# Hard X-Ray Synchrotron Imaging Techniques and Applications

Jean-Yves Buffière, José Baruchel

► To cite this version:

Jean-Yves Buffière, José Baruchel. Hard X-Ray Synchrotron Imaging Techniques and Applications. Synchrotron Radiation, Springer, pp.389-408, 2015, 9783642553141. 10.1007/978-3-642-55315-8_13. hal-01668784

HAL Id: hal-01668784

https://hal.science/hal-01668784

Submitted on 13 Jan 2023

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Hard X-Ray Synchrotron Imaging Techniques and Applications

Jean-Yves Buffière and José Baruchel

**Abstract** The features associated with modern Synchrotron Radiation (SR) machines (intense and coherent beams) result in a substantial extension of X-ray imaging capabilities in terms of spatial and temporal resolution, phase contrast, 3D images and combination of techniques. We describe some of the two and three-dimensional SR based imaging techniques, with emphasis on absorption, phase contrast and Bragg diffraction based imaging. In the last section selected examples illustrate the capabilities of these constantly evolving methods.

## 13.1 Introduction

A Synchrotron Radiation (SR) study of a sample involves using the adequate X-ray techniques (diffraction, absorption, scattering, ...) to extract the wished information. A very usual additional assumption is that the sample is homogeneous, and that by illuminating the whole volume the result corresponds to the one we could measure locally. This assumption is, of course, not valid when dealing with an inhomogeneous sample: in this case we need to use an “imaging” type approach, i.e. to measure “locally” to produce a map where each of these “local” measurements corresponds to an homogeneous area. The required size of the pixel for the “local” measurement is a function of size of the inhomogeneities. The “image” obtained from the ensemble of local measurements exhibits contrast, defined as the difference in detected signal that makes a feature distinguishable. The maximum contrast of an image is the contrast ratio or dynamic range.

J.-Y. Buffière (✉)

INSA Lyon, 20 avenue Albert Einstein, 69621 Villeurbanne, France
e-mail: Jean-yves.buffiere@insa-lyon.fr

J. Baruchel

European Synchrotron Radiation Facility, BP 220, 38043 Grenoble Cedex, France
e-mail: baruchel@esrf.fr
<figure><img src="image_2.png" /><figcaption>**Fig. 13.1** "Parallel" beam and "focussed" beam imaging schemes (see text)</figcaption></figure>

Two main experimental schemes, shown on Fig. 13.1, allow these “local” mea-
surements to be performed: (a) a parallel beam is used together with a pixelated
detector, in such a way that each pixel corresponds to a given volume in the sam-
ple, and the spatial resolution of the image associated with the pixel size (lensless
technique).

(b) the beam is focused on a given region of the sample, which is scanned in order to obtain a series of “local” measurements on these regions, the spatial resolution being associated with their size (X-ray lenses are required in this case).

For all imaging techniques, the recorded/observed image results from a convo-
lution of the signal emerging from the sample and the detector characteristics. The
observed size feature is a function of its physical size within the X-ray beam exit-
ing the sample and the point spread function of the detector; it also depends on the
statistical or instrumental noise, the geometry, .... Whereas X-ray imaging detectors
[1] are beyond the scope of the present paper, and will not be mentioned below, we
wish to point out that this is a very important aspect, which should not be neglected
when extracting information from an image.

X-ray imaging started over a century ago, with the discovery of X-rays, allowing the visualization of the volume of systems opaque to other probes. It was immediately noticed that these radiographs, which exploited the variation of the absorption of the beam when going through the sample, constituted an important tool for medical diagnostic. This led, during the First World War, at the initiative of Marie Curie, to have cars fitted with X-ray generators (their popular name being “petites Curies”) to be present in the neighbourhood of the battlefield to provide a quick diagnostic helping saving lives. The applications of radiography to materials were also rapidly developed.

For several decades, absorption radiography remained the only form of X-ray
imaging. About 50 years ago, Bragg diffraction imaging developed into practical
use. This “diffraction topographic” approach apply to single crystals and basically
consist of mapping the intensity and direction of the locally Bragg diffracted beams.
It reveals defects in the bulk of single crystals, and helped to develop production of
large, practically perfect crystals, for the microelectronics industry. These techniques
extended beyond semiconductor crystals, and are useful for investigating induced or
growth defects and distortions. Their range of applications dramatically grew when SR became available to condensed matter scientists.

A major breakthrough was performed when the computing improvements allowed producing three-dimensional (3D) images from a series of radiographs recorded at different angles (“tomography”).

All the X-ray imaging methods benefited from the use of SR, the improvements being even more pronounced when considering the new features of modern, “third generation”, SR machines. Real time and high spatial resolution experiments are nowadays routinely performed, and the high coherence of the beam allows exploitation of a novel form of radiography, in which contrast arises not only from absorption differences but also from phase variations across the transmitted beam. Several forms of phase contrast imaging developed over the last years. When the detector is located far from the sample (Fraunhofer regime) Coherent Diffraction Imaging (CDI) and, recently, ptychographic CDI, allow, from the recorded patterns, to reconstruct with very high resolution the local phase shift, and, consequently, the local sample density. Microradiography and its three-dimensional companion, phase microtomography, provide useful information on crystal growth-related features (porosities, inclusions, dendritic growth, ...). The spatial resolution of these two or three-dimensional “parallel beam” imaging techniques is now, routinely, in the µm range.

The highly brilliant sources of the modern SR facilities, coupled with new X-ray optics, allowed micro-beams in the µm or sub-µm range to be achieved. This leads to another type of images through the use of X-ray microbeam-based scanning approaches, probing for instance the fluorescence or the absorption near the absorption edges. In addition new devices under constant enhancement, allow nano-imaging to be performed, with a spatial resolution presently around 50 nm.

This brief introduction indicates that nearly all X-ray-matter type of interactions can be exploited within the frame of what we called “imaging approach”, i.e. a set of “local” measurements constituting a map or image. In the present paper we focus on images resulting from variations of absorption, phase, or Bragg diffraction, in their two- or three-dimensional (“microtomographic”) forms.

