用于提高自适应光学系统空间校正能力的组合变形镜波前校正技术研究
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摘要
自适应光学技术通过实时校正大气湍流等引起的波前动态误差,使光学系统可以适应外界环境的变化,始终保持最佳工作状态。波前校正器是自适应光学系统中的核心部件,如何提高波前校正器的空间校正能力是自适应光学理论和实验研究的重要内容之一。本文提出了利用光学共轭关系构造成组合变形镜实现波前校正的技术,可以在现有变形镜器件的基础上,使多个少驱动单元变形镜组合成一个等效的多驱动单元变形镜,从而有效的提高自适应光学系统的空间校正能力。论文围绕变形镜的空间特性,以连续表面分立压电驱动变形镜为对象,对组合变形镜波前校正技术的原理、特点和空间校正能力等进行了系统的理论和实验研究。
首先,系统的研究了连续表面分立压电驱动变形镜的空间特性。分析了变形镜面形的求解方法,指出利用高斯型影响函数独立加权叠加方法描述面形存在一定的近似性。研究了变形镜结构参数和空间拟合能力的关系,结果表明:增加驱动器密度、选择适当的高斯指数和交连值,有利于提高变形镜的空间校正能力。进一步,应用空间滤波器模型研究了变形镜对畸变波前的校正过程,从空间频域验证了变形镜特性和波前校正能力的关系。此外,论文尝试使用随机并行梯度下降(SPGD)优化算法求解针对特定像差的变形镜驱动器的优化排布方式,获得了有规律的图形,结果说明:适当增加有效孔径边缘的驱动器数量有利于变形镜空间校正能力的提高。
其次,提出了组合变形镜的系统结构,利用光学共轭关系可以将两个正方形排列或三个三角形排列的变形镜构成一个组合变形镜进行波前校正,甚至可以实现将不同种类的变形镜进行组合。分析了组合变形镜波前校正的原理,给出了以连续表面分立压电驱动变形镜构成的组合变形镜的整体面形表达式。仿真计算证明组合变形镜可以等效为一个单一变形镜,由于有效的增加了驱动单元数和交连值,因此可以明显的提高系统的空间校正能力。
进一步,分析了应用组合变形镜进行波前校正时引入的轴向和横向匹配误差对空间校正能力的影响。一方面,通过几何光学和物理光学计算,说明理想4F系统可以实现波前再现,同时也看到小像差畸变波前在大菲涅尔数情况下自由传播的变化很小,因此实验室条件下使用组合变形镜时可以省去4F系统连接。另一方面,通过仿真计算表明:闭环情况下组合变形镜校正能力对各镜之间横向空间匹配误差并不敏感,这将有利于系统的实现。
此外,分析和总结了各类多变形镜自适应光学系统中波前校正器的控制解耦方式,指出组合变形镜可以直接应用单变形镜的方法来控制,并具体分析了配合哈特曼波前传感器使用直接斜率法的控制方法。最后讨论了组合变形镜的应用前景。
在实验验证方面,首先使用平面干涉仪验证了组合变形镜波前校正的原理,生成了指定的像差面形,然后搭建了应用组合变形镜的完整的自适应光学系统,实现了系统的闭环校正。对静态像差的良好校正结果从实验上证明了组合变形镜波前校正技术在提高系统空间校正能力方面的可行性和优越性。
通过简单的方法,组合变形镜可以在现有器件上实现变形镜驱动单元密度的增加和排布方式的改变,从而提高自适应光学系统的校正能力。本文的研究结果将为变形镜的设计和组合变形镜系统的实际应用提供一定的理论参考和工程应用经验。
By compensating random optical wavefront distortions real-timely, the adaptive optics (AO) system can hold the best working state in despite of the variable ambient. The wavefront corrector is one of the key elements of AO system. And improvement of the spatial correction capability of correctors is the primary coverage of AO theory and experiment research. In this dissertation, a kind of new adaptive optics configuration, in which several existing deformable mirrors (DMs) with optical conjugation relationships are equivalent to a new single corrector with more actuators to compensate high-order aberrations, is proposed. It is proofed that the combinational deformable mirror (CDM) technique can improve the spatial compensation capability of current AO system effectively. Based on the continuous surface DM with discrete axial piezoelectric actuators, the principles, the characters and the spatial compensation capability of CDM technique are studied in theory and experiment.
