It is well known that the Wolter I design for focusing X-ray telescopes provides perfect on-axis images, while, despite the absence of spherical aberration, the off-axis angular resolution rapidly degrades because of coma, field curvature and astigmatism. However, more general mirror designs than Wolter's exist in which primary and secondary mirror profiles can be described by polynomial equations. These power series solutions are particularly well indicated to be optimized, in order to achieve high imaging performances even at large off-axis incidence angles, despite a small degradation of the on-axis response. The concept, derived from the Ritchey-Chretien telescope widely used in optical astronomy,
has already been experimentally proven for X-ray astronomical applications at the Brera Astronomical Observatory (Italy), in the context of the feasibility study of the Wide Field X-ray Telescope mission. Here we present a new design (including a model for slope errors and mechanical tolerances) for a X-ray telescope of medium-size class assuming monolithic mirror shells made of glass, optimized to have a Half Energy Width better than 5 arcsec over a 30 arcmin field of view (radius) and an effective area almost twice that one of Chandra. The use of polynomial mirrors seems extremely well suited also for the case of the XEUS optics. Indeed, the small aspect-ratio between the large focal length of the XEUS telescope (50 m) and the total mirror height (1 m) makes it very favorable to diminish the aberration effects due to the field curvature. With the
assumption of mirror shells with polynomial profile it would be
possible to achieve for XEUS an imaging response almost constant up to a field of view of 20 arcmin in radius.