## 13.2 Imaging Techniques

### 13.2.1 Absorption Radiography

The interaction of X-rays with matter can be expressed through the complex refractive index

$$n = 1 - \delta + i\beta \qquad (13.1)$$

that describes both the absorption (β) and the phase change (δ) with respect to a path in vacuum. The absorption of X-rays is usually described by the absorption
<figure><img src="image_3.png" /><figcaption>**Fig. 13.2** Transmission imaging (radiography): the contrast mechanism can be absorption or, when dealing with a coherent beam, phase</figcaption></figure>

coefficient $\mu$, such that the number of photons $N$ after transmission through the sample, with $N_0$ being the number of photons in the incident beam, may be written as:

$$ \ln(N_0(x, z)/N(x, z)) = \int_{\text{path}} \mu(x, y, z)dx \quad (13.2) $$

The absorption coefficient $\mu$ is related to $\beta$ through the simple expression $\beta = \lambda\mu/4\pi$, where $\lambda$ is the X-ray wavelength.

X-ray absorption imaging consists in detecting the photons transmitted through the investigated sample (Fig. 13.2). The “experimental data” are the **contrast** that results from the inhomogeneous response of the sample. When a two dimensional detector (film, CCD camera) is used, this directly produces a map of the integral of $\mu(x,y,z)$, the linear attenuation coefficient, along the X-ray path, as indicated in (13.2).

The behaviour of the linear attenuation coefficient $\mu$ is dominated by the photo-electric effect for X-ray energies E below 200 keV. $\mu$ is in this case proportional to $\rho Z^4 E^{-3}$ Where $\rho$ is the material density and Z is the atomic number. The separation between Z and $\rho$ implies performing experiments using at least two energies. Above 200 keV, the Compton effect is predominant and the above proportionality is not valid.

The absorption-related coefficient $\beta$ changes abruptly with the energy of the photons at an absorption edge. The absorption edges are element-specific, and the logarithmic subtraction of images recorded above and below the edge enhances the visibility of the distribution of the element considered. It is also possible, by tuning the energy of the probing photons on the high absorption side of the edge, to take advantage of the oscillations of the absorption curve (XANES). These oscillations reflect the molecular environment of a given atom and provide the basic mechanism for imaging with chemical sensitivity.
<figure><img src="image_4.png" /><figcaption>**Fig. 13.3** An image of the volume can be obtained by rotating the sample in the beam, around a vertical axis **z**, recording a series of radiographs on a 2D detector, and using a reconstruction software to obtain the 3D image ("tomography")</figcaption></figure>

### 13.2.2 Microtomography

The radiography of an object displays the resolution associated to the detector in the plane of this detector, but no depth resolution is achieved (Fig. 13.3). To recover the resolution in the depth direction, particularly important for a thick sample, several radiographs can be recorded at different angular positions of the sample with respect to the incoming beam, this sample being rotated, in the case of the figure, around a vertical axis located in its center.

This is the main idea of computer-assisted tomography, which provides the three-dimensional (3D) absorption image of a bulky object from the two-dimensional (2D) images (radiographs) recorded at various angular positions of the object, processed using appropriate algorithms and software. From the reconstructed 3D data any virtual slice, or perspective renditions, of the object can be obtained.

Microtomography, with a spatial resolution better than 20 µm, has been developed over recent years [2]. Several laboratory instruments using micro-sources providing a polychromatic cone beam are now commercially available, and reach spatial resolutions of ≈2–20 µm. However, the best quality images, in terms of signal-to-noise ratio and spatial resolution, are obtained on instruments located in SR facilities. The present text will discuss the SR-based technique.

Figure 13.3 corresponds to the scheme of the most commonly used SR-based tomographic acquisition. As the source is small (~30 µm) and far away (~100 m) the beam (monochromatic, with $\Delta E/E \approx 10^{-2}-10^{-4}$, or “pink”, i.e. filtered white beam) can be considered as parallel. This “parallel beam” approach implies that no magnification is obtained, and the spatial resolution mainly results from the effective pixel size of the detector. But this configuration exhibits the advantage that all the radiographs, recorded on the 2D detector, obtained by rotation of the sample about **z**, are such that each slice, at a given height z, is independent of the other slices. A radiograph (or $\ll$ projection $\gg$) corresponds to a given angle $\theta$, formed (Fig. 13.3) by the axes **x** (direction of the X-ray beam) and **v** (in the ($\mathbf{u},\mathbf{v},\mathbf{z}$) sample frame of reference).
Equation (13.2) can be rewritten, in this case, as a series of integrals (the projections $p_{\theta}(y,z)$), with $y$ perpendicular to $x$ and $z$ and $y = 0$ on the rotation axis

$$p_{\theta}(y, z) = \ln[N_0(y, z)/N_{\theta}(y, z)] = \int_{path} \mu[u(x, y, \theta), v(x, y, \theta), z] dx \quad (13.3)$$

In parallel geometry, $p_{\theta}(y, z) = p_{\theta+\pi}(-y, z)$, meaning that the acquisition of projections over a range $[0, \pi]$ is sufficient. For a given $z$ the ensemble $\{p_{\theta}(y,z), \theta \in [0, \pi]\}$ constitutes the Radon transform (or “sinogram”) of the 2D slice. The inverse transform provides the $\mu(u,v)$ map of the slice. The 3D problem reduces, in parallel geometry, to a sequence of 2D calculations. Let us note that this is not the case for laboratory tomographs, which produce a conical beam.

Several reconstruction algorithms, such as the filtered back-projection (FBP) or the algebraic reconstruction techniques (ART), have been developed. Their mathematical description is beyond the scope of the present paper, but can be found in [3, 4]. The commonly used reconstruction algorithm is FBP, because it provides a better ratio of “image quality/calculation time”: the inverse problem can be solved by firstly correcting the projections by a filter $H(f) = f, f$ being the spatial frequency, and then by performing a back-projection procedure.

