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X-Ray imaging: past and present

Ulrich Bonse Technical University Dortmund, Faculty of Physics, 44221 Dortmund, Germany

ABSTRACT

Because x-rays can penetrate almost any object and yield information of the interior of specimens opaque to visible light, they have been used as a powerful tool for the investigation of all kinds of materials and bodies right from their discovery by Conrad Roentgen1 in 1895. Among the multitude of different ways such studies can be performed the imaging methods play a predominant and most important role. The intent is to describe some interesting and relevant ways x-ray imaging has been employed up to now. Clinical tomography will be excluded here. Recent surveys exist in the literature, e.g.2. Keywords: x-ray imaging, x-ray topography, x-ray tomography, x-ray interferometry, x-ray scattering, crystal defects, attenuation contrast, phase contrast

1. INTRODUCTION Very soon after the discovery of x-rays1 their capability to penetrate objects opaque to visible light was seen as one of their most exciting properties. It became immediately clear that with x-rays the interior structure of an opaque object could be studied without the need to dissect it. Another exciting news was, that - according to the diffraction of x-rays by rock salt crystals3,4, a narrow slit of 5.5µm width5, and by a wire of 38µm diameter6 - the x-ray wavelength was found to be comparable to the size of single atoms, i.e. to be of the order of 10-10 m. From measurements of the angular dependence of the X-ray scattering7,8 by monatomic gases like He, Ne, Ar, and Hg the size of these atoms could be determined. Furthermore, studies of the scattering of gasses with diatomic molecules9,10 like H2, O2, N2 and with polyatomic10,11 molecules like CCl4 and CH2Cl2 yielded interesting information of their molecular structure. The important aspect is, that because x-rays have a wavelength comparable to the size of atoms and molecules, modulus and phase of scattering become angular dependent. These facts are fundamental to molecular structure determination in general, also for huge (inorganic) molecules. Here we present examples of X-ray imaging applied to solid state studies.

2. X-RAY STUDIES OF CRYSTAL DEFECTS In the wake of the invention of the transistor and the following development of semiconductor based electrical devices of all kinds the increasing need for perfect crystals of primarily Germanium and then Silicon promoted numerous studies devoted to understand the nature of crystal defects (Fig. 1) like impurity atoms, vacancies, interstitials, dislocations and

Edge dislocation, slipping with applied stress Low-angle grain boundary 29a

after Burgers

Screw dislocation

Fig.1.Left and middle (© Springer Verlag 197626 ): Edge dislocation, Screw dislocation, Burgers24, 25 vector b, and function of the Burgers vector, when slip occurs in the crystal. See the generation of 'spirals' along a screw dislocation under conditions of crystal growth. Right 29a : The structure of a low-angle grain boundary consisting of an array of parallel and equally spaced edge dislocations is indicated.

Circle: lattice strain which decays with 1/r (r : distanction) b is Burgers Vector; b denotes the shift along thepart of the crystal has undergone yielding to an applieof an ed

e from disloca- slip-plane which d stress. In the case

↓ b

dislocation b is normal ge (a screw) (parallel) to the direction of the dislocation, respectively.

Invited Paper

Developments in X-Ray Tomography VI, edited by Stuart R. Stock, Proc. of SPIE Vol. 7078, 707802, (2008) · 0277-786X/08/$18 · doi: 10.1117/12.794694

Proc. of SPIE Vol. 7078 707802-1

Downloaded From: http://proceedings.spiedigitallibrary.org/ on 04/29/2013 Terms of Use: http://spiedl.org/terms

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stacking faults. Starting about 1950, a number of X-ray imaging techniques12-21 called 'X-ray topography' were developed to detect and characterize defects in crystals. The X-ray techniques confirmed nicely the results of seeing single dislocations in Si crystals made visible on infra-red pictures by the Cu-decoration method developed by W.C. Dash22. The chief methods of X-ray topography are illustrated in Fig 2 below.

