If an object is illuminated with coherent electromagnetic radiation, e.g., by visible laser light or highly brilliant x-rays, a diffraction pattern is formed in the Fraunhofer far field that is related via a Fourier transform to the optical transmission function of the object.The aim of coherent diffractive imaging (CDI), or so-called lensless imaging, is to directly reconstruct the original optical transmission function of the specimen from its measured diffraction pattern. In principle, CDI allows one to obtain a resolution that is ultimately limited only by the wavelength of the radiation used and not by the quality of optical lenses. In xray microscopy, for instance, the resolution is presently limited to several tens of nanometres because of difficulties in manufacturing efficient high-quality nano-structured x-ray optical elements. Since CDI schemes allow the resolution to be increased beyond these limits they are among the most promising techniques for x-ray imaging applications in life and materials sciences on the nanometre scale.