### 13.2.3 Phase Imaging

The refractive index of materials (13.1) deviates slightly from unity through a decrement $\delta$, which is in the $10^{-5}-10^{-6}$ range. $\delta$ is proportional to the electronic density in the material, hence to its mass density; it involves a dispersion correction when the photon energy is near an absorption edge. Far from absorption edges, it can be written as:

$$\delta = (\lambda^2 r_0 / 2\pi V) \sum_j N_j Z_j \quad (13.4)$$

where $r_0$ is the classical electron radius (=2.82 fm), and $N_j$ is the number of atoms of atomic number $Z_j$ present in the volume $V$.

The passage of an X-ray beam through a sample entails a phase shift

$$\phi(x, y) = (2\pi/\lambda) \int_{path} \delta(x, y, z) dx \quad (13.5)$$

This phase shift is variable over the cross-section of the beam if the beam has passed through a sample with inhomogeneous thickness and/or density. This can produce an image if this “local” variation of the phase shift can be observed through interference
<figure><img src="image_5.png" /><figcaption>**Fig. 13.4** Some ratios $\delta/\beta$, as a function of the X-ray energy: $\delta/\beta > 10$ (10–100 keV)</figcaption></figure>

phenomena. This requires that the waves scattered by different regions of the sample display well correlated phases, i.e. that the “coherence length” of the incoming beam is large enough. Similarly, the classical “Young’s holes” experiment in visible optics only produces interferences if the holes are closer than the lateral coherence length $L_c = \lambda/2\alpha$, where $\lambda$ is the wavelength and $\alpha$ is the angular size of the source as seen from a point in the specimen. The X-ray beams produced at modern SR facilities exhibit a high degree of coherence, $\alpha$ being in the $\mu$ radian range, leading to $L_c \sim 100 \mu m$ ($\lambda = 1$ Å) at long beamlines (100–200 m) like ID19 or ID16 at the ESRF.

Phase images were obtained in the past using rather complex apparatus (systems involving several crystals). The qualitatively new aspect of modern SR beams is that they make it possible to reveal, through the “propagation” technique, with a reasonable instrumental simplicity, the phase variations of hard X-rays. As indicated above, the local phase variations can be changed into intensity variations through the interference of parts of the beam that undergo different phase shifts, but are mutually coherent. It can be described either in terms of Fraunhofer diffraction, when the distance D between sample and detector is large enough to apply the “far field” approximation, or in terms of Fresnel diffraction, when D is smaller. We will briefly describe below the X-ray imaging techniques developed for these configurations.

But let first point out that the great advantage of this new type of imagery is the increased sensitivity it provides. Figure 13.4 shows that $\delta (\sim 10^{-5}-10^{-6}) \gg \beta (\sim 10^{-9}-10^{-11})$ in the hard X-ray range ($E > 6$ keV). Indeed a thickness variation of $\sim 1-5 \mu m$, for instance associated with a “cavity” within the material, only involves a very small, usually not detectable, variation of absorption, but can be associated with a phase shift of the order of $\pi$, easy to detect. This increased sensitivity allows visualization of tiny objects such as cracks, micro-pipes, $\mu$m sized pores, or regions exhibiting even a weak (1%) density variation with respect to the matrix.
### 13.2.3.1 Fraunhofer Regime: CDI, Ptychography

Measured in the far field ($D \to \infty$, Fraunhofer regime), the intensity distribution of coherent light scattered by a specimen is related by a Fourier transform to the wave field directly past the specimen. These wave field variations are related to the local variations of the index of refraction integrated along the X-ray path within the sample. This means that, by selecting a coherent fraction of the incoming monochromatic “partially-coherent” synchrotron beam (for instance by setting slits that reduce the beam to a size smaller than the lateral coherence length), and using it to illuminate a sample, we are able to collect on a detector located in the far field a diffraction pattern allowing, in principle, through a inverse Fourier transform, reaching the electronic density of the sample (Fig. 13.5). However only intensities are measured, and additional analytical means are needed to retrieve the phase-related information. This phase retrieval is performed through iterative feedback algorithms that constitute a crucial ingredient of the technique known as X-ray Coherent Diffraction Imaging (CDI). These algorithms “replace” the objective lens of a typical microscope and allow recovering the local phase introduced by the sample, and, as a consequence, producing a high resolution real space image of this sample [5, 6]. It is clear that the wavefront at the exit side of the sample also incorporates the departures from the plane wave regime of the incident beam: CDI therefore usually requires a well prepared planar wavefront that completely illuminates an isolated sample. Very interesting results have been achieved, in 2D and in 3D, by combining CDI and tomography.

Most of the iterative feedback algorithms are based on the idea of “oversampling”, i.e. Shannon’s theorem, which states that if the diffraction pattern is sampled at twice the Nyquist frequency (inverse of sample size) or lower, it can yield a unique real space image [7]. This idea, coupled with the dramatic increase in computing power over the last decades, allowed the design of phase retrieval algorithms [8]. Random phases are initially combined with the amplitude information, a Fourier transform being then applied back and forth. During this process constraints (one of them being, in real space, the “support”, which restricts the resulting image to a confined space, the volume where the sample stands) are set in such a way that the result evolves into an image, by performing enough (typically hundreds to thousands) iterations. This led to the first demonstration of CDI [5].

The phase retrieval algorithms are under constant evolution, gradually solving the initially encountered problems on the convergence or non-unicity of the resulting image. Different implementations of CDI have been proposed [9–12], which extend the capabilities. Let us note that whereas CDI geometry may appear rather restrictive from a general perspective, it can be naturally implemented in the case of samples illuminated by a X-FEL beam (with specimens investigated by a single pulse per sample in a ‘diffract and destroy’ manner), and therefore these techniques exhibit a clear potential for the near future.

