We investigate the potential of large-scale diffractive-refractive normal-incidence transmission lenses for the development of space-based hard x-ray telescopes with an angular resolution in the range of (10-6-10-3) arcsec over a field of view that is restricted by the available detector size. Coherently stepped achromatic lenses with diameters up to 5 m for compact apertures and 13 m in the case of segmentation provide an access to spectrally resolved imaging within keV-wide bands around the design energy between 10 and 30 keV. Within an integration time of 106 s, a photon-limited 5σ sensitivity down to (10-9-10-7) s-1 cm-2 keV-1 can be achieved depending on the specific design. An appropriate fabrication strategy, feasible nowadays with micro-optical technologies, is considered and relies on the availability of high-purity carbon or polymer membranes. X-ray fluorescence measurements of various commercially available carbon-based materials prove for most of them the existence of a virtually negligible contamination by critical trace elements such as transition metals on the ppm level.