A wide field X-ray telescope for astronomical survey purposes: from theory to practice

X-ray mirrors are usually built in the Wolter I (paraboloid-hyperboloid) configuration. This design exhibits no spherical aberration on-axis but suffers from field curvature, coma and astigmatism, therefore the angular resolution degrades rapidly with increasing off-axis angles. Different mirror designs exist in which the primary and secondary mirror profiles are expanded as a power series in order to increase the angular resolution at large off-axis positions, at the expanses of the on-axis performances. Here we present the design and global trade off study of an X-ray mirror systems based on polynomial optics in view of the Wide Field X-ray Telescope (WFXT) mission. WFXT aims at performing an extended cosmological survey in the soft X-ray band with unprecedented flux sensitivity. To achieve these goals the angular resolution required for the mission is very demanding ~5 arcsec mean resolution across a 1-deg field of view. In addition an effective area of 5-9000 cm^2 at 1 keV is needed.