With the Schulz technique15 (Fig.2a) white X rays divergent from a point source are diffracted by the crystal and recorded on film. The use of white radiation ensures that there is no significant change of diffracted intensity due to different incident angles within the bundle. With dimensions shown (typical) rotations of 20 arcsec can be detected. In case of the Borrmann arrangement19 (Fig.2b) the contrast caused by imperfections, e.g. single dislocations, arises because lattice deformations reduce or even completely eliminate the anomalous high transmission (i.e. the Borrmann effect). Hence dislocations are seen as lines ('shadows') which reduce the transmitted intensity. The Lang scanning method18 (Fig.2c) uses a sufficiently collimated beam so that only one characteristic wavelength is diffracted by the crystal. A stationary opaque screen allows only the diffracted beam to reach the photographic plate. A large area/volume of crystal can be surveyed by scanning both the crystal and photographic plate in synchronism. Many different types of lattice defects have been observed by this technique.

Fig.2. Techniques for imaging defect structures in single crystals. (a) typical arrangement for the Schulz technique15, (b) the Borrmann arrangement for anomalous transmission topograpy19, (c) the Lang scanning technique18, 20, (d) the double-crystal geometry14, 16-17, 21, 23 , (e) the Berg-Barret arrangement12, 13.

The double-crystal method (or short: DC-method) (Fig.2d) uses X-rays from a line focus which are reflected from a perfect reference crystal and then from the specimen, and finally recorded on a film. Since reference crystal and specimen consist of the same kind of material and use the same spacing of reflecting planes, the shape of the rocking curve is independent of the spectral distribution �� of the radiation used (dispersion is eliminated). As a result the rocking curve becomes 10-100 times narrower than any spectral line. This makes the method very suitable for measuring very small lattice tilts (and likewise small relative changes �d/d of the lattice parameter d). When the specimen is slightly mis-set from the parallel position, i.e. on the flank of the rocking curve, tilts of ≤ 0.1 arcsec and corresponding strains of �d/d ≤ 10-8 to 10-9 result in detectable changes of reflected intensity. Deformations of this magnitude occur, e.g., at distances up to 50µ or 100µ from the core of single dislocations (see Figs.4 and 5 below), as growth bands of some Silicon crystals107 , or, in the case of natural Quartz crystals105, with growth striations and with lattice parameter increases induced by X-ray irradiation. The oldest method is the Berg-Barrett technique12,13 (Fig.2e). The crystal is set to Bragg-reflect the characteristic radiation from a line focus. By placing the film close to the crystal, geometric resolutions of � 1µm are realized. Across the diffracted beam variations of the integral reflection power due to imperfections in the crystal occur. The successful development and application of X-ray topography methods was essential in understanding the role of dislocations for the mechanical and electrical properties of crystallized solids.

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Mechanism of Frank-Read27 dislocation source:

LEFT (a): A-B is a dislocation in glide plane, X-V and U-Y are two dislocations connected with dislocation A-B at A, B , respectively. LEFT (b): Reaction of the source to external stress: A-B glides out,

disconnects from points A, B forming an independent dislocation loop. Repeating this mechanism, a sequence of new dislocation loops is

generated29b.

Dislocation pattern in a low-quality Si crystal 29b

X-Ray image of copper decorated Fran lane 97 k-Read Source on Si 111- p

Fig.3. Left, lower part: X-Ray image28 of dislocations in Si obtained with Lang scanning technique18. Left top 29b : Operation mechanism of Frank-Read27 source. Right 97: Image of Frank-Read source. Such a source generates - under applied stress - billions of new dislocations to facilitate macroscopic glide shifts.

