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构建光场相机的物理模型,用光场相机测量经过多层大气湍流相位屏后的入瞳光束,根据光场层析技术恢复出视场内整层大气的波前畸变。具体过程分为以下三步:
(1)基于光场相机的基本光学结构,从光场相机的波前探测理论分析入手,建立光场相机波前探测的理论模型,选择合适的衍射传输算法,进行光场波前的成像仿真。
(2)光场大气层析术需要利用波前探测器获得不同视线方向上的累积的湍流畸变波前信息,在进行数值模拟仿真过程中,运用泽尼克分解后计算解析式的方法,从完整波前中切分单个视角的波前,保证各视角波前重叠区域采样的零误差。
图1中,实线圆代表元瞳面区域(Metapupil)的波前相位,虚线圆代表足迹区域(Foot print)的波前相位,它们之间能够通过位置变换相互转换。假设图2中原大气湍流相位屏为蓝色区域,白色圆区域是需要提取出来的目标波前部分,将原大气湍流波前
$ {\rm{\varphi }}\left(x,y\right) $ 进行泽尼克模式分解,得到该波前的若干阶泽尼克模式,随后将每一阶泽尼克模式根据其系数进行波前复原,再对每一单阶泽尼克模式复原出来的波前$ {{\rm{\varphi }}}_{k}\left(x,y\right) $ 进行位置变换,使得位置与目标波前区域相同,最后将得到的泽尼克模式波前分别乘上其对应的泽尼克模式系数,最后求和,得到的结果即为单个视角的波前。(3)运用光场数字重聚焦技术、模式法大气层析技术,复原大视场完整波前。利用光场相机采集到的四维光场原始数据对物空间方向不同位置进行成像时,需要将采集到的光场重新聚焦到新的目标成像平面上,如图3所示。
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在光场层析自适应光学系统的建模仿真中,建立了目标导星分别为自然导星(目标距离无穷远)和激光导星(目标位于有限距离)情况下的光场层析模型,利用具体的数值模拟仿真验证光场相机波前探测系统的大气层析能力。假设探测器的口径为1 m,视场角为60″,大气高度分别位于0 km和6 km。图4展示了目标为三颗自然导星的情况下的模型概念图,图5为光场相机复原两层湍流相位屏的仿真结果。大气湍流波前符合 Kolmogorov 统计规律,复原效果评价指标利用复原波前与原波前残差的均方根RMS 表示:
图 4 两层大气湍流屏和三颗自然导星构成的光场层析模拟仿真系统概念图
Figure 4. Conceptual graph of two-layer atmosphere turbulence screens and three natural guide stars based light field tomography simulation system
图 5 采用自然导星情况下光场层析技术的数值模拟仿真结果。(a) 第一层大气湍流屏;(b) 第二层大气湍流屏。从上到下依次是原始大气像差、复原大气相位、残差、复原前后泽尼克系数
Figure 5. Numerical simulation results of light field tomography at situation of natural guide stars. (a) Fisrt layer of atmosphere turbulence screen; (b) Second layer of atmosphere turbulence screen. From top to bottom is the original atmosphere aberration, the restoration atmospheric phase, the residual error and the Zernike coefficient before and after reconstruction respectively
$$ {\rm RMS}={\left[{ \underset{S}{\iint }{(\phi (r)-\widehat{\phi }(r))}^{2}}{\rm d}{r}\right]}^{1/2}\times {\left[{ \underset{S}{\iint }{\phi }^{2}(r){\rm d}{r}}\right]}^{-1/2}$$ 由图5计算得到的复原前后两层大气湍流残差的 RMS 值分别为:6.04%,9.19%。
对目标为激光导星情况下进行光场层析模型的数值模拟仿真,假设口径为 1 m的探测器,在60″视场范围内分布着三颗位于不同高度的激光导星,分别为 80 km,90 km和100 km,如图6所示为该系统的概念模型。图7给出了光场相机复原两层湍流相位屏的仿真结果。
图 6 两层大气湍流屏和三颗激光导星构成的光场层析模拟仿真系统概念图
Figure 6. Conceptual graph of two-layer atmosphere turbulence screens and three laser guide stars based light field tomography simulation system
图 7 采用激光导星情况下光场层析技术的数值模拟仿真结果。(a) 第一层大气湍流屏;(b) 第二层大气湍流屏。从上到下依次是原始大气像差、复原大气相位、残差、复原前后泽尼克系数
Figure 7. Numerical simulation results of light field tomography at situation of laser guide stars. (a) Fisrt layer of atmosphere turbulence screen; (b) Second layer of atmosphere turbulence screen. From top to bottom is the original atmosphere aberration, the restoration atmospheric phase, the residual error and the Zernike coefficient before and after reconstruction respectively
由图7计算得到复原前后两层大气湍流残差的 RMS 值分别为:8.72%,15.16%。可以看到激光导星引起的聚焦非等晕性使重构大气像差的误差显著增大了。
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笔者利用Seelight中的光场相机模块与PZT变形镜模块搭建了自适应光学仿真系统,如图8所示。验证以光场相机作为波前传感器,与89单元变形镜配合在闭环工作模式下校正大气湍流相位屏的效果。
大气湍流相位屏模型采用基于傅里叶谱的数值方法[10],大气垂直传输距离10 km,湍流强度Cn2为10−15。光场相机模型的参数为:光束口径6 mm,探测波长633 nm,主透镜的f数为30,微透镜阵列的大小为10×10,微透镜元口径200 μm,微透镜阵列f数15,CCD像元尺寸5 μm,动态调制半径为d,d为微透镜元的口径。89单元变形镜致动器以六边形排布。点光源发出光经过湍流相位屏后到达望远镜入瞳处的波前畸变和变形镜的致动器排布方式分别如图9和图10所示。
