Novel high resolution x-ray methods which are based on the availability of coherent or partially coherent x-ray light are currently under rapid development to image biological samples at the nanoscale. We compare two alternative approaches, based (A) on far-field diffraction and (B) on free space propagation of a coherent wave, considering image formation and object reconstruction, illustrated with recent examples [1-4]. We sketch out, how biomolecular samples and cells can be imaged by the highly divergent and coherent x-ray beam exiting an x-ray waveguide and/or KB mirror system, creating a magnified phase contrast projection image and/or hologram of the sample. We show by scaling arguments (on blackboard) and by experimental results (ppt slides) that a 5nm lipid membrane illuminated tangentiallyin water can be imaged by propagation imaging using a highly curved wave front (A. Beerlink et al., unpublished).

1. [1] K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. Kewish, M. Dierolf, F. Pfeiffer, T. Salditt, Quantitative biological imaging by ptychographic x-ray diffraction microscopy, Proc.Natl..Acad..Sci. 107, 529-534 (2010).
2. [2] K. Giewekemeyer, H. Neubauer ,S. Kalbfleisch, S. P. Krüger and T. Salditt, Holographic and diffractive x-ray imaging using waveguides as quasi-point sources, New J. Phys. 12, 035008 (2010)
3. [3] A.Beerlink, M. Mell, M. Tolkiehn, and T. Salditt Hard x-ray phase contrast imaging of black lipid membranes Applied Physics Letters 95, 203703 (2009); as well as unpublished extension of the work
4. [4] K. Giewekemeyer, S. Krüger, S. Kalbfleisch, C. Beta, T. Salditt, Lensless biological X-ray microscopy using waveguides, 2010, unpublished manuscript.