次镜刚体校正实验。
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次镜刚体位移对五组位置失配误差的校正前后对比如图8和图9所示。次镜刚体位移对非失配误差有良好的校正效果,每组像差的RMS值均降低至原RMS值的9%以下。以剩余球差最小的第五组数据为例,对各项Zernike系数的前后变化进行研究,如表2所示,倾斜、离焦、彗差得到大量校正,剩余量受Hexapod精度影响无法降低,球差也得到了改善,由0.131 μm降低至0.089 μm,剩余像差主要以光路透镜引入的球差为主,分析灵敏度矩阵,降低剩余的球差会产生更大量的离焦,无法进一步校正。
图 8 位置失配误差引起像差的波前图校正前后对比。(a1)~(a5) 校正前;(b1)~(b5) 校正后
Figure 8. Wavefront diagram of aberration caused by position mismatch error. (a1)-(a5) Before correction; (b1)-(b5) After correction
图 9 位置失配误差引起像差的RMS值校正前后对比。(a) 校正前;(b) 校正后
Figure 9. RMS of aberration caused by position mismatch error. (a) Before correction; (b) After correction
表 2 第五组实验数据-位置失配误差引起像差校正(单位:μm)
Table 2. Group 5 experimental data-correction of aberration caused by position mismatch error (Unit: μm)
Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 RMS Before correction −1.257 0.437 0.019 −0.050 −0.024 −0.111 0.020 0.131 1.343 After correction −0.001 0.018 0.044 −0.027 −0.033 −0.028 0.003 0.089 0.113 -
次镜刚体位移对五组非失配误差的校正前后对比如图10和图11所示。次镜刚体位移对非失配误差有较好的校正效果,每组像差的RMS值均降低至原RMS值的40%以下,以剩余球差最小的第六组数据为例,对各项Zernike系数的前后变化进行研究,如表3所示,倾斜、离焦得到了大量校正,Z8项Y方向彗差由0.148 μm降低至0.107 μm,但并未完全校正,分析灵敏度矩阵,其原因是Dx和Ty对Z2、Z8项的影响相同,校正Z8项会产生更大量的倾斜,故无法进一步校正。
图 10 非失配误差引起像差的波前图校正前后对比。(a1)~(a5) 校正前;(b1)~(b5) 校正后
Figure 10. Wavefront diagram of aberration caused by non-mismatch error. (a1)-(a5) Before correction; (b1)-(b5) After correction
图 11 非失配误差引起像差的RMS值校正前后对比。(a) 校正前;(b) 校正后
Figure 11. RMS of aberration caused by non-mismatch error. (a) Before correction; (b) After correction
表 3 第六组实验数据-非失配误差引起像差校正(单位:μm)
Table 3. Group 6 experimental data-correction of aberration caused by non-mismatch error (Unit: μm)
Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 RMS Before correction 0.016 0.443 0.103 −0.005 0.115 −0.001 0.148 0.012 0.492 After correction 0.031 0.036 0.037 0.006 0.121 −0.002 0.107 −0.008 0.172 -
次镜刚体位移对五组多源混合误差的校正前后对比如图12和图13所示。次镜刚体位移多源混合像差有较好的校正效果,每组像差的RMS值均降低至原RMS值的15%以下,以初始像差值最大的第15组数据为例,对各项Zernike系数的前后变化进行研究,如表4所示,倾斜、离焦得到了大量校正,Z5、Z6项像散也得到了校正,分析灵敏度矩阵,其原因在于初始像差中存在较大量的倾斜,能够按一定比例校正像散。
图 12 多源混合误差引起像差的波前图校正前后对比。(a1)~(a5) 校正前;(b1)~(b5) 校正后
Figure 12. Wavefront diagram of aberration caused by multi-source mixed error. (a1)-(a5) Before correction; (b1)-(b5) After correction
图 13 多源混合误差引起像差的RMS值校正前后对比。(a) 校正前;(b) 校正后
Figure 13. RMS of aberration caused by multi-source mixed error. (a) Before correction; (b) After correction
表 4 第15组实验数据-多源混合误差引起像差校正(单位:μm)
Table 4. Group 15 experimental data-correction of aberration caused by multi-source mixed error (Unit: μm)
Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 RMS Before correction −2.029 0.809 −0.576 −0.090 −0.054 −0.068 −0.009 0.127 2.265 After correction −0.023 −0.003 0.014 −0.012 −0.0007 0.102 −0.035 0.108 0.155
Low spatio-temporal frequency wavefront aberration correction technology of solar telescope
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摘要: 针对大口径太阳望远镜系统运行过程中由于静态位置失配误差、风载弯沉等准静态位置失配误差以及热变形等非失配误差引起的波前像差导致成像质量下降的问题,在对太阳望远镜系统波前像差时空分频的基础上,提出采用次镜刚体位移对太阳望远镜低时空频率波前像差校正的方法,建立起次镜刚体位移与像差校正量的关系,并通过数值仿真及实验验证了采用次镜刚体位移对上述来源像差的校正能力。数值仿真和实验结果表明:次镜刚体位移能够对望远镜系统运行过程中的低时空频率波前像差进行有效校正,其中,对位置失配误差校正后像差RMS值低于原值的9%,对非失配误差校正后像差RMS值低于原值的40%,对多源混合误差校正后像差RMS值低于原值的15%。Abstract:
Objective Solar telescopes are important equipment for conducting solar physics research and predicting space weather. During operation, large aperture solar telescope systems are affected by factors such as optical and mechanical structural deformation caused by solar radiation, gravitational deflection in different directions, wind-borne optical structural deformation, and environmental temperature changes, resulting in wavefront aberrations, leading to significant degradation in the imaging quality of the solar telescope system, and restricting the resolution of solar atmospheric imaging. Adaptive optical systems are the main means of correcting low spatio-temporal frequency aberrations during the operation of solar telescopes, but their correction of low-order aberrations wastes a large amount of travel and sacrifices their ability to correct high-order aberrations. Therefore, it is necessary to correct the low spatio-temporal frequency aberrations during the operation of the solar telescope without increasing the complexity of the solar telescope system. Methods