The capability of future X - ray telescopes depends on the quality of their Point Spread Function ( PSF ) and the size of their field of view . Traditional designs , such as Wolter , and Wolter - Schwarzschild telescopes are stigmatic on the optical axis but their PSF degrades rapidly off - axis . At the optimal focal surface , their PSFs can be significantly improved . We present a simple optimization process for Wolter ( W ) , Wolter - Schwarzschild ( WS ) and Hyperboloid - Hyperboloid ( HH ) telescopes that substantially improves the off - axis PSF for either narrow or wide field of view applications . In this paper , we will compare the optical performance of conventional and optimized W- , WS- , and HH - telescopes for a wide range of telescope diameters that can be used to build up future x - ray telescopes .