Fig. 4. DC-topographs of a low-quality LiF (left 28) and a high-quality Ge crystal (right 30 ). A, B & C denote dislocation lines which run at constant depths t beneath the surface. For t=25µm a rough estimate yields a relative surface strain of 10-6 at 50µm distance

In Fig.3 at lower right we see a Lang18 image of a Frank-Read source27 found in a Si crystal. Under stress induced deformation new dislocations have to be generated inside the crystal to facilitate macroscopic glide movements. The Frank-Read source is one possible mechanism to allow gliding. In the lower left of Fig.3 a Lang transmission topograph of dislocations in a low-quality Si crystal is shown. Fig.4 displays DC-topographs of a LiF (a, b) and of a Ge crystal with

Ge � 2x103 disl./cm2

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dislocation densities of 7x105/cm2 and 2x103/cm2, respectively. In the case of LiF we see a rather complex structure of intersecting dislocation lines. On the other hand, the topographs of the Ge crystal show only three distinct lines running at slightly different depths below the (111) surface in [0 -1 1] direction and a few other lines which intersect the surface and are seen end-on.

Fig. 5. Application of DC-topography to the explicit measurement of lattice deformation caused by a near-surface edge dislo-cation in a Ge-crystal30 and comparison with deformation calculated using isotropic elasticity theory28,31. ε is the angle between goniometer axis ng and line direction nt. Lattice tilts contribute to the measured Combined Strain only for ε = 0° or 180°.

Using a series of DC-topographs, dislocation type and Burgers vector can be determined for dislocation lines running under the surface at constant depth. Details are given in Fig. 5.

X-ray topography has been used to study implantation of high energy ions, e.g. N+ of about 2 MeV energy, into Si crystals. As explained in Fig.6, the implantation results in forming a kind of bicrystal composed of a thick perfect bulk crystal topped by a thin practically perfect layer crystal. Both crystals have the same crystallographic orientation and the same lattice constant but the layer crystal underwent a small rigid body displacement due to the heavy lattice damage the ions cause at their stopping range which is between layer and bulk crystal. Contrast and geometry of the observed interference patterns agree with the theoretical pattern a layer/bulk bicrystal model32, 32a

Fig.6. 2 MeV ions transfer energy and cause lattic et at the end of their range resulting in the formation of a bicrystal system32 consisting of the slightly lifted layer crystal above the sheet and the bulk crystal below. The bicrystal system's geometry can be found out from the X-ray fringe pattern seen in Laue transmission mode shown at left.

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3. MICRO-TOMOGRAPHY USING SYNCHROTRON RADIATION (SR)99

3.1. Setup at HASYLAB for synchrotron Att.-µCT and Phase-µCT with EX-ray = 6…200 keV

Fig. 7. (a) the typical setup for Attenuation Micro tomography (Att-µCT). (b) the setup for implementing Phase contrast Micro tomography (Phase-µCT) by using an X-ray interferometer33,34,35,36,37. (c) the typical detector for SR.

The cause of attenuation can be absorption, inelastic or incoherent scattering, etc.. Included is any mechanism by which the Intensity of the detected signal is decreased. Other ways of detecting phase contrast than using a crystalline X-ray interferometer will be considered in connection with their application. Note that for higher energies lens and CCD-camera have to be protected against hard X-rays by a beam stop. There are five reviews regarding the use of SR for µCT in the literature, two describing part of the older work38,39 and three more recent40,41,42.

3.2. Comparison of SR-Att.-µCT and histological cut43,44,45 :

Fig. 8. Complete correspondence has been found between tomogram and histological cuts. Note that - different from histological slicing - tomography is nondestructive which allows to re-examine obtained results if wanted.

c

Eoptical mirrors if X-ray >30 keV

3D reconstruction of human iliac bone obtained through biopsy

histological slice ccut of tomogram



3.3. Imaging of normal and osteoporotic bone by SR-Att.-µCT44-46

Fig. 9. Att.-µCT on bone biopsies taken of human iliac crest43. Left: normal bone. Right: Osteoporotic bone.

3.4. Study of middle ear ossicles by SR-Att.-µCT47,48

Ossicles of the human middle ear (Fig. 10) were imaged using SR-Att.-µCT41,45. There were three main objectives for obtaining these data: 3D or pseudo-3D imaging for general visualization purposes (clinics, pathology, education ...), 3D geometry data derivation for basic anatomy and related sciences, and 3D imaging and data conversion for geometric modeling, e.g. for finite element analysis (mesh generator). The access to volume geometry data acts as a necessary condition for the acousto-mechanic modeling of the function of hearing.

