【作者】 任百川；

【导师】 金光；

【作者基本信息】 中国科学院研究生院（长春光学精密机械与物理研究所） ， 光学工程， 2012， 博士

【摘要】 偏轴光学系统通过元件偏心倾斜消除传统共轴系统的中心遮拦，是近年来用于研究设计无遮拦反射式光学系统从而扩大视场的一种结构形式，而矢量像差理论是分析偏轴光学系统最重要和适合的理论方法。本论文针对矢量像差理论展开研究，主要内容为矢量像差理论和偏轴系统的像差特性研究、矢量像差计算及其指导偏轴光学系统的设计。基于传统共轴光学系统的像差理论，矢量像差理论的像差表达式由标量形式写成矢量形式；偏轴光学系统像差场的表征上出现节点及像差贡献中心偏移的现象；概念上引入光轴光线替代共轴系统的旋转对称轴来描述偏轴系统的基本参量。对偏轴光学系统的一阶特性进行了分析，详细推导了球面和非球面光学元件的像差贡献中心。基于一阶特性给出偏轴系统像差的波差表达式和赛德尔表达式。从球面基准部分和非球面偏离部分两方面的像差贡献详细阐述了偏轴光学系统的五个三阶单色像差特性，特别的是用射影变换的方法分析了梯形畸变。给出三级矢量像差理论的赛德尔表达式，这使得矢量像差理论进一步可以用来进行偏轴系统的像差计算。我们用矢量像差的方法计算了偏心倾斜两镜系统的三阶自由彗差点，结果与R.N.Wilson使用Schiefspiegler方法所求得结果一致，从而验证我们计算的准确性。通过这种方式首次实现使用矢量波像差理论做完整且准确的像差计算，并验证了计算的准确性。这是本论文核心的创新工作。矢量像差理论分析偏轴系统的像差特性，从而可用于指导偏轴光学系统设计和优化，但目前还并不完善。论文最后我们给出一个两片镜子的偏轴系统设计和一个大视场全反射的偏轴四镜系统设计举例，总结了偏轴光学系统设计难点，提出一些像差校正原则。更多还原

【Abstract】 Off-axis optical system, namely optical system with tilted component, is onestructural style for designing wide-field reflecting optical system. Vector aberrationtheory is the significant and adaptive method to analyze off-axis optical system. Theprimary coverage in this dissertation is research of vector aberration theory,calculation of vector aberration theory and optical design of off-axis optical systemunder guidance of vector aberration theory. As a direct extension of rotationallysymmetrical wave aberration theory, expression of vector aberration theory can bewritten in a vector approach; aberration field of off-axis optical system appears thecharacteristic of aberration nodal and aberration displacement； Replacement ofrotationally symmetrical axis in centred system, Optical Axis Ray is to describeoff-axis optical system. The first-order properties of decentered and tilted opticalsystems are analyzed in detail, the relation formula between aberration contributioncenter and decenter and tilt of each optical component is derived. Based on first-orderproperties of off-axis optical system, vector aberration theory is given by the ways ofwavefront aberration and Seidel aberration. Two independent sets of aberrations areintroduced by each surface: one induced by the base sphere and the other induced bythe aspheric departure of the surface. These two sets of aberration terms can becombined vectorially to yield the final aberration contribution for the surface. The fivethird-order aberrations in decentered and tilted optical systems are described in detail. The distortion is analyzed based on a collinear transformation between the object andimage spaces.Seidel aberration for third-order vector aberration theory is given. Thus vectoraberration theory can be used to calculate the aberration of off-axis optical system.Equations for third-order coma are derived by a vector approach. Coma-freecondition to remove misalignment induced coma was obtained. The coma-free pointin two-mirror telescopes is found as a conclusion of our coma-free condition, whichis in highly agreement with the result solved by R. N. Wilson using Schiefspieglertheory. By this way the aberration calculation of off-axis optical system isimplemented using vector aberration theory. This is the key originality innovation inthe dissertation.It is pointed out that vector aberration theory is very effective in the aberrationanalyses of off-axis optical system; vector aberration theory can be used to calculateaberration of off-axis optical system; vector aberration theory can give useful designinsights for off-axis optical system. Based on the vector aberration theory conceivedby Shack, we design an tilted-component four-mirror optical system by cancel out its3rd-order coma and balance the astigmatism. Some problems in the design oftilted-component optical system are generalized, and some solutions are supplied forreference.更多还原