The combination of CDI with “ptychography”, a phase retrieval method proposed in the 1960s for electron microscopy, allowed to substantially enhance the capabilities of these far-field pattern based phase retrieval techniques [13]. Indeed, phases can be determined from far field intensity data when the sample is scanned, with
<figure><img src="image_6.png" /><figcaption>**Fig. 13.5** Scheme of Fraunhofer-type phase contrast imaging: the incoming beam is reduced to a size smaller than the coherence length. The sample-to-detector distance is such that the Fraunhofer approximation is fulfilled. The scattered beam allows retrieving, with the help of adapted iterative algorithms, the phase locally introduced by the sample. If the sample is bigger than the beam size, a translation with a step smaller than the beam size is used (ptychography) to produce the phase image. An additional rotation of the sample is necessary when wishing a 3D, tomographic, phase image</figcaption></figure>

a coherent beam and overlapping regions. It has been shown in recent years that this “ptychographic CDI”, where the coherent beam is translated laterally in steps smaller than the beam size, and the ensemble of patterns scattered by the sample are recorded in the far field, can greatly improve the convergence rates of iterative reconstruction schemes. This approach which is now usually called “ptychography”, allows strongly relaxing the demands and the required pre-knowledge on the illuminating wavefield that were required for the CDI single-image techniques. When applying ptychography the lateral extension of the sample may be much larger than the size of the illumination. In addition the incident wave can substantially depart from an ideal spherical or planar wavefront. As various parts of the sample are illuminated multiple times allows the reconstruction of both illumination and object in parallel [13–16].

### 13.2.3.2 Fresnel Regime

When the sample is illuminated by a large, parallel, partially coherent beam, and the detector is not set in the far field, but at an intermediate distance D (typically a few $10^{-1}$ m) from the specimen (Fresnel regime) another type of phase-sensitive image is obtained. An absorption image is obtained if D is small ($10^{-3}$ m range). This corresponds to the fact that the region in the sample that effectively determines the image at a point of the detector, the first Fresnel zone, has a size $r_F = (D/\lambda)^{1/2}$. When D is in the mm range, the separation of the fringes originating from an area $r_F$ is below the resolution of the detector (µm range), and no interference will be observed, hence the image will be purely due to absorption. For D larger, but such that $r_F$ remains smaller than the size $\tau$ of the object to be imaged, the edges of the
image behave independently, and provide the only phase contribution to the image. For D even larger, interference fringes built up. The best sensitivity for an object with size $τ$ is obtained for $D \approx τ^2/2λ$.

Phase variations across the beam exiting the sample lead to variations in intensity, hence to contrast, provided the phase has a two-dimension Laplacian $\nabla^2\phi(y, z) \neq 0$. They show up, for increasing distance D, first through the appearance of a black-white line at the phase discontinuities ("edge enhancement"), then a more and more obtrusive Fresnel fringe system ("holography") which progressively changes towards the Fraunhofer regime [17, 18].

Phase imaging based on the visualization of the edges is very useful to show, qualitatively, relevant features present in the sample like inclusions, holes, or fractures. But it is not a quantitative technique, and its spatial resolution is limited by the occurrence of the fringes used to visualize the borders. Quantitative phase determination implies developing a procedure for the retrieval of the phase maps. Several algorithms were produced [19, 20], and showed to be able, when combined with microtomography, to reconstruct the local phase shift introduced by a volume within the sample. These quantitative phase mapping combined procedures are now routinely used, and provide an invaluable tool for the characterization of condensed matter (from materials science [21] to biological samples) on the µm and sub-µm scale.

### 13.2.4 Microbeam Based X-Ray Imaging Techniques/Nano Imaging

The absorption or phase-based imaging techniques described above cannot provide information on the local elemental composition and/or local crystallographic structure. This requires combining scattering measurements with scanning of the sample. The X-ray beams produced at modern SR sources can, because they originate from a very small source, be focused into a very fine spot ($5.10^{-8}$–$5.10^{-6}$ m range) with extremely high intensity. Various focusing elements are currently used to produce small section beams: they include curved crystals, Fresnel zone plates, tapered capillaries, compound refractive lenses, waveguides, and “Kirkpatrick-Baez” focusing mirrors or multilayers ([22] and references therein, and Chap. 3 of the present book). It is then possible to scan the sample and collect quantitative information. This information, displayed in the form of a (y,z) map corresponding to the position of the beam, is the “image” we are concerned with.

X-ray microfluorescence allows mapping of the presence and concentrations of elements on the sample [23]. A beam of energy $E_0$ is produced ($\Delta E/E \approx 10^{-4}$), a mirror eliminating the hard ($E > E_0$) radiation and focused on a small area of the sample. A solid-state detector is set at 90° with respect to the incident beam. A given element produces fluorescence with a characteristic energy $E_f$. The spatial resolution is, in the hard X-ray range where the depth of focus is usually large ($\approx 100$ µm), mainly determined by the spot size. These experiments, whereas producing unique
<figure><img src="image_7.png" /><figcaption>**Fig. 13.6** Scheme of the magnified propagation phase contrast imaging tomography: the incoming beam is focused to a few tens of nm sized spot; this spot acts as a secondary source emitting a conical coherent beam. The magnification is obtained (distances x₁ and x₂) by setting the sample at different distances from the source</figcaption></figure>

results, can be time-consuming. The problem is substantially simplified when the element of interest is “heavy” with respect to the matrix (like uranium in soils, or chromium in organic materials).

Fluorescence is not the only quantity that can be mapped: wide angle diffracted X-rays, or small-angle scattered X-rays, absorption, or secondary electrons, provide additional information. Scanning imaging simultaneously exhibits high spatial resolution (µm scale in the hard X-ray range) and elevated chemical selectivity. Local information on different chemical states within systems having the same elemental composition is therefore possible. In addition, combined transmission, fluorescence and Compton microtomography was implemented (“integrated tomographic technique” [24, 25]). It allows a quantitative reconstruction of the internal elemental composition and crystallographic structure of the measured slice.