Fig. 1047,48. (a) Cut through cochlea. (b) View onto modiolus. (c) Cut through cochlea with segmented lamina spiralis ossea. (d) Stapes. (e) Morphometric parameters of stapes footplate (in mm). (f) Geometry model of stapes footplate with 5082 elements.

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3.5. Aluminum reinforced by Al2O3 - fibers (Al-Composite) investigated49 with SR-Att.-µCT

Fig. 11b49: Tomograms of the stack of slices ("cuts C288 to C293" as indicated in the center of Fig. 11a) show the alloy phases to form a network of mesh size �15µm which - in addition - seems to form clusters about 150µm apart

4. GENERAL COMPARISON OF PHASE VERSUS ATTENUATION CONTRAST50

4.1 "1% -thickness": t1% is defined by the material thickness dξ which weakens the intensity signal by 1% (Att.-µCT) or which changes the phase by 1 % (Phase-µCT). In the case of Att.-µCT we assume optimum51 sample thickness topt, i.e. τ• topt = 2 (τ is the attenuation coefficient) and find50 t1% Att = 0.0739/τ (1) In the case of Phase-µCT we approximate the phase-dependence on material thickness-change by the linear "triangle curve" shown below and find50: t1% Ph = t�/200 (2)

with t� = 2�/(re � Z N) the λ-thickness, i.e the thickness of the material needed to shift the phase by 2π. re is electron radius, � wavelength, Z atomic number, and N number of atoms per volume. 4.2 "Advantage factor": At . In a micro-tomographic measurement, a given material or element is the more easily detected, the thinner a just detectable layer of the material can be. Hence the detectability scales with 1/t1%. On this basis

Fig 11a49. Above: location of tomographic slices in the cylindrical specimen of an Aluminum cylinder reinforced with Al2O3 fibers 2 to 4µm in diameter and 50 to 80µm in length.

Right: Tomgram of slice S47. Brighter areas represent increased absorption due the presence of higher Z-elements

contained in alloy phases embedded in the Al matrix



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we define an advantage factor of applying phase contrast over attenuation contrast to detect a given element in a composite material by the quotient Advantage Factor 50: At ≡ t1% Att/ t1% Ph = 14.78/(τ·tλ) of phase-contrast over attenuation contrast. This holds when we use I(Φ) = 1+cos(Φ) � 2•(1-Φ/�) and dI(�)/d� = -2/� "triangle" curve (Fig 12a). The superiority of phase-contrast over attenuation-contrast for imaging soft tissue is illustrated in Fig. 12b:

Fig. 13. Left 50: Calculated 1% thickness curves for attenuation contrast (above) and phase contrast (bottom). Advantage factor At of phase contrast over attenuation contrast (middle) is ~500 at 10keV, ~ 1000 at 200 keV, with a maximal value of ~2400 at 30keV. All curves apply to water. An overview of recent advances in X-ray phase imaging can be found in the literature85. Fig 13. Right50: Calculated Advantage factors of Au and Ca compared to the value of water. Note the influence of L- and K-absorption edges in the case of Au.- From the calculated values the general advantage to use phase contrast is obvious, and this is true even for elements with high atomic number Z, although with large Z the advantage is 1 to 2 orders of magnitude smaller. On the other hand, to employ phase contrast is generally more complicated than working with attenuation contrast.

