Wolter-I-like X-ray telescope structure using one conical mirror and one   quadric mirror
  Nested multilayer mirrors are commonly used in X-ray telescope structures to increase the collecting area. To balance the difficulty and cost of producing these mirrors, the classical Wolter-I structure has previously been replaced with a conical Wolter-I structure, but it can lead to significantly poorer angular resolution. In this paper, we consider changing one of the mirror shapes (paraboloid or hyperboloid) of the Wolter-I structure to a conical mirror shape, while the other mirror shape remains a quadric surface-type structure, which could thus ensure the imaging quality. Based on a theoretical analysis and the results of simulations, the cone-hyperboloid and paraboloid-cone structures are found to provide the best angular resolutions, and the cone-hyperboloid structure is shorter than the paraboloid-cone structure at the focal length. The cone-hyperboloid structure is then nested to obtain the best on-axis angular resolution and off-axis images. 
Sheng-Hao Chen, Shuang Ma, Zhan-Shan Wang
astro-ph.IM