Synchrotron radiation hard X-ray imaging has a specific and crucial role to play in nano-imaging, both for biology and biomedicine and nano-materials in general because it can combine high spatial resolution and reasonable sample thickness in 3D and, on the same specimen, different imaging modalities such as phase contrast and fluorescence analysis, all this on specimens close to their native state and without sample-modifying, cumbersome preparation procedures. These nano-imaging techniques rest on the continuous progress in source brilliance coupled with long beamlines and improvements of X-ray optics. The Kirkpatrick-Baez mirrors can nowadays, with enhanced mirrors/multilayers, routinely produce focal spots in the 15–25 keV range and the few tens of nm size, while retaining a high enough monochromaticity (~10⁻²) and a high intensity (>10¹¹ photons/s). This provides the spatial resolution and elemental sensitivity needed to investigate the presence and metabolism of metals in biological systems, i.e. the growing field of metallomics. When coupled with tomography and phase contrast it allows zooming into the structure of tissues or cells close to their native state, as well as into the nanostructures
<figure><img src="image_8.png" /><figcaption>**Fig. 13.7** Basic principle of the Bragg diffraction imaging methods (see text)</figcaption></figure>

produced for semiconductor devices: projection microscopy (Fig. 13.6) is a magnified version of propagation phase imaging, but can also be considered as Coherent Diffraction Imaging with a curved wavefront [26]. This technique can also be combined with ptychography (“near field ptychography”), obtaining an improved robustness of propagation-based X-ray phase tomography [27].

**13.2.5 X-Ray Bragg Diffraction Imaging**

Knowing the grain structure in polycrystalline materials, as well as the distortion within a given grain, is often essential to understand their physical properties. A variety of well established techniques give clues on these topics: they include classical light microscopy, as well as transmission, scanning and electron backscatter diffraction. In recent years synchrotron based techniques are of increasing relevance in this field of non-destructive microstructure characterization, through the combination of X-ray imaging (and in particular tomography) and diffraction techniques. In the present section we briefly present Bragg diffraction-related imaging techniques, which allow characterizing the shapes, orientation and crystalline quality of the grains [28] in polycrystals or, when applied to a single grain, or a single crystal (“X-ray diffraction topography” [29, 30]), investigating inhomogeneous distortion.

Bragg diffraction is associated by many scientists with “reciprocal space”. But a Bragg diffracted beam can also be used to form an image in direct space. Figure 13.7 schematically shows, for a platelet shaped single crystal, the basic concept of the diffraction imaging methods. The diffracted beam is recorded on a 2D-detector. Contrast can be observed on S if a volume V (Fig. 13.7) behaves differently from the remaining of the sample from the diffraction point of view (intensity, direction...).

**13.2.5.1 Diffraction Contrast Tomography**

Several methods, which combine imaging with Bragg diffraction, provide information on the three-dimensional structure (grain shape, orientation, distortion) of
<figure><img src="image_9.png" /><figcaption>**Fig. 13.8** Diffraction contrast tomography setup</figcaption></figure>

polycrystalline materials [31, 32]. We will here briefly describe one of these methods, the ≪ Diffraction Contrast Tomography ≫ (DCT) [28], which recently developed at several synchrotron radiation centres. It combines a microtomographic recording of the radiographic images with the analysis of the Bragg diffracted spots produced by the different grains composing the polycrystal during the rotation of the sample. Indeed during this rotation a given grain goes, for certain angles, through a Bragg position for a particular set of crystallographic planes. Part of the energy is therefore transferred from the incident to the diffracted direction, leading to a simultaneous loss of intensity at the grain location in the transmitted beam, and to a Bragg spot which is recorded, outside the transmitted beam footprint. This procedure is schematically shown on Fig. 13.8 for one selected grain: it allows, with the help of adequate algorithms, which are under constant development, to retrieve the shape and orientation of the grains in the polycrystal [33].

### 13.2.5.2 Diffraction “Topography” and Rocking Curve Imaging

Bragg imaging (“X-ray diffraction topography”) is a well-established method for the visualization and analysis of crystal defects in high quality single crystals [29, 30]. The local variations of the amplitude or direction of the diffracted beam provide information on crystal inhomogeneities. The inhomogeneities are visualized because they can entail a distortion of the crystal lattice (lattice rotation $\delta\theta$ and/or lattice parameter variation $\Delta d/d$); these inhomogeneities include defects such as dislocations, twins, subgrain boundaries, domain walls, inclusions, and macroscopic deformations like bending.

The ≪ Rocking Curve Imaging ≫ (RCI) technique is a fully quantitative counterpart of X-ray topography, which takes advantage of the features of synchrotron radiation beams (flux, weak divergence) and from the substantially increased computer power which is today available [34]. Figure 13.9 shows its principle: the crystal, illuminated by a monochromatic beam, is rotated through the Bragg position for a
<figure><img src="image_10.png" /><figcaption>**Fig. 13.9** Scheme of Rocking Curve Imaging: the incoming monochromatic beam is Bragg diffracted by the crystal. A small rotation around the Bragg position (angle $\omega$) allows recording the $\ll \text{local} \gg$ rocking curves for each pixel of the 2D detector</figcaption></figure>

given set of crystallographic planes, and the diffracted beam is recorded, for each angular position along the diffraction rocking curve, on a “pixelated” detector. The “maps / images” are obtained from the data recorded for the ensemble of angular positions. When taking into account that the incoming beam is nearly parallel, we can consider, and this proved to be a very good approximation, that the “local” rocking curves for each of the pixels correspond to a given area in the sample. Three of these “images” are particularly interesting (1) the $\ll \text{integrated intensity} \gg$ image, i.e. the surface associated to the ‘local’ rocking curve, which indicates the local crystalline quality (2) the “peak position”, which gives access to the variation of lattice parameter, and/or to the respective bending of the various regions of the sample and (3) the full width at half maximum (FWHM), which provides information on the “local mosaic spread” in the sample. Crystalline defects like dislocations are visible on these images, and the distortion they induce is immediately quantified. The spatial resolution of RCI is directly associated with the pixel size, typically in the $\mu$m-few $\mu$m range.

In the case of projection diffraction imaging in transmission (Figs. 13.7 and 13.8) a 2D image of the 3D actual volume is produced: in other words, a high spatial resolution ($\mu$m range) is obtained along the crystal plate surface, whereas the resolution along the crystal depth is poor. Several ways were proposed to solve this problem and obtain depth sensitivity on the images. A “topo-tomography” approach was shown to be able to produce a 3D image of defects in some cases [35]. A more general approach consists in restricting the width of the incident beam by an entrance slit of width $s$, with $s \approx 10–20\mu$m. In this case (“section” diffraction imaging) a good resolution is also reached along the crystal depth, but at the cost of a drastic reduction of the investigated volume.
The same idea applies for << Rocking Curve Imaging >>, and leads to a three-dimensional extension (<< 3D-RCI >>) of this technique, which allows imaging the whole crystal/grain volume [36]. We will report, in the next section, the unique information provided by this method on the inception of deformation in a tri-crystalline sample.