5. EXAMPLES OF PHASE-CONTRAST IMAGING USING CRYSTAL-MONOCHROMATIZED SR In Fig. 14 (page 9) five topographs are shown of a periodically domain-inverted LiNbO3 specimen52. For reflection the 006 planes with 2 θBragg = 25° were used. The film-to-sample distance R is varied from 5mm (topograph 1) to 0.5m (topograph 4). Topograph (5) is an enlargement of a region in topograph (3), rotated by 90°. The broader lines on the topographs correspond to domain walls. Thinner lines in-between are due to the interference of wave field pairs T2 ,T’2

exited by adjacent domain pairs of opposite sign53. The two sets of domains of opposite electric polarization are slightly tilted with respect to each other. For a given distance R of observation (= sample-to-film-distance), each set contributes with a slightly different excitation point (T2, T'2 ). The difference between excited wave field pairs shrinks with increasing distance to the observation point i.e. the film distance. Therefore, the number of interference fringes seen per domain decreases with increasing film distance, i.e from five fringes between domain walls on topograph 5 (0.2m film

Fig 12a Att.-µCT

Fig 12b98 Comparison of Att.-µCT and Phase-µCT

of mouse kidney E = 12 keV γ

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distance) to two fringes on topograph 4 (0.5m film distance). Hence the observation of those fringes is a phase-contrast effect. On the right in Fig. 14 the observed fringe profile (top) is compared with a numerical simulation54 of fringes (bottom) based on Takagi-Taupin55, 55a equations.

Fig 15 shows hologram profiles of a 20µm polypropylene fiber measured56 at varied distances R1 from the fiber. Using a Gabor in-line holography approach, i.e. assuming that the detector records the interference between nearly spherical waves scattered by the sample with plane reference waves coming directly from the illuminating source57,58, the hologram profiles shown on left of each measured profile were obtained. The agreement is quite good. - As an application the phase-contrast

12.4 keV

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||Diffraction plane is to domain walls.

simulation

3 R =0.2 m 1 R =5 mm

Simulation agrees quite well with measurement54

5 R =0.2m 2 R =0.1 m

LiNbO3 Perowskit-Structure

Trigonal space group R3c Fig. 1452,54 Topographs of a periodically domain-inverted LiNbO3 specimen

using the 006 reflection; 2 θBragg = 25. 4 R =0. 5 m

R1 = 0.25 m

R1 = 0.5 m

R1 = 1 m

R1 = 2 m

R1 R0= 40

Above: Experimental X-ray holographic phase-contrast

image56 of the green photographic paper used for

alignment purposes

Fig 14 reprinted by permission from Macmillan Publ. Ltd.: [52] © (1998) and IOP Publ. Ltd.: [54] © (1999).

Fig. 15 reprinted with permission from American Institute of Physics: [56] ©

(1995)



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image of some paper used for alignment purposes with SR sources is shown. Holographic diffraction by the various fibers contained in the paper is clearly visible. The holographic phase-contrast method has also been applied successfully to image surface morphology, individual grains and cracks of polycrystalline diamond59.

6. PHASE-CONTRAST µ-CT USING CRYSTAL X-RAY INTERFEROMETERS WITH SR

6.1. Phase-µCT of rat trigeminal nerve60 and of rat cerebrum50

Fig. 17. Phase-µCT of rat cerebrum50. (1) black: epoxy embedding; light grey: cerebrum; surface of cerebrum; gray and white matter can be distinguished. In (2) the cut made for visualizing the data is 250µm further back. 7.5 µm voxel size, E= 12 keV.

Fig 16: Trigeminal nerve60 At right: Slice of tomogram 40µm below the histological cut shown at left. Dark: brain; gray: nerve tissue. Nerve/brain interface is clearly outlined. Bundles with individual nerve fibers can be distinguished. Arrow: area with higher density of cell nuclei seen on either image. �, �, � mark locations of fiber positions, intervals between fibers, and more dense regions near the nerve edge, respectively. E=12keV. Voxel size and slice thickness is 5.4µm

6.2. Two crystal X-ray interferometer for phase-contrast tomography61-66, 82-84

Fig. 18 Top: First two-crystal, skew symmetric X-ray interferometer64; note auxiliary cross X-ray beam for alignment about the longitudinal axis. Insert at right: Interferograms taken during alignment of interferometer components about longitudinal axis. Bottom: (Optical Society of America66 © (2003)). (a) First large two-crystal skew-symmetric X-ray-interferometer66. (b) Empty-beam interferogram of large interferometer66.

