Aberration calculation of catadioptric combined optical system with oblique incidence
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摘要: 基于平面对称光栅反射镜系统的像差理论，根据光学元件材料折射率对成像光束波像差进行修正，将像差理论扩展到平面对称折射光学系统，使得该理论可应用于光束斜入射的折反射组合光学系统的像差计算；指出在折反射组合光学系统中考虑物像方空间折射率的关系，以及入射角方向的定义，使得波像差的计算表达式保持统一；应用扩展后的像差理论对折反射椭球镜面形检测光学系统进行像差分析计算，并与Zemax光线追迹结果进行对比，验证波像差理论的有效性。该像差理论为光束斜入射的折反射组合光学系统的设计、像质评价及优化提供了有效的分析手段。Abstract: First, based on the aberration theory of the plane symmetric grating reflector system, the wave aberration of the imaging beam was corrected according to the optics material refractive index, and the aberration theory was extended to the plane symmetric refractive optical system, which made this theory can be applied to the aberration calculation of the catadioptric combined optical system with beam oblique incidence. Secondly, it was pointed out the computational expressions of wavefront aberration should be kept uniformed in view of the refractive index relationship between object and image spaces and the definition of direction of incident angle. Finally, the analysis and calculation were carried out on the aberration of the catadioptric ellipsoid mirror shape detection optical system by applying the extended aberration theory, and compared with the Zemax ray-tracing results to verify the effectiveness of the wave aberration theory. This aberration theory provides effective measures for the design of the catadioptric combined optical system with beam oblique incidence, the evaluation and optimization of image quality.
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Keywords:
- aberration theory /
- plane-symmetric optical system /
- oblique incidence /
- catadioptric
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图 1 平面对称反射/折射光学系统成像示意图
Figure 1. Imaging schematic of plane-symmetric catadioptric optical system
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图 2 椭球镜面形检测光学系统示意图
S为激光光纤光源；$ S'$为观察显微镜；OE1为待测椭球镜；OE2为聚焦透镜；STO为孔径光阑
Figure 2. Schematic diagram of surface-shape detection optical system of ellipsoidal mirror
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图 3 椭球镜面形检测系统的光线点列图
Figure 3. Ray of light spot diagrams of surface-shape detection optical system of ellipsoidal mirror
表 1 椭球镜面形检测系统的光学参数
Table 1 Optical parameters of surface-shape detection optical system of ellipsoidal mirror
光学面 曲率半径R/mm 元件间距d/mm 材料 圆锥系数 1 38.74 200 Mirror −0.98 STO Infinite 2.39 − 0 2 15.00 12.00 BK7 0 3 75.00 32.068 − 0 注：椭球镜的顶点曲率半径$R = {{{b^2}} / a}$；椭球镜的半长轴$a{\rm{ = 1 937}}$ mm；半短轴$b{\rm{ = 273}}{\rm{.93}}$ mm。 
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