First, the spatial character of continuous surface DM with discrete actuators is analyzed. The description of the surface displacement of DM is deduced and the limitation in linear superposition of Gauss influence functions is indicated. The relations between constructional parameter of DM and its spatial correction capability are analyzed. Results show that, with the increasement of the density of actuators, optimization of the Gauss index and the coupling coefficient, the correction capability can be effectively improved. And this result is verified in spatial frequency based on the principle of spatial filter. In addition, the stochastic parallel gradient (SPGD) algorithm is introduced into our work to optimize the actuator distribution of DM. And the optimized distributions for each order of 3-20 Zernike wavefront have been obtained, the results show that it is advisable to arrange some of the actuators around the out edge of the effective aperture.
The configuration of combinational deformable mirror (CDM) is introduced in detail. Two DMs with square-array actuators or three DMs with triangle-array ones, even different kinds of DMs can be combined by 4F optical system to correct waverfront aberrations. The wavefront correction principle of CDM is analyzed and the analytic expression of its displacement has been deduced. Numerical calculation results show that the CDM is equivalent to one single DM with more actuators and larger coupling coefficient. Thus, the spatial compensation capability of CDM AO system can be improved effectively.
The influence on spatial correction capability caused by axial and transversal matching errors of the CDM technique is analyzed. According to the theory of geometrical optics and diffraction optics it can be obtained that, the wavefront changes inconspicuously when a small aberration propagates with a large Fresnel Number and the 4F optical system can be left out from the CDM AO system, which is setup in laboratory. The analysis also proves that the CDM AO system is not sensitive to the spatial matching errors of DMs.
Various existing control algorithms in multi-DM AO systems are compared. It is concluded that the direct-gradient control algorithm, which is widespreadly used in single DM AO system, is also suitable for CDM AO systems. Finally, the application prospect of CDM is discussed.
The first CDM AO experimental system for wavefront correction is built up, which consists of two 32-element continuous surface discrete axial piezoelectric DMs with the square-array actuators. In the open-loop state, a definite surface displacement can be reconstructed. When this system works in closed-loop, static aberrations are compensated better than only by using one DM. The feasibility and advantage at improving spatial compensation capability of CDM AO systems are proved.
In summary, the CDM AO system can improve the wavefront spatial compensation capability by increasing the actuators density or changing their distribution. This dissertation will provide some reference and experience for the design of DM and applications of CDM AO system.
首先,系统的研究了连续表面分立压电驱动变形镜的空间特性。分析了变形镜面形的求解方法,指出利用高斯型影响函数独立加权叠加方法描述面形存在一定的近似性。研究了变形镜结构参数和空间拟合能力的关系,结果表明:增加驱动器密度、选择适当的高斯指数和交连值,有利于提高变形镜的空间校正能力。进一步,应用空间滤波器模型研究了变形镜对畸变波前的校正过程,从空间频域验证了变形镜特性和波前校正能力的关系。此外,论文尝试使用随机并行梯度下降(SPGD)优化算法求解针对特定像差的变形镜驱动器的优化排布方式,获得了有规律的图形,结果说明:适当增加有效孔径边缘的驱动器数量有利于变形镜空间校正能力的提高。
其次,提出了组合变形镜的系统结构,利用光学共轭关系可以将两个正方形排列或三个三角形排列的变形镜构成一个组合变形镜进行波前校正,甚至可以实现将不同种类的变形镜进行组合。分析了组合变形镜波前校正的原理,给出了以连续表面分立压电驱动变形镜构成的组合变形镜的整体面形表达式。仿真计算证明组合变形镜可以等效为一个单一变形镜,由于有效的增加了驱动单元数和交连值,因此可以明显的提高系统的空间校正能力。
进一步,分析了应用组合变形镜进行波前校正时引入的轴向和横向匹配误差对空间校正能力的影响。一方面,通过几何光学和物理光学计算,说明理想4F系统可以实现波前再现,同时也看到小像差畸变波前在大菲涅尔数情况下自由传播的变化很小,因此实验室条件下使用组合变形镜时可以省去4F系统连接。另一方面,通过仿真计算表明:闭环情况下组合变形镜校正能力对各镜之间横向空间匹配误差并不敏感,这将有利于系统的实现。
此外,分析和总结了各类多变形镜自适应光学系统中波前校正器的控制解耦方式,指出组合变形镜可以直接应用单变形镜的方法来控制,并具体分析了配合哈特曼波前传感器使用直接斜率法的控制方法。最后讨论了组合变形镜的应用前景。
在实验验证方面,首先使用平面干涉仪验证了组合变形镜波前校正的原理,生成了指定的像差面形,然后搭建了应用组合变形镜的完整的自适应光学系统,实现了系统的闭环校正。对静态像差的良好校正结果从实验上证明了组合变形镜波前校正技术在提高系统空间校正能力方面的可行性和优越性。
通过简单的方法,组合变形镜可以在现有器件上实现变形镜驱动单元密度的增加和排布方式的改变,从而提高自适应光学系统的校正能力。本文的研究结果将为变形镜的设计和组合变形镜系统的实际应用提供一定的理论参考和工程应用经验。
