Workshop on "X-ray Science with Coherent Radiation"

Some Consequences of Focusing in Coherent Diffraction

K. D. Finkelstein

CHESS Wilson Lab, Cornell University, Ithaca, New York 14853
A quantitative understanding of incident beam angle and energy spread, and similar information about the detector are needed to understand the resolution in an x-ray scattering experiment. Are the consequences of these considerations different when the incident beam is a coherent wave front? We report on simulations made to explore the influence on the diffraction pattern of very simple systems, when the incident beam is focused on the specimen. The results offer some guidance on when concentrating optics may be useful, and how sensitive the scattering pattern is to phase variation in the incident beam.

Lessons from an Experiment of High Resolution Fourier Transform Holography with Coherent Soft X-rays
H. He, S. Marchesini, M. Howells, U. Weierstall, G. Hembree, and J. C. H. Spence

Lawrence Berkeley Nation Lab. and Arizona State University

A well separated reference wave and an unknown object together with the coherence of the beam source are the basic needs to do a Fourier transform holography (FTH) experiment. Holograms from a 2D random array of 50 nm gold balls that fulfill such conditions has been recorded accidently in beamline 9.0.1 in Adavanced Light Source using coherent soft X-rays at 2.1 nm wavelength. Reconstruction using direct numerical Fourier transform is readily obtainable and features better than 50 nm is resolvable. Attempt of higher resolution reconstruction with deconvolution will be reported. Various experimental approaches that satisfy FTH conditions will be discussed. Comparison of FTH to other reconstruction methods will be made.
Poster Abstracts

Time-Resolved Phase Contrast Radiography and DEI with Partial Coherent Hard X-Ray at BSRF

G. Li, Z Y Wu

Beijing Synchrotron Radiation Facility, IHEP, Beijing 10039, China
Continuously nice phase contrast images of different specimens, characterized by a negligible absorption contrast, have been obtained at Beijing Synchrotron Radiation Facility (BSRF), using the wiggler source of one of the last first-generation synchrotron ring still in operation. These phase contrast images shows details of the specimens and some interesting change related to the inner physiological and chemistry process of the specimens, when the object-film distance is between 5 and 100 cm, which can not be observed in any conventional radiographic images, that appear such as the defocused images of those recorded using the phase contrast method. These experiments at BSRF demonstrates that phase contrast radiographic methods, although limited by the partial coherence of the source, can achieve significant improvements in image quality and that this technique may have a wide range of applications in life science, biology, biomedicine and of course materials science.
Invalidity of low-pass filtering in atom-resolving x-ray holography
D. V. Novikov ¹, S. S. Fanchenko², A. Schley¹, M.Tolkiehn¹, G. Materlik<sup>3

1</sup>Hamburger Synchrotronstrahlungslabor HASYLAB am Deutschen Elektronen-Synchrotron DESY, D-22607 Hamburg, Germany

²Institute of Information Technologies, RRC Kurchatov Institute, Kurchatov square 1, Moscow 123182, Russia

³Diamond Light Source Limited, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, United Kingdom
Atom-resolving x-ray holography is a recently developed method for direct imaging of local three-dimensional structures at the atomic level. We investigate analytically and numerically additional effects arising from the long-range order in an object. It is shown that they are not correctly taken into account by existing image reconstruction procedures used commonly in the analysis of experimental data. We prove that low-pass filtering may lead to strong artefacts and cannot be used for extracting information about the short-range order in crystalline samples. Possible ways for solving the problem are discussed.
Poster Abstracts

Measurements of Spatial Coherence of X-ray Laser

from Recombining Al Plasma

Yuuji Okamoto, Naohiro Yamaguchi, Hideki Yamaguchi, and Tamio Hara

Toyota Technological Institute, 2-12-1 Hisakata, Tempaku, Nagoya 468-8511, Japan
Tabletop x-ray lasers which operate at wavelengths shorter than 20 nm are promising tools for many important applications such as x-ray photoelectron spectroscopy, x-ray microscopy, x-ray holography and x-ray lithography. The x-ray lasers are characterized by its high brightness, high coherence and monochromatic radiation. Especially, the degree of coherence of radiation plays a critical role in many of novel applications.

We measured the spatial coherence of the soft x-ray laser from the recombining Al plasma under various x-ray amplification configurations for the first time. A theoretical calculation model which was based on two-beam interference with partially coherent and quasimonochromatic light was developed to analyze the observed fringe patterns. The x-ray source was assumed to have a Gaussian intensity distribution, and a deviation of x-ray source from the optical axis of the Young’s interference experiment was introduced. Then we can

reproduce a fringe pattern, numerically which fits to an observed fringe pattern, though it has an asymmetric pattern. In the experiments, the fringe pattern representing the interference from the pair of Young’s slits has been observed for the Al XI 3d-4f line (15.47 nm), while there has not been observed the fringe visibility for the other non-lasing lines. It is clarified that spatial coherence of the Al XI 3d-4f line is developed in accordance with its amplification.


Avoidance and Removal of Phase Vortices in Reconstruction of Noisy Coherent X-ray Diffraction Patterns
Mark Pfeifer, University of Illinois at Urbana-Champaign
Phasing the oversampled X-ray diffraction from a coherently illuminated crystal provides sufficient information to reconstruct the density function of the diffracting crystal. This phasing, which is accomplished through use of an error reduction or hybrid input-output algorithm, can result in non-physical phase vortices in the reciprocal space reconstruction if the noise level of the data is too high. These vortices can cause significant error in the reconstructed image and are very difficult to remove since they are global defects in the phase- two vortices of opposite chirality must annihilate each other to be removed. While acquiring data with low levels of noise is preferable, it is sometimes not possible in experiments with time dependence or very small particles. Patching the amplitude and phase around vortices with random values can sometimes remove them from two-dimensional patterns, but this procedure is not feasible in three dimensions. Attempts are being made to avoid vortices or drive them by selection of starting conditions or modification of the input data.
Poster Abstracts

Pushing the Limits of Coherent X-Ray Diffraction: Imaging Single Sub-Micrometer Silver Nanocubes