Optimization of grazing incidence mirrors and its application to surveyingX-ray telescopes

Grazing incidence mirrors for X-ray astronomy are usually designed in the p arabola-hyperbola (Wolter I) configuration. This design allows for optimal images on-axis, which however degrade rapidly with the off-axis angle. Mirr or 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 incid ence telescopes for X-ray astronomy. We improve the angular resolution over existing (wide-field) designs by similar to 20%. We further consider the c orrections for the different plate scale and focal plane curvature of the m irror shells, which sharpen by another similar to 20% the image quality. Th is results in a factor of similar to2 reduction in the observing time neede d to achieve the same sensitivity over existing wide-field designs and of s imilar to5 over Wolter I telescopes. We demonstrate that such wide-field X- ray telescopes are highly advantageous for deep surveys of the X-ray sky.