By compensating random optical wavefront distortions real-timely, the adaptive optics (AO) system can hold the best working state in despite of the variable ambient. The wavefront corrector is one of the key elements of AO system. And improvement of the spatial correction capability of correctors is the primary coverage of AO theory and experiment research. In this dissertation, a kind of new adaptive optics configuration, in which several existing deformable mirrors (DMs) with optical conjugation relationships are equivalent to a new single corrector with more actuators to compensate high-order aberrations, is proposed. It is proofed that the combinational deformable mirror (CDM) technique can improve the spatial compensation capability of current AO system effectively. Based on the continuous surface DM with discrete axial piezoelectric actuators, the principles, the characters and the spatial compensation capability of CDM technique are studied in theory and experiment.
First, the spatial character of continuous surface DM with discrete actuators is analyzed. The description of the surface displacement of DM is deduced and the limitation in linear superposition of Gauss influence functions is indicated. The relations between constructional parameter of DM and its spatial correction capability are analyzed. Results show that, with the increasement of the density of actuators, optimization of the Gauss index and the coupling coefficient, the correction capability can be effectively improved. And this result is verified in spatial frequency based on the principle of spatial filter. In addition, the stochastic parallel gradient (SPGD) algorithm is introduced into our work to optimize the actuator distribution of DM. And the optimized distributions for each order of 3-20 Zernike wavefront have been obtained, the results show that it is advisable to arrange some of the actuators around the out edge of the effective aperture.
The configuration of combinational deformable mirror (CDM) is introduced in detail. Two DMs with square-array actuators or three DMs with triangle-array ones, even different kinds of DMs can be combined by 4F optical system to correct waverfront aberrations. The wavefront correction principle of CDM is analyzed and the analytic expression of its displacement has been deduced. Numerical calculation results show that the CDM is equivalent to one single DM with more actuators and larger coupling coefficient. Thus, the spatial compensation capability of CDM AO system can be improved effectively.
The influence on spatial correction capability caused by axial and transversal matching errors of the CDM technique is analyzed. According to the theory of geometrical optics and diffraction optics it can be obtained that, the wavefront changes inconspicuously when a small aberration propagates with a large Fresnel Number and the 4F optical system can be left out from the CDM AO system, which is setup in laboratory. The analysis also proves that the CDM AO system is not sensitive to the spatial matching errors of DMs.
Various existing control algorithms in multi-DM AO systems are compared. It is concluded that the direct-gradient control algorithm, which is widespreadly used in single DM AO system, is also suitable for CDM AO systems. Finally, the application prospect of CDM is discussed.
The first CDM AO experimental system for wavefront correction is built up, which consists of two 32-element continuous surface discrete axial piezoelectric DMs with the square-array actuators. In the open-loop state, a definite surface displacement can be reconstructed. When this system works in closed-loop, static aberrations are compensated better than only by using one DM. The feasibility and advantage at improving spatial compensation capability of CDM AO systems are proved.
In summary, the CDM AO system can improve the wavefront spatial compensation capability by increasing the actuators density or changing their distribution. This dissertation will provide some reference and experience for the design of DM and applications of CDM AO system.
引文
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