中文摘要：

针对国内硬X射线天文观测的需求，研究了1～30keV能段圆锥嵌套Wolter—I型X射线天文望远镜的光学设计，推导了嵌套层之间的结构递推关系，给出了合理的望远镜初始结构。在最内层和最外层之间，设计了6组W／B4C宽带非周期多层膜，模拟得到系统的有效集光面积和分辨力。理论有效集光面积达到127cm。（在2keV处）和71cm。（在30keV处），系统角分辨力约10”。系统实际成像质量还受到公差的影响，引起像质下降的公差主要有辐条位置公差、镜面位置公差和镜面面形公差。目前演示实验方便改善的公差是辐条位置公差，给出了此公差的计算方法并对系统进行光线追迹，得到了成像点列图和分辨力改变情况。辐条位置公差从±15μm缩小到±3μm后，系统分辨力由1’提高到13”。

英文摘要：

Optical design of nested conical Wolter-I X-ray telescope covering energy band from 1 to 30 keV was investigated. Recurrence relation of the nested structure was deduced. Depending on the needs for hard X-ray astronomical observations in China, the initial structure was presented, for which six groups of W/B4C aperiodic multilayers were designed between the innermost and the outermost shell of mirror. The simulation results showed that the effective area could achieve 127 cmz （at 2 keV） and 71 cmz （at 30 keV）, and the resolution was estimated to be - 10＂ in half-power diameter. The actual image quality is also affected by tolerance. The main tolerances lowering image quality are position error, figure error and offroundness. Tolerance to be improved most easily in the lab is off-roundness caused by bar. The spot diagram distribution and resolution was given after calculating off-roundness and ray tracing. When the bar position tolerance was changed from ±15μm to ±3μm, the responding resolution was improved from 11 to 131.