将光场相机测得光场数据经过动态调制后,利用直接斜率法计算重构矩阵,生成电压信号控制变形镜致动器形成共轭面形补偿波前畸变。表1给出了在闭环控制模式下对大气湍流波前畸变校正后远场光斑随着迭代次数的变化趋势。从结果中可以看出在动态调制时光场相机的闭环校正效果明显,远场光斑的收敛显著,当迭代进行到第三次时远场光斑已经趋于稳定。
表 1 自适应光学系统闭环控制下远场光斑变化趋势
Table 1. Far field spot distribution changing tendency at closed loop of AO system
Number of iterations 0 1 2 3 Closed loop Number of iterations 4 5 6 7 Closed loop
Simulation research on adaptive optics system based on light field camera
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摘要: 在自适应光学系统中,采用传统的哈特曼波前传感器只能在较小视场范围内对大气湍流进行有效校正,而以光场相机作为波前探测器具有视场大、一次曝光可获得多视角方向湍流信息等特点,可以替代传统多层共轭自适应光学(MCAO)系统中的多个波前探测器,达到简化系统,节约成本的效果。文中采用自主研发的光学系统仿真软件Seelight中的光场相机模块,结合光场数字重聚焦技术、模式法大气层析技术,复原了大视场完整波前,并搭建了自适应光学仿真系统,模拟与89单元变形镜配合实现在闭环工作模式下对大视场的大气湍流引起波前畸变的有效校正。Abstract: In adaptive optics (AO) system, the traditional Hartmann wave-front sensor can only be used to effectively correct atmospheric turbulence within a small field of view, while the light field camera served as the wave-front sensor has the characteristics of large field of view and multi-angle directional turbulence information obtained by one single exposure, which can replace multiple wave-front sensors in the traditional multi-layered conjugation adaptive optics (MCAO) system and simplify the system and save costs. In this paper, the light field camera module in Seelight, an optical system simulation software independently developed, was used to restore the complete wavefront of the large field of view combining the optical field digital refocusing technology and the mode atmospheric analysis technology. An adaptive optical simulation system was built with a light field camera and a 89 unit deformable mirror. The simulation results show that the optimized AO system can effectively correct the wavefront distortion caused by atmospheric turbulence in a large field of view under the closed loop working mode.
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Key words:
- wavefront sensing /
- light field camera /
- multi-layered conjugation /
- simulation system
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图 5 采用自然导星情况下光场层析技术的数值模拟仿真结果。(a) 第一层大气湍流屏;(b) 第二层大气湍流屏。从上到下依次是原始大气像差、复原大气相位、残差、复原前后泽尼克系数
Figure 5. Numerical simulation results of light field tomography at situation of natural guide stars. (a) Fisrt layer of atmosphere turbulence screen; (b) Second layer of atmosphere turbulence screen. From top to bottom is the original atmosphere aberration, the restoration atmospheric phase, the residual error and the Zernike coefficient before and after reconstruction respectively
图 7 采用激光导星情况下光场层析技术的数值模拟仿真结果。(a) 第一层大气湍流屏;(b) 第二层大气湍流屏。从上到下依次是原始大气像差、复原大气相位、残差、复原前后泽尼克系数
Figure 7. Numerical simulation results of light field tomography at situation of laser guide stars. (a) Fisrt layer of atmosphere turbulence screen; (b) Second layer of atmosphere turbulence screen. From top to bottom is the original atmosphere aberration, the restoration atmospheric phase, the residual error and the Zernike coefficient before and after reconstruction respectively
表 1 自适应光学系统闭环控制下远场光斑变化趋势
Table 1. Far field spot distribution changing tendency at closed loop of AO system
Number of iterations 0 1 2 3 Closed loop Number of iterations 4 5 6 7 Closed loop -
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