title: Phase recovery and lensless imaging by iterative methods in optical, X-ray and electron diffraction.
abstract: Thomas Young's quantitative analysis of interference effects provided the confidence needed to revive the wave theory of light, and firmly established the concept of phase in optics. Phase plays a similarly fundamental role in matter-wave interferometry, for which the field-emission electron microscope provides ideal instrumentation. The wave-particle duality is vividly demonstrated by experimental 'Young's fringes' using coherent electron beams under conditions in which the flight time is less than the time between particle emission. A brief historical review is given of electron interferometry and holography, including the Aharonov-Bohm effect and the electron Sagnac interferometer. The simultaneous development of phase-contrast imaging at subnanometre spatial resolution has greatly deepened our understanding of atomic processes in biology, materials science and condensed-matter physics, while electron holography has become a routine tool for the mapping of electrostatic and magnetic fields in materials on a nanometre scale. The encoding of phase information in scattered farfield intensities is discussed, and non-interferometric, non-crystallographic methods for phase retrieval are reviewed in relationship to electron holography. Examples of phase measurement and diffraction-limited imaging using the hybrid input-output iterative algorithm are given, including simulations for soft X-ray imaging, and new experimental results for coherent electron and visible-light scattering. Image reconstruction is demonstrated from experimental electron and visible-light Fraunhofer diffraction patterns. The prospects this provides for lensless imaging using particles for which no lenses exist (such as neutrons, condensates, coherent atom beams and X-rays) are discussed. These new interactions can be expected to provide new information, perhaps, for example, in biology, with the advantage of less damage to samples.
authors.affiliation: Department of Physics and Astronomy, Arizona State University, Tempe, AZ 85287-1504, USA.
authors.forename: J C H
authors.initials: JC
authors.lastname: Spence
authors.forename: U
authors.initials: U
authors.lastname: Weierstall
authors.forename: M
authors.initials: M
authors.lastname: Howells
mesh_terms: D000465:Algorithms; D006696:Holography / Q000295:instrumentation / Q000379:methods; D006801:Humans; D007089:Image Enhancement / Q000295:instrumentation / Q000379:methods*; D007909:Lenses; D008854:Microscopy, Electron / Q000295:instrumentation / Q000379:methods*; D008857:Microscopy, Interference / Q000295:instrumentation / Q000379:methods*; D019047:Phantoms, Imaging; D014961:X-Ray Diffraction / Q000295:instrumentation / Q000379:methods*