Astronomical applications of grazing incidence telescopes with polynomial surfaces

The report has examined the claim that grazing incidence telescopes having surfaces described by generalized equations have image characteristics superior to those of the paraboloid-hyperboloid and Wolter-Schwarzschild configurations. With emphasis on specific applications in solar and cosmic X-ray/EUV astronomy, raytracing has shown that in many cases there is no advantage in the polynomial design, and in those cases where advantages are theoretically to be expected, the advantages are outweighed by practical considerations.