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.

The development of wave optics for light brought many new insights into our understanding of physics, driven by fundamental experiments like the ones by Young, Fizeau, Michelson-Morley and others. Quantum mechanics, and especially the de Broglie’s postulate relating the momentum p of a particle to the wave vector k of an matter wave: k = 2 λ = p/ℏ, suggested that wave optical experiments should be also possible with massive particles (see table 1), and over the last 40 years electron and neutron interferometers have demonstrated many fundamental aspects of quantum mechanics [1].

/pdf/optics-and-interferometry-with-atoms-and-molecules-1vnuwajb51.pdf

Optics and interferometry with atoms and molecules

X-ray computer tomography (CT) is fast becoming an accepted tool within the materials science community for the acquisition of 3D images. Here the authors review the current state of the art as CT transforms from a qualitative diagnostic tool to a quantitative one. Our review considers first the image acquisition process, including the use of iterative reconstruction strategies suited to specific segmentation tasks and emerging methods that provide more insight (e.g. fast and high resolution imaging, crystallite (grain) imaging) than conventional attenuation based tomography. Methods and shortcomings of CT are examined for the quantification of 3D volumetric data to extract key topological parameters such as phase fractions, phase contiguity, and damage levels as well as density variations. As a non-destructive technique, CT is an ideal means of following structural development over time via time lapse sequences of 3D images (sometimes called 3D movies or 4D imaging). This includes information nee...

https://www.tandfonline.com/doi/pdf/10.1179/1743280413Y.0000000023

Quantitative X-ray tomography

Phase-contrast x-ray imaging (PCI) is an innovative method that is sensitive to the refraction of the x-rays in matter. PCI is particularly adapted to visualize weakly absorbing details like those often encountered in biology and medicine. In past years, PCI has become one of the most used imaging methods in laboratory and preclinical studies: its unique characteristics allow high contrast 3D visualization of thick and complex samples even at high spatial resolution. Applications have covered a wide range of pathologies and organs, and are more and more often performed in vivo. Several techniques are now available to exploit and visualize the phase-contrast: propagation- and analyzer-based, crystal and grating interferometry and non-interferometric methods like the coded aperture. In this review, covering the last five years, we will give an overview of the main theoretical and experimental developments and of the important steps performed towards the clinical implementation of PCI.

http://iopscience.iop.org/article/10.1088/0031-9155/58/1/R1/pdf

X-ray phase-contrast imaging: from pre-clinical applications towards clinics

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

The fabrication and testing of planar refractive hard X-ray lenses made from bulk CVD diamond substrates is reported. The lens structures were generated by electron-beam lithography and transferred by reactive-ion etching into the diamond. Various lens designs were fabricated and tested at 12.4 and 17.5 keV photon energy. Efficiencies of up to 71% and gains of up to 26 were achieved. A line focus of 3.2 micro m (FWHM) was measured. These lenses should be able to withstand the extreme flux densities expected at the planned fourth-generation X-ray sources.

/pdf/diamond-planar-refractive-lenses-for-third-and-fourth-1tafn7ngtp.pdf

Diamond planar refractive lenses for third- and fourth-generation X-ray sources.

We have developed a two-grating interferometer for hard X rays that
can be used for phase imaging and tomography. A silicon phase
grating positioned just downstream of the object under study splits
the distorted wavefront into essentially a positive and a negative
first-order beam. At a given distance from this beam-splitter grating, where the two beams still mostly overlap, they form a
pattern of interference fringes that is distorted according to the
wavefront distortions. The fringes may be finer than the resolution
of an area detector used to record the signal, but an absorption
grating with suitable pitch, put in front of the detection plane,
allows the detection of intensity variations that correspond to the
derivative of the wavefront phase taken along the direction perpendicular to the grating lines. A combination of this technique
with the phase-stepping method, in which several exposures are made
which differ in the phase of the fringe pattern, allows to eliminate
effects of non-uniform intensity due to inhomogeneous illumination
and edge-enhancing inline phase contrast. Several examples of
tomograms taken under different experimental conditions are shown,
including a polychromatic "pink-beam" setup.

Hard x-ray phase imaging and tomography with a grating interferometer

We report on the fabrication and testing of linear transmission Fresnel zone plates for hard x rays. The diffractive elements are generated by electron beam lithography and chemical wet etching of 〈110〉 oriented silicon substrates. By tilting the cylindrical lenses with respect to the x-ray beam, the effective path through the phase shifting zones can be varied. This makes it possible to optimize the diffraction efficiency over a wide range of photon energies, and to obtain effective aspect ratios not accessible with untilted optics. The diffraction efficiency of such a lens was measured as a function of the tilt angles for various energies between 8 and 29 keV. Values close to the theoretical limit were obtained for all energies. Because of the coherence preserving properties of diffractive optics, the method opens up opportunities for experiments using coherent hard x rays.

/pdf/wavelength-tunable-diffractive-transmission-lens-for-hard-x-1qwovtsgx8.pdf

B. Nöhammer

Papers

Differential x-ray phase contrast imaging using a shearing interferometer

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

Diamond planar refractive lenses for third- and fourth-generation X-ray sources.

Hard x-ray phase imaging and tomography with a grating interferometer

Wavelength tunable diffractive transmission lens for hard x rays