A thin foil reflector X-ray telescope is proposed for ESA's high throughput spectroscopic X-ray mission, one of the cornerstone projects. Based on astrophysical requirements the performance specifications include large effective area at an X-ray energy of 8 keV and angular resolution better than 30 arcsec. To achieve this goal with 7 telescope units the radius of the outer mirror should be at least 30 cm, the focal length 8 m, and the mirror length 20 cm. The mirror thickness should be limited to 0.2 mm. Various mirror technologies such as dip-lacquered aluminium and electro formed nickel foils are examined. The surface roughness must also be controlled because scattering can ruin the focussing ability. A test assembly consisting of three representative mirrors has been used to investigate different supporting principles for the mirrors. The positions and surface shapes are measured mechanically and a ray-tracing program is used to translate the measurements into focussing properties.