掠入射X射线反射镜离轴有效面积的解析计算
Analytical computation of the off-axis Effective Area of grazing incidence X-ray mirrors
摘要：
用于掠入射X射线望远镜的聚焦镜是在70年代推出的，其特征在于其成像质量和有效面积，这反过来又决定了它们的灵敏度。尽管轴上有效面积通常被假定为表征X射线光学器件的收集能力，但成像扩展X射线源的望远镜能力也由其有效面积随离轴角的变化来确定。[...]为未来的X射线望远镜设计光学系统是一项复杂的任务，需要对成像质量和轴上和轴外有效面积进行详细计算。由于它们明显的复杂性，到目前为止，这两个方面都是通过使用射线跟踪例程来处理的，该例程旨在模拟X射线光子与给定聚焦系统的反射表面的相互作用。虽然这种方法已经被广泛地利用并且被证明是有效的，但是从分析的观点来考虑相同的问题，以利用比射线跟踪例程更简单的计算来评估X射线光学模块的光学设计也将是有吸引力的。[...]在双锥近似下，我们推导出了双反射镜离轴有效面积的解析公式，在给定入射角下，只需要积分和标准程序就可以计算出X射线涂层的反射率。[...]代数表达式提供的反射镜的几何面积，作为离轴角的函数。最后，这里提出的分析计算的结果进行了验证，通过与相应的预测的射线跟踪代码。
英文摘要：
Focusing mirrors for X-ray telescopes in grazing incidence, introduced in the 70s, are characterized in terms of their performance by their imaging quality and effective area, which in turn determines their sensitivity. Even though the on-axis effective area is assumed in general to characterize the collecting power of an X-ray optic, the telescope capability of imaging extended X-ray sources is also determined by the variation in its effective area with the off-axis angle. [...] The complex task of designing optics for future X-ray telescopes entails detailed computations of both imaging quality and effective area on- and off-axis. Because of their apparent complexity, both aspects have been, so far, treated by using ray-tracing routines aimed at simulating the interaction of X-ray photons with the reflecting surfaces of a given focusing system. Although this approach has been widely exploited and proven to be effective, it would also be attractive to regard the same problem from an analytical viewpoint, to assess an optical design of an X-ray optical module with a simpler calculation than a ray-tracing routine. [...] We have developed useful analytical formulae for the off-axis effective area of a double-reflection mirror in the double cone approximation, requiring only an integration and the standard routines to calculate the X-ray coating reflectivity for a given incidence angle. [...] Algebraic expressions are provided for the mirror geometric area, as a function of the off-axis angle. Finally, the results of the analytical computations presented here are validated by comparison with the corresponding predictions of a ray-tracing code.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
