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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 field of view. In addition an effective area of 5–9000 cm  2   at 1 keV is needed.

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