A simulation system and an experimental system have been established for the 60 cm POST solar telescope system. The sensitivity matrix of the displacement of the secondary mirror rigid body is calculated, and the low spatio-temporal frequency aberration is introduced using a deformable mirror to simulate low-order aberrations. The aberration of the optical system's field of view on the axis is observed using a Hartmann camera. The displacement of the secondary mirror rigid body required for correcting the aberration is calculated using the sensitivity matrix method. Finally, the introduced low spatio-temporal frequency aberration is corrected by adjusting the position of the secondary mirror rigid body. The results of the system fine assembly are shown (Fig.4). Results and Discussions The low spatio-temporal frequency aberrations for simulated solar telescope systems are corrected, the ability of secondary mirror rigid body displacement is quantitatively analyzed to correct different types of low-order aberrations, and the principles for correcting low spatio-temporal frequency aberrations are provided. The simulation results are verified through experiments, where the RMS value of the aberration after correction for the position mismatch error of the secondary mirror pair is lower than 9% of the original value (Fig.9), the RMS value of the aberration after correction for the non-mismatch error is lower than 40% of the original value (Fig.10), and the RMS value of the aberration after correction for the multi-source mixing error is lower than 15% of the original value (Fig.11). Conclusions A wavefront correction algorithm and implementation system for specific scenes have been constructed with adaptive optics. The real-time wavefront correction has been completed using a hexapod driven secondary mirror. The studies of correction for position mismatch error, non-mismatch error, and multi-source mixed error have been conducted, and multiple sets of experiments have been conducted. Without increasing the complexity of the optical system, the low spatio-temporal frequency aberration of the system has been reduced, and the imaging resolution of the solar telescope has been improved. The secondary mirror rigid body displacement correction method can reduce the low spatio-temporal frequency aberration during the operation of solar telescope systems without adding optical components, and has good development prospects and application value. -
Key words:
- imaging system /
- aberration correction /
- sensitivity matrix method /
- secondary mirror /
- solar telescope
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图 3 Zernike系数受次镜五个自由度方向位移影响曲线图。 (a) x方向平移;(b) y方向平移;(c) z方向平移;(d) x方向旋转;(e) y方向旋转
Figure 3. Curve of Zernike coefficients affected by the displacement in the direction of five degrees of freedom of secondary mirror. (a) Translation around x axis; (b) Translation around y axis; (c) Translation around z axis; (d) Rotation around x axis; (e) Rotation around y axis
表 1 望远镜参数
Table 1. Telescope parameters
Surface Mechanical diameter d/mm Radius of curvature r/mm Interval D/mm Conic factor Primary mirror 600 −2 040 −1320 −1 Secondary mirror 180 504.812 - −0.466 表 2 第五组实验数据-位置失配误差引起像差校正(单位:μm)
Table 2. Group 5 experimental data-correction of aberration caused by position mismatch error (Unit: μm)
Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 RMS Before correction −1.257 0.437 0.019 −0.050 −0.024 −0.111 0.020 0.131 1.343 After correction −0.001 0.018 0.044 −0.027 −0.033 −0.028 0.003 0.089 0.113 表 3 第六组实验数据-非失配误差引起像差校正(单位:μm)
Table 3. Group 6 experimental data-correction of aberration caused by non-mismatch error (Unit: μm)
Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 RMS Before correction 0.016 0.443 0.103 −0.005 0.115 −0.001 0.148 0.012 0.492 After correction 0.031 0.036 0.037 0.006 0.121 −0.002 0.107 −0.008 0.172 表 4 第15组实验数据-多源混合误差引起像差校正(单位:μm)
Table 4. Group 15 experimental data-correction of aberration caused by multi-source mixed error (Unit: μm)
Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 RMS Before correction −2.029 0.809 −0.576 −0.090 −0.054 −0.068 −0.009 0.127 2.265 After correction −0.023 −0.003 0.014 −0.012 −0.0007 0.102 −0.035 0.108 0.155 -
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