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平面反射系统系指由平面反射镜系和若干反射棱镜组合而成的系统。本文着重讨论了在会聚光路中,各种型式的平面反射系统围绕空间任意轴微量转动后所产生的象点空间位移问题,推导出了既方便于工程使用又具有明确物理意义的通用计算公式。 本文给出的分析与算法与同类论文比较具有如下特点: 1.应用了误差独立作用原理,将系统绕任意方位轴线转动这个多种因素的综合影响,适当分离为若干相互独立作用的影响因素,把一个复杂的问题转化为若干简单的基本问题。然后应用对于这些基本问题已有的分析结论,能够方便地、且物理意义明确地推导出其通用计算公式。 2.遵照GB1224—76的统一规定,采用了物理空间的标准标定坐标系,从而确立并简化了平面反射系统作用矩阵的表达式。这样就容易以数学表达式揭示出系统在各种条件下的成象规律。因此,我们可以从一般的平面反射系统入手,直接对其运用矩阵分析的数学方法推导出求解的通用计算公式。当然它也必然适用于任何具体情况。另外,由于系统的作用矩阵和绕任意轴的转动矩阵都属于“正交矩阵”,便使得所推导出的通用计算公式的表达形式简单、计算方便。 本文所得结论对处于会聚光路中的平面反射系统的“光学校正”工作有着直接地指导意义,对合理地设计光学仪器的结构具有重要的参考价值。 最后需要说明:在本文之前,笔者习作了《平行光路中的平面反射系统》和《会聚光路中平面反射系统的平移》两篇文章,本文在某些独立影响因素的计算中,引用了其有关结论公式。
Planar reflection system refers to the combination of a plane mirror system and a number of reflective prism system. This paper focuses on the spatial displacement of the image point generated by various types of planar reflection systems around the arbitrary axis of the space in convergent light path, and deduces a general formula that is convenient for engineering use and has definite physical meaning. Compared with similar papers, the analysis and algorithm presented in this paper has the following characteristics: 1. By applying the principle of independent function of error, the comprehensive influence of the system rotation around any azimuth axis can be properly separated into several influencing factors that act independently of each other, Transform a complex problem into a few simple basic problems. Then, by applying the existing conclusion of the analysis on these basic problems, we can derive its general formula conveniently and physically. 2. According to the uniform regulation of GB1224-76, the standard calibration coordinate system of the physical space is adopted, so as to establish and simplify the expression of the action matrix of the planar reflection system. In this way, it is easy to reveal the law of imaging of the system under various conditions by mathematical expressions. Therefore, we can start from the general plane reflection system, and directly apply the mathematical method of matrix analysis to derive the general formula for solving. Of course it must also apply to any specific situation. In addition, since the system action matrix and the rotation matrix around any axis belong to the “orthogonal matrix”, the expressions of the generalized calculation formulas are deduced to be simple and easy to calculate. The conclusion obtained in this paper has a direct guiding significance for the “optical correction” work of the plane reflection system in the converging light path, and has an important reference value for the rational design of the optical instrument structure. Finally, we need to explain: Before this article, I made two articles, “Planar Reflecting System in Parallel Optical Path” and “Panning of Planar Reflective System in Concentrated Optical Path”. In this paper, some independent influencing factors are calculated, Conclusion formula.