In order to be able to investigate specimens larger than a few61 cm with interferometric phase-µCT it became necessary to build X-ray interferometers which are no longer monolithic but consist of at least 2 separate crystal components. Typical stability requirements for the components with respect to each other are: relative shifts << 10-10m and relative rotations << 10-6 rad. In 1968 the first symmetric two-crystal interferometer62 was operated. Its defocusing properties

21

Horizontal plane

64Skew-symmetric two-crystal X-ray interferometer

Insert64

Cross X-ray beam for stability control

Vertical plane

65,66 Large two-crystal interferometer

Proc. of SPIE Vol. 7078 707802-10


Cancer tissues Normal tissues

—I 1mm

e WI D

were studied63 in detail by 1971. The skew-symmetric type64 followed in 1974. While these interferometers were still small, large skew-symmetric two-crystal interferometers were realized65,66 by 2002 and applied in studies of rat liver tissue65,82, stdies of the development of implanted tumors83, and studies of pathological amyloid plaques in cerebral cortex and hippocampus tissues of mice84.

1 500µ

2

Fig 19. (1) (©IUCR65 http://journals.iucr.org/).Liver of rabbit with VX2 cancer viewed with large two-crystal interferometer. Gray level for cancer tissues are lower than those for normal tissue; large two-crystal X-ray interferometer used. (2) (Optical Society of America66 © (2003)) Tissue of rat kidney66 measured67 by phase-µCT using the LLL X-ray interferometer with analyzer thinned to 40 µm68,69

7. DIFFRACTION ENHANCED IMAGING (DEI)70-74

7.1. Coherence enforced by reduced divergence70-73, 90

7.2. Coherence enforced by point source 72,74,87

DEI implemented at a monochromatic synchrotron source was used92 to compare radiological CT images of tumor-bearing breast tissue samples with histological examinations. DEI-CT images map accurately collagen strands and micro-calcifications down to less than 0.1 mm.

As indicated in Fig. 2071 a parallel beam is generated between beam expander and the first face of the dual-face analyser. Without sample a homogonous beam is registered on

the film (Fig. 21a). Phase shifts by the sample cause deformations of the wave front which are transposed into intensity changes by the dual-face analyser and are registered on the film as seen in Fig. 21b71. Figs. 20,

21a and 21b are adapted by permission from Macmillan Publ. Ltd. (1995)71 Fig. 20 Fig. 21a Fig. 21b

In Fig.2274 s is a micro-focus X-ray source (20µm diameter)

giving a small lateral coherence length d⊥ (e.g. d⊥�1.5µm at

R1+R2~0.5m.) Fig.2374 is the image of the fantail of an aquarium fish, R1=1,1m,

R2=1mm, 100 min exposure, tube voltage 60kV. Figs. 22 and 23 adapted by permission from Macmillan Publ. Ltd. (1996)74

Fig.22 Fig.23

Proc. of SPIE Vol. 7078 707802-11


20

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8. PROPAGATION MODE X-RAY IMAGING75-81

8.1 Holotomography using hard synchrotron X-rays75-78, 89, 96,104

Fig. 25

Fig. 28

Fig. 27

Fig. 26

Fig. 29. Voids in Arabidopsis seeds

Fig. 24

©NAS 200678 Fig. 24. Exploiting the Talbot effect77 (when using a coherent SR-beam) the phase can be retrieved numerically in 3 dimensions from images recorded at different distances D and with varied angular specimen positions75,76. Fig. 25. One of 4 phase sensitive Fresnel diffraction patterns of polystyrene foam recorded at 4 different distances. Fig. 26. Phase map reconstructed from 4 Fresnel diffraction patterns. Fig. 27. Volume rendering showing the enclosed foam cell. Fig. 28. Tomographic slice through cell. The method is particularly suited to image objects with high spatial frequencies or outlining objects with sharp edges like grains or voids as shown in Fig. 29. Figs.24 to 28 © American Institute of Physics (1999) 76. Fig.29 © National Academy of Sciences of the USA (2006) 78. 8.2. X-ray phase-contrast imaging by combining a phase- with an absorption grating at coherent SR-source79, 88, 93

