基于三级象差理论,分析了几何象差对正入射望远镜性能的影响,总结了弥散斑角宽度θ随着系统f数和半视场角uP的变化趋势.弥散斑的角宽度θ随着半视场角uP的增大而增大,随着系统f数的增大而减小.当f数小于10或者半视场角uP大于0.005弧度时,弥散斑角宽度θ变化比较剧烈.详细讨论了四种典型的反射系统,Dall-Kirkham系统和反Dall-Kirkham系统的弥散斑角宽尺寸在一个数量级上,大约为卡塞格林系统的十倍.R-C系统的弥散斑角宽最小,几乎是卡塞格林系统的十分之一.通过本文的结论公式可以估算一个光学系统的象差尺寸并避免进行光线追迹.

Based on the third-order aberration theory of two-mirror reflecting system, the influence of the geometrical aberrations on the performance of normal incidence telescopes was analyzed. The change trends of the angular size of the blur spot θ with the f-number and half-field angle uP were concluded. The angular blur spot θ increased with the increase of the half-field angle uP and the decrease of f-number, and the θ increased more sharply when the f-number was less than 10 or the half-field angle uP was more than 0.005. And, four kinds of typical reflecting systems were discussed in detail. Comparing the results, it is found that the angular blur spots in a Dall-Kirkham system and an inverse Dall-Kirkham system are at the same order of magnitude, which is almost ten times of a Cassegrain system′s. The θ of an R-C system is the smallest, which is one tenth of a Cassegrain system′s. It is useful to estimate the size of the aberration blur by the formulae without going to the trouble of making a raytrace analysis.