Phase retrieval methods applied to coherent imaging

Modern microscopy techniques are developing towards high-resolution imaging, and tremendous progress has been made in past decades; however, the imaging of individual biological macromolecules at atomic resolution using short-wavelength radiation such as electrons or X-rays has not yet been achieved. The construction of free-electron lasers in many countries around the world arises from the desire to develop new imaging techniques by employing coherent radiation to image individual macromolecules. This work deals with coherent imaging and related phase retrieval techniques, with an emphasis on their application in the imaging of individual biological macromolecules. An introduction to the imaging of non-crystalline objects with coherent waves is provided in Section 1. An overview of experimental schemes for realizing coherent imaging is given in Section 2. These schemes use no optical elements between the sample and the detector, in order to avoid aberrations and to achieve the highest possible resolution, limited only by diffraction. The images of samples are created using numerical reconstruction, an unusual aspect compared to conventional microscopy techniques. In coherent diffraction imaging, the result is equally dependent on the experimental setup and the numerical procedure used to recreate the structure. Section 3 describes the achievements of Professor Hans-Werner Fink's group at the University of Zurich, whose main interest is in coherent imaging with low-energy electrons. Examples of reconstructed holograms and diffraction patterns recorded with low-energy electrons are given. Section 4 describes the relevant advances that have been achieved in numerical analysis, such as three-dimensional deconvolution in holography, merging holography and CDI, and the extrapolation of recorded coherent images. The final section summarizes the future prospects of the coherent imaging of non-crystalline objects in general, and discusses prospective applications for the methods described in this work