### 13.3 Selected Examples of the Application of Synchrotron Radiation Imaging Techniques

With the availability of third generation synchrotron sources the spatial resolution of X-ray imaging techniques has rapidly evolved to reach the micrometer range routinely. This level of resolution, which is comparable to that obtained with optical microscopy, has triggered a wide interest in the scientific community because of the specific aspects of X-rays compared to visible light i.e. the ability to penetrate opaque materials non destructively, the huge number of photons which yields very high signal to noise ratio images very quickly (a fraction of seconds for topographs, milliseconds for radiographs), the possibility to couple imaging with another signal (fluorescence, diffraction ...). As a result, the number of papers devoted to X-ray imaging and, more specifically, to tomography has dramatically increased in the literature. The range of studied materials has widened to include all kind of structural materials (polymers, ceramics, metals, composites), cellular solids but also, mainly thanks to phase contrast, biological samples (among which bones), fossils, cultural heritage and extra terrestrial materials. Dedicated symposia are regularly organised in conferences (E-MRS, Euromat and TMS conference series) and, more recently, dedicated conferences on 3D imaging/materials science have appeared. Giving an exhaustive view of the applications of synchrotron imaging is therefore out of the scope of this chapter. In the field of 3D characterisation some reviews have now been published for the interested reader [37]. In what follows we are highlighting a few studies which illustrate some recent developments.

As explained in the previous sections, the images obtained from X-rays can be recorded in situ in two or (indirectly) three dimensions. In the former category, a striking example of the potential of X-rays to capture images of very fast phenomena, is the work from Wang et al. [38], who used radiography at the Advanced Photon Source to monitor in situ pure and aerated liquid jets used to increase combustors efficiency. The key feature of this experiment is the ultrafast imaging capability of the setup which provides an exposure time of 170 ps. The images obtained give an invaluable description of the internal organisation of the gas/liquid mixture within the jet.

Increased recording times are the price to pay for 3D imaging. While this is clearly not an issue for classical 3D observation of a “static” sample like a fossil or a foam, 3D characterisation of dynamical processes has long been restricted by exposure times of the order of ten to twenty minutes. The development of new experimental
<figure><img src="image_11.png" /><figcaption>**Fig. 13.10** 3D rendering of the formation of Al dendrites during the solidification of an Al-10%wt Cu alloy [40]</figcaption></figure>

set ups has however pushed those limits by several orders of magnitude in the last
10 years. By optimising the number of photons in the beam (pink beams with Δλ/λ
~ 10⁻²–10⁻³ or even white beams), scintillators, camera (CMOS), rotations stages
(constant velocity fast air bearing motors) hundreds of images can now be recorded
with a spatial resolution close to 1 µm in less than 1 s. Figure 13.10 illustrates the
3D development of dendrites in an Aluminium Copper alloy during cooling rates of
the order of 3 °C min⁻¹. Such high acquisition rates have been pioneered at ESRF
by a scientific community interested in metal solidification; Nguyen-thi et al. have
recently reviewed the work in this field [39] and shown that, besides tomography, in
situ fast radiography of solidifying metals also reveal details of the dendrites growth
such as dendrite torsion and bending. Such mechanisms can be related, when coupled
with topography, to the local crystallographic orientation of the growing crystals.

Fast X-ray imaging is a rapidly evolving field, in particular in the case of tomography, and has already found numerous applications e.g. in the study of damage development in metals under mechanical loading or phase transformation [41]. Developments of phase reconstruction using a single distance have also enabled the fast tomography of weakly attenuating objects allowing, for example, to follow the temporal evolution (coarsening) of a beer foam, and even in vivo monitoring of a fly [42].

For increasing the spatial resolution of 3D images, several possibilities have been
explored. In the case of classical absorption tomography a contrast agent can reinforce
the visibility of small features as shown for example by Plouraboué et al. [43] for
a large micro vascular network in biological tissue samples. Imaging above and
below an absorption edge to increase the contrast has been applied first in medical
applications [44] and recently this technique has found some application also in
materials science: for the 3D characterisation of particle and pores of a sand (imaged
at energies below and above the Cs K-edge) [45] as well as the Zn distribution within
the cell walls of an Al–Zn–Mg foam [46].

The sensitivity of phase contrast to very small changes in electron density, as
explained above, is another very efficient way to increase the spatial resolution of
3D imaging, without focusing optics. Very different sub-voxel features such as cracks
<figure><img src="image_12.png" /><figcaption>**Fig. 13.11** 3D rendering of the internal air space network in Arabidopsis seed (300 nm resolution)</figcaption></figure>

in metals [47], or the osteocyte lacunocanalicular network in bones [48], have been imaged in this way with a voxel size down to 0.3 µm (see [37] for a review).

Focusing optics can bring the spatial resolution/voxel size below 100 nm at the expense of a reduced sample size (diameter below a few hundreds micrometers) and strict requirements in terms of mechanical and thermal stability. Up to now this has severely restricted the possibility to perform this kind of observation in situ with a changing sample environment. Nevertheless internal features have been imaged in various kind of samples with unprecedented accuracy. In the case of biological samples, for example, Cloetens et al. have shown the existence of a 3D network of intercellular air space (see Fig. 13.11) in a plant seed (*Arabidopsis*) that can allow exchange for energy supply during germination and/or serve for rapid water uptake and distribution during imbibition [49]. The technique is however not restricted to “soft” material as Tolnai et al. have shown some evolution of the shape of intermetallic phases during (ex situ) solution heat treatment of an Al–Si alloy [50].

The images obtained using far field techniques, usually combined with tomography, are able to produce high quality images. As an example, let us mention the spectacular results that were obtained by [51] on mouse femur bone samples, where osteocyte lacunae and the interconnective canalicular network were imaged with high spatial resolution (100 nm range).

