Efficient Fresnel x-ray optics made simple

A practical design for upcoming spaceborne x-ray telescopes with ultrahigh angular resolution is proposed. Particular attention is directed to technological simplicity and robust as well as cheap components. Based on dispersion corrected Fresnel lenses, an optimized arrangement will be identified with respect to the instrumental sensitivity for a given focal spot size. We show that this optical Gamow peak essentially depends on the radial transmission profile of a diffractive-refractive aperture. Examples for energies above 4 keV illustrate astronomical capabilities for large-scale compact and segmented objectives as well. The spectral and spatial resolutions of conventional semiconductor detectors are very well matched to imaging characteristics of those achromatic lenses. The constraints to fabrication techniques using most promising materials like Li, Be, and plastics are discussed.