离轴反射光学系统计算机辅助装调技术研究
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摘要
随着光学设计技术与光学制造技术的不断进步，光学系统逐渐从轴对称系统发展为离轴反射系统。离轴反射光学系统的装调是实现离轴光学系统高成像质量必不可少的一部分，离轴反射光学系统的高性能装调也越来越依赖高技术的支持。计算机辅助装调技术作为离轴光学系统研制过程中不可缺少的技术保障手段正逐渐成为空间光学系统研究的关键技术之一，而且计算机辅助装调技术的发展也极大的促进了光学设计与先进光学加工技术的进一步发展。
本论文主要针对计算机辅助装调技术在离轴反射光学系统中的应用进行研究。主要研究内容如下：
1.轴对称光学系统像差特性的研究
利用轴对称光学系统的矢量波像差理论分析了轴对称光学系统失调时初级球差、彗差、像散特性，建立了轴对称失调光学系统波像差Zernike系数与视场之间的关系式。将矢量波像差应用于常用的轴对称RC、TMA系统的装调过程，研究获得RC、TMA系统在装调过程中球差、彗差、像散的相关性质，分析了不能依据轴上视场成像质量判断光学系统装调状态的原因；同时对不同元件失调像差相互补偿进行了研究，指导了光学系统的设计。
2.离轴光学系统像差特性的研究
利用坐标变换建立了离轴（孔径离轴）光学系统与对应轴对称光学系统波像差Zernike系数的转化关系；引入矢量坐标变换将矢量波像差理论应用到离轴光学系统，获得了离轴光学系统、失调离轴光学系统初级像差的矢量表达式，研究结果表明离轴光学系统、失调离轴光学系统初级像差依然由球差、彗差、像散组成，不同像差与视场的依据关系不同；以离轴RC、TMA系统为例分析了失调情况下离轴反射光学系统的球差、彗差、像散特性；同时利用坐标变换研究了大口径反射镜初级面形误差对光学系统像差特性的影响；对光学元件面形误差引入像差与光学元件失调像差相互校正来实现光学系统设计进行了研究，指导基于自由曲面的反射光学系统设计。
3.离轴光学系统元件失调量的分析
对于离轴三反光学系统的装调需求，建立了基于矢量波像差理论的轴对称光学系统、离轴光学系统元件失调模型（失调矩阵）。模拟离轴光学系统失调量不同数量级情况下的装调过程，通过模拟分析可知随着失调量的增加系统在装调过程中的调整次数也不断的增加，失调量数量级较大的情况下可能出现越调越坏的情况（算法不收敛），利用矢量波像差理论分析了失调量较大情况下算法不收敛的原因。
4.实际离轴光学系统元件失调量的计算
在利用离轴光学系统元件失调模型计算元件失调量的过程中，分析了实际装调过程中计算元件失调量不准确的原因，提出了设置失调矩阵奇异值阈值的方法来解决该问题，提高了算法的稳定性。详细介绍了离轴光学系统粗装调的过程，结果表明基于矢量波像差理论的离轴光学计算机辅助装调模型可以准确的获得该离轴反射系统中待装调元件的失调量，最终指导完成光学系统的实际装调，系统全视场的波像差小于0.09λ(λ为632.8nm)。
With the development of optical design and optical manufacture technology，thereflective optical system style have been development from axial symmetry tooff-axis or eccentric. The assemble of off-axis optical system is absolutelynecessarily to achieve the diffraction-limited system image quality, and thehigh-powered mount off-axis system are more and more depended on high tech.Computer–aided alignment (CAA) technology has been developed to solve thedifficulties of high quality optical system alignment in recent years, which play thekey role in the process of system development, and the development of CAA willpromote the optical design and optical manufacture.
The theory of CAA technology and some issues about its application in off-axissystem are studied in this paper, the main research contents are as follows:
1. The misalignment induced aberrations of symmetry optical system
Using the vector aberration theory, we analyzed the third order aberration fieldsof misaligned symmetry optical system, the relationship between perturbed systemwavefront error Zernike coefficients and system field have been found. Themounting process of symmetry RC and TMA is analyzed by vector aberration theory,the characteristic of3rdspherical aberration and3rdcoma and3rdastigmatism ofmisaligned RC TMA is obtained, the reason that the alignment of optical systemcannot be accomplished using on-axis performance data alone is analyzed. Thedifferent element misaligned induced aberration compensate is studied and theconclusion guided the process of optical design.
