自由曲面表征函数及其应用研究

	自由曲面表征函数及其应用研究
	王超
学位类型	博士
导师	张新
	2014-07
学位授予单位	中国科学院大学
学位专业	光学
摘要	自由曲面是指非旋转对称的、各处曲率不同的光学表面，针对自由曲面的研究是近年来光学界的热点之一。研究方向包括自由曲面表征函数、自由曲面光学系统设计、自由曲面加工和检测，自由曲面像差理论等方面。目前自由曲面已经被逐渐地应用在光学工程领域，但随着设计视场、相对孔径增大，自由曲面光学系统非对称高阶像差在逐步增大。然而当前的自由曲面表征函数，如泽尼克、高斯径向基函数和Q-TYPE函数等不能提供更多空间变化自由度来平衡逐渐增大的非对称像差，所以限制了自由曲面在高分辨率反射望远系统中的应用。因此，构建新型自由曲面表征函数对于自由曲面的广泛应用具有重要意义。对于离轴自由曲面光学系统设计设计者来说，构建合适的初始结构需要消耗大量的时间。因此，提出一种快速的离轴自由曲面光学系统初始结构设计方法对于光学设计也同样具有重要意义。近些年，在具体工程中采用方形和六边形的非圆形孔径的离轴自由曲面光学系统的应用越来越广泛。在非圆形孔径下泽尼克多项式并不正交，在离轴自由曲面光学系统装调中采用何种函数解析非圆形孔径离轴自由曲面光学系统的波前；所有以上问题均为自由曲面表征函数应用于光学系统时所必须要解决的问题。本论文基于以上问题针对自由曲面表征函数及其应用进行研究，目的在于解决目前表征函数对于大多数面型表征和优化能力的不足的问题；解决离轴自由曲面光学系统初始结构构建耗时太长的问题；解决在非圆形孔径下自由曲面系统装调时泽尼克多项式不正交的问题。主要的研究内容总结为以下几个方面： (1)采用理论分析方法，对当前主流自由曲面表征函数，如泽尼克多项式、Q-TYPE、切比雪夫多项式和高斯径向基函数等的构造理论、优点和缺点，以及与像差项的对应关系进行深入研究；在此基础上构建新型表征函数-新函数；并提出了非圆形域正交多项式构造理论。而且还从理论上解释了节点像差理论不适于指导带有偏心和倾斜量面型的离轴自由曲面光学系统装调。（2）采用数值分析方法研究第二章中所提到的自由曲面表征函数，分析自由曲面表征函数对于选取的具有代表性的自由曲面拟合精度和优化能力，以突出新型表征函数-新函数对于各种面型拟合精度的绝对优势；并利用数值分析方法证明不能直接采用泽尼克多项式解析系统波前。 (3)针对离轴自由曲面光学系统初始结构构建耗时长的问题，提出了一种快速的离轴自由曲面初始结构构造理论；结合新函数设计了一种大视场（60°）离轴自由曲面光学系统，对此光学系统成像质量和采用面型的可加工性进行了分析，分析结果满足指标要求。 (4)利用方形域正交多项式-勒让德正交多项式解析方形孔径系统波前，结合灵敏度矩阵方法对设计的方形孔径超大视场离轴自由曲面系统进行装调，装调结果表明了此装调方法的正确性，对于其他非圆形离轴自由曲面光学系统装调具有借鉴意义。
其他摘要	Free-form surface, which is non-rotational symmetric optical surface, has become a hot research area in the optical industry. The direction of research contains the free-form surface characterization function, the free-form surface optical system design, the free-form surface fabrication with testing, and the free-form surface aberration theory. At present, free-form surface is widely and gradually used in the field of optical engineering. However, with the enhancing requirement of large designing field of view (FOV), relative aperture enlargement, and imaging quality, the non-rotational high-order aberration of the free-form surface system is increased step by step. But the current characterization functions of free-form surface, such as Zernike Function, Gaussian Radial Basis Function (GRBF), and the Q-TYPE Function, cannot provide enough spatial variables to balance the gradually increased non-rotational aberration, which has limited the application of the free-form surface in the system of high-resolution reflecting telescope. Therefore, the creation of new-type characterization function has big significance on the widespread use of free-form surface. It takes a long time to construct the appropriate initial structure for the designers of the off-axis free-form surface system. Therefore, it is also greatly significant to propose an efficient approach to build initial structure of the off-axis free-form surface system for optical design. In recent years, the rectangle and hexagon surfaces, which are non-circular aperture, are widely used in the off-axis free-form surface system. The Zernike Polynomial is not orthogonal over the non-circular aperture, and which function should be utilized to analyze wave-front of the off-axis free-form surface system with non-circular aperture in alignment. All the problems mentioned above must be settled when the free-form surface is applied in the off-axis free-form surface system. This dissertation refers to the research on the free-form surface characterization function and the application of the free-form surface characterization function based on the problems mentioned above. The destination is listed as follows: solve the limitation of surface characterization ability and optimization ability by using most of the existing functions; solve the time-consuming problem when build the initial system structure; solve the non-orthogonal features of the Zernike Polynomial which is used to align off-axis free-from surface system with non-circular aperture. The research contents are mainly explained as follows: (1) By using theoretical analyzing method, firstly, the theory, the advantages and disadvantages, and the corresponding relationship with aberration items of the popularly characterization functions of free-form surface, such as Zernike Polynomial, Q-TYPE, Chebyshev Polynomial, and GRBF are researched deeply. Secondly, one new-type characterization function named New function is established on the basis of the research above. In the meantime, the non-circular orthogonal polynomial theory is proposed. At last, the reason why nodal aberration is not appropriate to guide the alignment of the free-form surface with decentration and tilt is explained. (2) The free-form surface characterization function mentioned in the Section Two is researched by using numerical analysis method. For the selected typical free-form surface, the fitting precision and the optimization ability by using the characterization function are analyzed in order to highlight the fitting precision advantage of the New function. And it is proved that the Zernike Polynomial cannot be directly used in resolving by means of numerical analysis. (3) Focusing on the time consuming problem of constructing initial free-form surface optical system structure, an efficient method for structuring the off-axis free-form surface is proposed. Then, one large field of view (60°) off-axis free-from surface system is designed by integrating New function. The imaging quality and the processing possibility of the optical system are analyzed. The result meets the requirement. (4) The rectangle aperture wave-front is analyzed by using rectangle area orthogonal polynomial named Legendre Polynomial. By integrating the sensitivity matrix method, the rectangle aperture free-form surface system with large field of view is aligned. The result shows that the alignment method is correct, which can use for reference to other non-circular aperture off-axis free-form surface system alignment.
语种	中文
文献类型	学位论文
条目标识符	http://ir.ciomp.ac.cn/handle/181722/41474
专题	中科院长春光机所知识产出
推荐引用方式 GB/T 7714	王超. 自由曲面表征函数及其应用研究[D]. 中国科学院大学,2014.

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