Optimization of grazing incidence mirrors and its application to surveying X–ray telescopes

Grazing incidence mirrors for X–ray astronomy are usually designed in the parabola-hyperbola (Wolter I) configuration. This design allows for optimal images on-axis, which however degrade rapidly with the off-axis angle. Mirror surfaces described by polynomia (with terms higher than order two), have been put forward to improve the performances over the field of view. Here we present a refined procedure aimed at optimizing widefield grazing incidence telescopes for X–ray astronomy. We improve the angular resolution over existing (wide-field) designs by ∼ 20%. We further consider the corrections for the different plate scale and focal plane curvature of the mirror shells, which sharpen by another ∼ 20% the image quality. This results in a factor of ∼ 2 reduction in the observing time needed to achieve the same sensitivity over existing wide-field designs and of ∼ 5 over Wolter I telescopes. We demonstrate that such wide-field X–ray telescopes are highly advantageous for deep surveys of