Dose requirements for resolving a given feature in an object by coherent x-ray diffraction imaging

We address the question of what dose is required to image an object by coherent x-ray diffraction imaging (CXDI) and to resolve a certain sub-unit or feature of that object. We show that a necessary condition for being able to resolve the detail is that the feature can be imaged by itself. The quality of the reconstruction of the feature is nearly independent of the surrounding, whether it is embedded in a larger object or not. This allows one to easily estimate the dose requirements for identifying atoms and clusters in larger objects. We illustrate the result by a numerical example and give an estimate for the dose required to resolve single atoms of different elemental species in CXDI experiments at free-electron laser and synchrotron radiation sources.

[1]  B. Lengeler,et al.  Focusing hard x rays to nanometer dimensions by adiabatically focusing lenses. , 2005, Physical review letters.

[2]  Ian McNulty,et al.  Nanoscale imaging of buried structures with elemental specificity using resonant x-ray diffraction microscopy. , 2008, Physical review letters.

[3]  Qun Shen,et al.  Diffractive imaging of nonperiodic materials with future coherent X-ray sources. , 2004, Journal of synchrotron radiation.

[4]  J. Miao,et al.  Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens , 1999, Nature.

[5]  E. Anderson,et al.  Soft X-ray microscopy at a spatial resolution better than 15 nm , 2005, Nature.

[6]  M. Burghammer,et al.  Coherent x-ray diffraction imaging with nanofocused illumination. , 2008, Physical review letters.

[7]  S. Marchesini,et al.  High-resolution ab initio three-dimensional x-ray diffraction microscopy. , 2005, Journal of the Optical Society of America. A, Optics, image science, and vision.

[8]  J. Miao,et al.  High resolution 3D x-ray diffraction microscopy. , 2002, Physical review letters.

[9]  T. Ishikawa,et al.  Efficient focusing of hard x rays to 25nm by a total reflection mirror , 2007 .

[10]  C. Schroer Focusing hard x rays to nanometer dimensions using Fresnel zone plates , 2006 .

[11]  H. C. Kang,et al.  Nanometer linear focusing of hard x rays by a multilayer Laue lens. , 2006, Physical review letters.

[12]  J. Miao,et al.  Direct determination of the absolute electron density of nanostructured and disordered materials at sub-10-nm resolution , 2003 .

[13]  Tsumoru Shintake,et al.  Possibility of single biomolecule imaging with coherent amplification of weak scattering x-ray photons. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  J. Kirz,et al.  Biological imaging by soft x-ray diffraction microscopy , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[15]  J. Miao,et al.  An approach to three-dimensional structures of biomolecules by using single-molecule diffraction images , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[16]  U Weierstall,et al.  Dose, exposure time and resolution in serial X-ray crystallography. , 2007, Journal of synchrotron radiation.

[17]  J. Kirz,et al.  An assessment of the resolution limitation due to radiation-damage in x-ray diffraction microscopy. , 2005, Journal of Electron Spectroscopy and Related Phenomena.

[18]  W. H. Benner,et al.  Femtosecond diffractive imaging with a soft-X-ray free-electron laser , 2006, physics/0610044.

[19]  Jörg Maser,et al.  Focusing of hard x-rays to 16 nanometers with a multilayer Laue lens , 2008 .

[20]  J. Hajdu,et al.  Potential for biomolecular imaging with femtosecond X-ray pulses , 2000, Nature.

[21]  Hidekazu Mimura,et al.  High-resolution diffraction microscopy using the plane-wave field of a nearly diffraction limited focused x-ray beam , 2009 .

[22]  T. Ishikawa,et al.  Breaking the 10 nm barrier in hard-X-ray focusing , 2010 .

[23]  Q. Shen,et al.  Takagi-taupin description of x-ray dynamical diffraction from diffractive optics with large numerical aperture. , 2007, 0704.3982.

[24]  Garth J. Williams,et al.  Three-dimensional mapping of a deformation field inside a nanocrystal , 2006, Nature.

[25]  W. H. Benner,et al.  Single particle X-ray diffractive imaging. , 2007, Nano letters.

[26]  Jingjuan Zhang,et al.  Phase-retrieval algorithms applied in a 4-f system for optical image encryption: a comparison , 2005, SPIE/COS Photonics Asia.

[27]  M. Burghammer,et al.  Hard x-ray nanoprobe based on refractive x-ray lenses , 2005 .

[28]  Xiaojing Huang,et al.  Signal-to-noise and radiation exposure considerations in conventional and diffraction x-ray microscopy. , 2009, Optics express.

[29]  I. Robinson,et al.  Three-dimensional imaging of microstructure in Au nanocrystals. , 2003, Physical review letters.

[30]  Q. Shen,et al.  Hard x-ray microscopy with Fresnel zone plates reaches 40 nm Rayleigh resolution. , 2008 .

[31]  J. Miao,et al.  Quantitative image reconstruction of GaN quantum dots from oversampled diffraction intensities alone. , 2005, Physical review letters.

[32]  I. Robinson,et al.  Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction. , 2001, Physical review letters.