2. The misalignment induced aberrations of off-axis optical system
By introducing the coordinates transform, the relationship between axialsymmetry system and off-axis system wavefront error Zernike coefficients have beenfound, and using a transformed pupil vector into the aberration expansions of ansymmetry optical system, the vector aberration expansions through third order ofoff-axis optical system are obtained. The result show that the off-axis and misalignedoff-axis optical system's aberrations are still make up of3rdspherical aberration and3rdcoma and3rdastigmatism, different aberration have different field dependencies.By the vector aberration expansions of off-axis system, the characteristic of3rd spherical aberration and3rdcoma and3rdastigmatism of misaligned off-axis RC andoff-axis TMA is obtained. Based on the coordinates transform, the influence ofsurface-profile error of larger mirror on aberrations characteristics of optical systemis gained. The aberrations compensate relation between element misaligned inducedand surface-profile error induced is studied and the conclusion guided the process ofoptical design based on free form surface.
3. The analysis misalignment of off-axis optical system's element
According to the demand for the alignment of off-axis three-mirror reflectiveoptical system in an engineering project, the misaligned model of co-axis opticalsystem and off-axis optical system is build by vector aberration theory. Thealignment process is simulate at different misaligned magnitude, the result show thatthe adjust time increased with the misaligned magnitude. It may be getting a worseassemble result by CAA arithmetic at biggish misalignment, the reason is analyzedby the vector aberration theory.
4. The calculation misalignment of a real off-axis optical system's element
A singular value decomposition method is applied to the CAA arithmetic, thecausation of poor solution of the alignment is analyzed by the matrix conditionnumber and the singular value, the threshold of singular value is proposed to achievethe correct result. The coarse alignment process is introduced, the stimulantcalculation is processed to an off-axis three-mirror reflective optical system underthe different signal noise ratio and the result shows that the method in this paper isrational and effective and steady, and the off-axis three-mirror reflective opticalsystem is well aligned by this method, the off-axis system produced a measuredwavefront error less than0.09λ RMS at λ equal to632.8nm across all image plane.
本论文主要针对计算机辅助装调技术在离轴反射光学系统中的应用进行研究。主要研究内容如下：
1.轴对称光学系统像差特性的研究
利用轴对称光学系统的矢量波像差理论分析了轴对称光学系统失调时初级球差、彗差、像散特性，建立了轴对称失调光学系统波像差Zernike系数与视场之间的关系式。将矢量波像差应用于常用的轴对称RC、TMA系统的装调过程，研究获得RC、TMA系统在装调过程中球差、彗差、像散的相关性质，分析了不能依据轴上视场成像质量判断光学系统装调状态的原因；同时对不同元件失调像差相互补偿进行了研究，指导了光学系统的设计。
2.离轴光学系统像差特性的研究
利用坐标变换建立了离轴（孔径离轴）光学系统与对应轴对称光学系统波像差Zernike系数的转化关系；引入矢量坐标变换将矢量波像差理论应用到离轴光学系统，获得了离轴光学系统、失调离轴光学系统初级像差的矢量表达式，研究结果表明离轴光学系统、失调离轴光学系统初级像差依然由球差、彗差、像散组成，不同像差与视场的依据关系不同；以离轴RC、TMA系统为例分析了失调情况下离轴反射光学系统的球差、彗差、像散特性；同时利用坐标变换研究了大口径反射镜初级面形误差对光学系统像差特性的影响；对光学元件面形误差引入像差与光学元件失调像差相互校正来实现光学系统设计进行了研究，指导基于自由曲面的反射光学系统设计。
3.离轴光学系统元件失调量的分析
对于离轴三反光学系统的装调需求，建立了基于矢量波像差理论的轴对称光学系统、离轴光学系统元件失调模型（失调矩阵）。模拟离轴光学系统失调量不同数量级情况下的装调过程，通过模拟分析可知随着失调量的增加系统在装调过程中的调整次数也不断的增加，失调量数量级较大的情况下可能出现越调越坏的情况（算法不收敛），利用矢量波像差理论分析了失调量较大情况下算法不收敛的原因。
4.实际离轴光学系统元件失调量的计算
在利用离轴光学系统元件失调模型计算元件失调量的过程中，分析了实际装调过程中计算元件失调量不准确的原因，提出了设置失调矩阵奇异值阈值的方法来解决该问题，提高了算法的稳定性。详细介绍了离轴光学系统粗装调的过程，结果表明基于矢量波像差理论的离轴光学计算机辅助装调模型可以准确的获得该离轴反射系统中待装调元件的失调量，最终指导完成光学系统的实际装调，系统全视场的波像差小于0.09λ(λ为632.8nm)。