an incoming SR-plane wave, the phase grating of periodicity g would generate a pattern of interference e Talbot self-imaging distances Dn. Structures in the sample distort the front of the incoming plane wave nterference fringes to be displaced by an amount d. Scanning the

orption grating yields for each detector pixel dij at position (i,j) an intensity-sin/cos curve from which the linear integration) finally the phase Φ(i,j) is obtained. Fig. 31 shows the image of a small spider (size �

1.6mm) obtained with this method. Figs. 30 and 31 © SPIE (2006) 79.

Silicon grating period g=4µm Gold grating period g/2=2 µm Fig.30

SR-source

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Fig.31

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Proc. of SPIE Vol. 7078 707802-12


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8.3. Hard-X-ray phase-contrast imaging with grating interferometer at low-brilliance X-ray source80

Fig. 32. The use of a low-brilliance source is accomplished by introducing absorption grating G0 thereby transforming the setup of section 8.2 into a Talbot-Lau-type hard -X-ray imaging interferometer. G2 is a transmission gratings and G1 a phase grating. p0, p1, p2, are the grating periods. Fig.33. For p1 ~ 5µm a coherence length � s

� 10-6 m is needed. The source size w determines the final image resolution: wd/l. In order to each line source to contribute constructively to the image the geometry should satisfy p0 = p2 x l/d. Fig 34. Images of transmission, phase gradient, and phase for PTFE and PMMA spheres. Fig.35 conventional transmission, Fig.36 differential phase-contrast image. Fig.37 displays magnified details of parts shown in Figs. 35 and 36, respectively. The superior quality of differential phase contrast over conventional transmission contrast is obvious.

8.4. Hard-X-ray dark-field imaging with grating interferometer at low-brilliance X-ray source81

Fig. 38a to Fig. 38c. Setup and kind of source and gratings G0, G1, G2 are very similar to what was used in Section 8.3 above. The essential point is, that G1 can be set with respect to G2 so that the contribution of the sample to zeroth order

Adapted by permission from Macmillan Publ. Ltd.80 (2006)

Fig.34

Fig.32

Object transmission Phase gradient d�/dx [ mm-1] Object phase shift �(x)

Fig. 34

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Fig.33y coherent slit sources

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Adapted by permission from Macmillan Publ. Ltd.81 (2008)

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Chicken wing Chicken wing

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(i.e. "transmission without scattering") is eliminated. In that case only scattered radiation is measured (Fig.39b). Likewise, gratings G1 and G2 can be set to let only the unscattered radiation pass which would correspond to measure the conventional X-ray absorption radiograph. In Figs. 39a, 39b the conventional absorption image of a chicken wing is compared to the correspondig dark-field image. The gain of information is remarkable. Recently, this method was successfully applied to high-resolution hard X-ray phase-contrast CT of a mouse tail86 and of a rat brain94. Furthermore, reconstruction algorithms for phase images can also be used with differential-phase projections in order to obtain three-dimensional images with differential phase contrast95,100.

9. CONCLUSION Since their discovery in 1895 X-rays have been used in numerous fields of research and manufacture. Although only a few applications could be considered in an article of this kind, the amount of information encountered was already very impressive. The author hopes that the selection of topics which he had to make turns out to be a fair compromise between personal taste and objective relevance. Not treated, for example, was zone-plate based X-ray microscopy, although - just to give an example - quantitative X-ray phase tomography using such a microscope was established91 a few years ago. Interesting nano-scale details including substructures in yeast cells and in Escheria coli bacteria could be investigated three dimensionally101-103 .- Last not least I have to thank many colleagues and their publishers for letting me reproduce their excellent pictures.

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