J. Appl. Cryst.の発刊に際して

A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

羟氨苄青霉素引起大疱性类天疱疮样疹

Interpretation of X-ray Powder Diffraction Patterns . By H. Lipson and H. Steeple. Pp. viii + 335 + 3 plates. (Mac-millan: London; St Martins Press: New York, May 1970.) £4.

X-Ray Diffraction

X-ray radiographic absorption imaging is an invaluable tool in medical diagnostics and materials science. For biological tissue samples, polymers or fibre composites, however, the use of conventional X-ray radiography is limited due to their weak absorption. This is resolved at highly brilliant X-ray synchrotron or micro-focus sources by using phase-sensitive imaging methods to improve the contrast1,2. However, the requirements of the illuminating radiation mean that hard-X-ray phase-sensitive imaging has until now been impractical with more readily available X-ray sources, such as X-ray tubes. In this letter, we report how a setup consisting of three transmission gratings can efficiently yield quantitative differential phase-contrast images with conventional X-ray tubes. In contrast with existing techniques, the method requires no spatial or temporal coherence, is mechanically robust, and can be scaled up to large fields of view. Our method provides all the benefits of contrast-enhanced phase-sensitive imaging, but is also fully compatible with conventional absorption radiography. It is applicable to X-ray medical imaging, industrial non-destructive testing, and to other low-brilliance radiation, such as neutrons or atoms.

http://xrm.phys.northwestern.edu/research/pdf_papers/2006/pfeiffer_naturephys_2006.pdf

Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources

Using a high-efficiency grating interferometer for hard X rays (10-30 keV) and a phase-stepping technique, separate radiographs of the phase and absorption profiles of bulk samples can be obtained from a single set of measurements. Tomographic reconstruction yields quantitative three-dimensional maps of the X-ray refractive index, with a spatial resolution down to a few microns. The method is mechanically robust, requires little spatial coherence and monochromaticity, and can be scaled up to large fields of view, with a detector of correspondingly moderate spatial resolution. These are important prerequisites for use with laboratory X-ray sources.

/pdf/x-ray-phase-imaging-with-a-grating-interferometer-4px897qwex.pdf

X-ray phase imaging with a grating interferometer.

An x-ray interferometer has been developed that uses two transmission phase gratings to analyze wave front distortions in the hard x-ray range. The interferometer is insensitive to mechanical drift and vibrations, and it is tunable over a wide range of photon energies. This setup was used for differential phase contrast imaging of low-absorbing test objects. We obtained micrographs with moire fringes of good visibility, which revealed the local phase shift gradient caused by the objects. A comparison with numerically simulated images indicates that quantitative analysis of unknown phase objects is possible.

Differential x-ray phase contrast imaging using a shearing interferometer

We present an interferometric method to measure the shape of a hard-x-ray wavefront. The interferometer consists of a phase grating as a beam splitter and an absorption grating as a transmission mask for the detector. The device can be used to measure wavefront shape gradients corresponding to radii of curvature as large as several dozens of meters, with a lateral resolution of a few microns. This corresponds to detected wavefront distortions of approximately 10−12m or λ∕100. The device was used with 12.4 keV x rays to measure the slope error and height profile of an x-ray mirror. Surface slope variations with periods ranging from less than 1 mm to more than 1 m can be detected with an accuracy better than 0.1μrad.

/pdf/x-ray-wavefront-analysis-and-optics-characterization-with-a-4hj2r5lm28.pdf

X-ray wavefront analysis and optics characterization with a grating interferometer

We present a new method to analyze quantitatively the wave front of a partially coherent x-ray beam. The technique is based on the use of two-dimensional speckle patterns combined with digital image correlation algorithms and offers a pixel size resolution, a high accuracy, and a reduced sensitivity to mechanical vibrations thanks to a very simple setup. The requirements on transverse and longitudinal coherence are also low. Finally, we show how the method can be used for phase contrast imaging applications by a single sample exposure process.

/pdf/two-dimensional-x-ray-beam-phase-sensing-5csqaev5td.pdf

Two-dimensional x-ray beam phase sensing.

A new approach is proposed for the design of wide band-pass multilayer optical elements operating in the hard X-ray spectral region. The method, based on the combination of analytical and numerical methods, solves the inverse problem consisting of inferring the composition profile of a depth-graded multilayer coating. The key feature of our approach consists in using an analytical expression for the depth-distribution of the period as initial solution for direct computer calculations. This allows a global minimization of the merit function and a many-fold decrease of the computer run time. Simulations of two particular cases are presented: a constant reflectivity over a wide spectral range and a complicated reflectivity profile. The best choice of material pairs for composing a depth-graded multilayer structure is discussed from the viewpoint of maximum achievable reflectivity and least number of bi-layers. Features of depth-graded multilayer mirrors, which are distinctive from conventional periodic mirrors, are examined. The factors influencing the optical quality of broad-band multilayers are also considered.

Eric Ziegler

Papers

X-ray phase imaging with a grating interferometer.

Differential x-ray phase contrast imaging using a shearing interferometer

X-ray wavefront analysis and optics characterization with a grating interferometer

Two-dimensional x-ray beam phase sensing.

Design of X-ray supermirrors