Finally, one important feature of X-ray radiation, as mentioned above, is that it can be coupled with the detection of a complementary signal like diffraction or fluorescence. For example, Kim et al. have visualized the spatial distribution of Iron in *Arabidopsis* using X-ray fluorescence microtomography [52]. Diffraction has been used in combination with tomography to monitor creep induced evolution of a brass alloy: voids initiation and growth, together with dislocations density and texture evolution, have been measured [53]. Other examples include phase transformation accompanying microstructural evolution during annealing of superconducting wires [54], or the coupling between damage evolution and stress distribution in metal matrix composites [55].

As explained above the diffraction signal can be used to reconstruct a 3D image of the spatial distribution of grains in crystalline sample [56]. Further tests can be applied to this sample to study, by tomography, the evolution of the microstructure during, for example, a thermal heat treatment [57], or a mechanical test [58].
<figure><img src="image_13.png" /><figcaption>**Fig. 13.12** 3D rendering of a snow sample, showing (a) the ice single-crystalline grains and (b-c) a cut of a fraction of the previous image in absorption mode (b) and diffraction mode (c), with colours associated to crystals with different orientation</figcaption></figure>

Figure 13.12 shows an example of the use of diffraction contrast tomography to study snow, which is a conglomerate of ice crystals [59]. On Fig. 13.12a each grain has a colour associated with the orientation of the six-fold axis of the hexagonal structure of ice. Figure 13.12b, c show the difference between an absorption image (b), which suggests the occurrence of 3 grains, and the diffraction image (c), which shows the presence of six crystals in the same area.

The 3D-RCI technique we mentioned above was used to follow the first steps of the deformation of an ice polycrystal. The values of local mosaic spread in the neighbourhood of the defects (initially dislocations, then glide planes and finally the inception of a subgrain boundary) have been measured over two orders of magnitude within the bulk of the crystal [60].

## 13.4 Conclusion

Synchrotron radiation based X-ray imaging techniques, which exploit most of the photon-matter interactions, exhibit an impressive development over the last years. Imaging techniques are, in this way, one of the key topics for the upgrade programmes of nearly all major synchrotron facilities in the world, because associated with very high level scientific results in very different fields that go from materials science to cultural heritage and biomedical topics. In situ and real-time investigations are increasingly used and allow phenomena such as the growth, fracture or phase transitions to be studied. These techniques are in constant evolution, and spatial resolution improvements, new tools for image processing, and extension to new topics, are constantly observed.
References

1. T. Martin, A. Koch, J. Synchrotron Rad. **13**, 180–194 (2006)

2. B.P. Flannery, H.W. Deckman, W.G. Roberge, K. D'Amico, Science **237**, 1439–1444 (1987)

3. A.C. Kak, M. Slaney, *Principles of Computerized Tomographic Imaging* (IEEE Press, New York, 1988)

4. F. Peyrin, L. Garnero, I. Magnin, Traitement du Signal **13**, 381–413 (1996)

5. J. Miao, P. Charalambous, J. Kirz, D. Sayre, Nature **400**, 342–344 (1999)

6. H.M.L. Faulkner, J.M. Rodenburg, Phys. Rev. Lett. **93**, 023903 (2004)

7. D. Sayre, Acta Cryst. **5**, 843–845 (1952)

8. J.R. Fienup, J. Opt. Soc. Am. A **4**, 118–123 (1987)

9. H.M. Quiney, J. Mod. Opt. **57**, 1–57 (2010)

10. K.A. Nugent, Adv. Phys. **59**, 1–99 (2010)

11. P. Thibault, V. Elser, Ann. Rev. Condens. Matter Phys. **1**, 237–255 (2010)

12. B. Abbey, L.W. Whitehead, H.M. Quiney, D.J. Vine, G.A. Cadenazzi, C.A. Henderson, K.A. Nugent, E. Balaur, C.T. Putkunz, A.G. Peele, G.J. Williams, I. McNulty, Nat. Photonics **5**, 420–424 (2011)

13. J.M. Rodenburg, A.C. Hurst, A.G. Cullis, Ultramicroscopy **107**, 227–231 (2007)

14. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, Science **321**, 379–382 (2008)

15. M. Guizar-Sicairos, J.R. Fienup, Opt. Lett. **33**, 2668–2670 (2008)

16. A.M. Maiden, J.M. Rodenburg, Ultramicroscopy **109**, 1256–1262 (2009)

17. A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, I. Schelokov, Rev. Sci. Instrum. **66**, 5486–5492 (1995)

18. P. Cloetens, R. Barrett, J. Baruchel, J.P. Guigay, M. Schlenker, J. Phys. D: Appl. Phys. **29**, 133–146 (1996)

19. P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J.P. Guigay, M. Schlenker, Appl. Phys. Lett. **75**, 2912–2914 (1999)

20. D.M. Paganin, *Coherent X-Ray Optics* (Oxford University of Press, Oxford, 2006)

21. J. Baruchel, J.Y. Buffière, E. Maire, P. Merle, G. Peix (eds.), *X-Ray Tomography in Material Science* (Hermes, Paris, 2000)

22. P. Dhez, P. Chevallier, T.B. Lucatorto, C. Tarrio, Rev. Sci. Instrum. **70**, 1907–1920 (1999)

23. F. Adams, K. Janssens, A. Snigirev, J. Anal. At. Spectrom. **13**, 319–331 (1998)

24. B. Golosio, A. Simionovici, A. Somogyi, M. Lemelle, M. Chukalina, A. Brunetti, J. Appl. Phys. **94**, 145–156 (2003)

25. M. Álvarez-Murga, P. Bleuet, G. Garbarino, A. Salamat, M. Mezouar, J.L. Hodeau, Phys. Rev. Lett. **109**, 025502 (2012)

26. K.A. Nugent, J. Opt. Soc. Am. A **24**, 536–547 (2007)

27. M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, P. Thibault, Sci. Rep. **3**, 1927 (2013)

28. A. King, G. Johnson, D. Engelberg, W. Ludwig, J. Marrow, Science **321**, 382–385 (2008)

29. J. Baruchel, J. Härtwig, *Encyclopaedia of Condensed Matter Physics*. X-Ray Topography (Elsevier, Amsterdam, 2005), pp. 342–348

