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 wide-field 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 the X-ray sky.