With the development of optical design and optical manufacture technology，thereflective optical system style have been development from axial symmetry tooff-axis or eccentric. The assemble of off-axis optical system is absolutelynecessarily to achieve the diffraction-limited system image quality, and thehigh-powered mount off-axis system are more and more depended on high tech.Computer–aided alignment (CAA) technology has been developed to solve thedifficulties of high quality optical system alignment in recent years, which play thekey role in the process of system development, and the development of CAA willpromote the optical design and optical manufacture.
The theory of CAA technology and some issues about its application in off-axissystem are studied in this paper, the main research contents are as follows:
1. The misalignment induced aberrations of symmetry optical system
Using the vector aberration theory, we analyzed the third order aberration fieldsof misaligned symmetry optical system, the relationship between perturbed systemwavefront error Zernike coefficients and system field have been found. Themounting process of symmetry RC and TMA is analyzed by vector aberration theory,the characteristic of3rdspherical aberration and3rdcoma and3rdastigmatism ofmisaligned RC TMA is obtained, the reason that the alignment of optical systemcannot be accomplished using on-axis performance data alone is analyzed. Thedifferent element misaligned induced aberration compensate is studied and theconclusion guided the process of optical design.
2. The misalignment induced aberrations of off-axis optical system
By introducing the coordinates transform, the relationship between axialsymmetry system and off-axis system wavefront error Zernike coefficients have beenfound, and using a transformed pupil vector into the aberration expansions of ansymmetry optical system, the vector aberration expansions through third order ofoff-axis optical system are obtained. The result show that the off-axis and misalignedoff-axis optical system's aberrations are still make up of3rdspherical aberration and3rdcoma and3rdastigmatism, different aberration have different field dependencies.By the vector aberration expansions of off-axis system, the characteristic of3rd spherical aberration and3rdcoma and3rdastigmatism of misaligned off-axis RC andoff-axis TMA is obtained. Based on the coordinates transform, the influence ofsurface-profile error of larger mirror on aberrations characteristics of optical systemis gained. The aberrations compensate relation between element misaligned inducedand surface-profile error induced is studied and the conclusion guided the process ofoptical design based on free form surface.
3. The analysis misalignment of off-axis optical system's element
According to the demand for the alignment of off-axis three-mirror reflectiveoptical system in an engineering project, the misaligned model of co-axis opticalsystem and off-axis optical system is build by vector aberration theory. Thealignment process is simulate at different misaligned magnitude, the result show thatthe adjust time increased with the misaligned magnitude. It may be getting a worseassemble result by CAA arithmetic at biggish misalignment, the reason is analyzedby the vector aberration theory.
4. The calculation misalignment of a real off-axis optical system's element
A singular value decomposition method is applied to the CAA arithmetic, thecausation of poor solution of the alignment is analyzed by the matrix conditionnumber and the singular value, the threshold of singular value is proposed to achievethe correct result. The coarse alignment process is introduced, the stimulantcalculation is processed to an off-axis three-mirror reflective optical system underthe different signal noise ratio and the result shows that the method in this paper isrational and effective and steady, and the off-axis three-mirror reflective opticalsystem is well aligned by this method, the off-axis system produced a measuredwavefront error less than0.09λ RMS at λ equal to632.8nm across all image plane.
引文
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