30. A. Authier, *Dynamical Theory of X-Ray Diffraction* (Oxford University of Press, Oxford, 2001)

31. B.C. Larson, W. Wang, G.E. Ice, J.D. Budai, J.Z. Tischler, Nature **415**, 887–890 (2002)

32. H.F. Poulsen, *Three Dimensional X-Ray Diffraction Microscopy* (Springer, Berlin, 2004)

33. W. Ludwig, P. Reischig, A. King, M. Herbig, E.M. Lauridsen, G. Johnson, T.J. Marrow, J.Y. Buffière, Rev. Sci. Instrum. **80**, 033905 (2009)

34. D. Lübbert, T. Baumbach, J. Härtwig, E. Boller, E. Pernot, Nucl. Inst. Meth. Phys. Res. B **160**, 521–527 (2000)

35. W. Ludwig, P. Cloetens, J. Härtwig, J. Baruchel, B. Hamelin, P. Bastie, J. Appl. Cryst. **34**, 602–607 (2001)

36. R.T. Kluender, A. Philip, J. Meyssonier, J. Baruchel, Phys. Status Solidi A. **208**, 2505–2510 (2011)
37. S. Stock, *Micro Computed Tomography: Methodology and Applications* (CRC Press, Boca Raton 2009)

38. Y. Wang, X. Liu, K.S. Im, W.K. Lee, J. Wang, K. Fezzaa, D.L.S. Hung, J.R. Winkelman, Nat. Phys. **4**, 305–309 (2008)

39. H. Nguyen-Thi, L. Salvo, R.H. Mathiesen, L. Arnberg, B. Billia, M. Suery, G. Reinhart, C.R. Phys. **13**, 237–245 (2012)

40. N. Limodin, L. Salvo, E. Boller, M. Suery, M. Felberbaum, S. Gailliegue, K. Madi, Acta Mater. **57**, 2300–2310 (2009)

41. E. Gouillart, M.J. Toplis, J. Grynberg, M.H. Chopinet, E. Sondergard, L. Salvo, M. Suery, M. Di Michiel, G. Varoquaux, J. Am. Ceram. Soc. **95**, 1504–1507 (2012)

42. R. Mokso, F. Marone, S. Irvine, M. Nyvlt, D. Schwyn, K. Mader, G.K. Taylor, H.G. Krapp, M. Skeren, M. Stampapanoni, J. Appl. Phys. (2013) (In press)

43. F. Plouraboué, P. Cloetens, C. Fonta, A. Steyer, F. Lauwers, J.M. Vergnes, J. Microsc. **215**, 139–148 (2004)

44. F. Esteve, H. Elleaume, B. Bertrand, A.M. Charvet, S. Fiedler, G. Le Duc, S. Corde, C. Nemoz, M. Renier, J.L. Lefaix, J.J. Leplat, P. Suortti, W. Thomlinson, J.F. Le Bas, Acad. Radiol. **9**, S92–S97 (2002)

45. C.S. Willson, N. Lu, W.J. Likos, Geotech. Test. J. **35**, 911–923 (2012)

46. Z. Qiang, H. Toda, Acta Phys. Sin. **60**, 911–923 (2011)

47. P. Cloetens, M. Pateyron-Salomé, J.Y. Buffière, G. Peix, J. Baruchel, F. Peyrin, M. Schlenker, J. Appl. Phys. **81**, 5878–5886 (1997)

48. A. Pacureanu, M. Langer, E. Boller, P. Tafforeau, F. Peyrin, Med. Phys. **39**, 2229–2238 (2012)

49. P. Cloetens, R. Mache, M. Schlenker, S. Lerbs-Mache, PNAS **103**, 14626 (2006)

50. D. Tolnai, G. Requena, P. Cloetens, J. Lendvai, H.P. Degischer, Mat. Sc. Eng. **A550**, 214–221 (2012)

51. M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C.M. Kewish, R. Wepf, O. Bunk, F. Pfeiffer, Nature **467**, 436–440 (2010)

52. S.A. Kim, T. Punshon, A. Lanzirotti, L. Li, J.M. Alonso, J.R. Ecker, J. Kaplan, M.L. Guerinot, Science **314**, 1295–1298 (2006)

53. A. Pyzalla, B. Camin, T. Buslaps, M. Di Michiel, H. Kaminski, A. Kottar, A. Pernack, W. Reimers, Science **308**, 92–95 (2005)

54. C. Scheuerlein, M. Di Michiel, M. Scheel, J. Jiang, F. Kametani, A. Malagoli, E.E. Hellstrom, D.C. Larbalestier, Supercond. Sci. Tech. **24**, 115004 (10 p) (2011)

55. Y.C. Hung, J.A. Bennett, F.A. Garcia-Pastor, M. Di Michiel, J.Y. Buffière, T.J.A. Doel, P. Bowen, P.J. Withers, Acta Mater. **57**, 590–599 (2009)

56. W. Ludwig, A. King, M. Herbig, P. Reischig, J. Marrow, L. Babout, E.M. Lauridsen, H. Proudhon, J.Y. Buffière, JOM **62**, 22–28 (2010)

57. A. Lyckegaard, H.F. Poulsen, W. Ludwig, R.W. Fonda, E.M. Lauridsen, in *Proceedings of Recrystallization and Grain Growth IV*, ed. by E. Palmiere, B. Wynne (2012)

58. M. Herbig, A. King, P. Reischig, H. Proudhon, E.M. Lauridsen, J. Marrow, J.Y. Buffière, W. Ludwig, Acta Mater. **59**, 590–601 (2011)

59. S.R. du Roscoat, A. King, P. Reischig, W. Ludwig, F. Flin, J. Meyssonnier, Adv. Eng. Mater. **13**, 128–135 (2011)

60. A. Philip, J. Meyssonnier, R.T. Kluender, J. Baruchel, J. Appl. Cryst. **46**, 842–848 (2013)