The effect of the total reflection of the incident beam into the 222 reflected beam in the Renninger (222/113) case in Si was experimentally observed by using a highly monochromatic beam with high angular collimation in both the vertical and horizontal planes.
X-ray optical schemes capable of producing a highly monochromatic beam with high angular collimation in both the vertical and horizontal planes have been evaluated and utilized to study high-resolution diffraction phenomena in the Renninger (222/113) case of three-beam diffraction in silicon. The effect of the total reflection of the incident beam into the nearly forbidden reflected beam was observed for the first time with the maximum 222 reflectivity at the 70% level. We have demonstrated that the width of the 222 reflection can be varied many times by tuning the azimuthal angle by only a few µrad in the vicinity of the three-beam diffraction region. This effect, predicted theoretically more than 20 years ago, is explained by the enhancement of the 222 scattering amplitude due to the virtual two-stage 000 113 222 process which depends on the azimuthal angle.
dynamical diffraction; multiple diffraction; X-ray optics; plane wave; synchrotron radiation
A high-resolution study of (002, 113, 11−1) four-beam diffraction in Si was performed both experimentally and theoretically. Excellent coincidence between theory and experiment was achieved. The forbidden two-beam 002 reflection was excited with the maximum reflectivity of 80%.
The results of a high-resolution study of the (002, 113, ) four-beam diffraction in Si are presented. The incident synchrotron radiation beam was highly monochromated and collimated with a multi-crystal arrangement in a dispersive setup in both vertical and horizontal planes, in an attempt to experimentally approach plane-wave incident conditions. The Renninger scheme was used with the forbidden reflection reciprocal-lattice vector 002 normal to the crystal surface. The azimuthal and polar rotations were performed in the crystal surface plane and the vertical plane correspondingly. The polar angular curves for various azimuthal angles were measured and found to be very close to theoretical computer simulations, with only a small deviation from the plane monochromatic wave. The effect of the strong two-beam 002 diffraction was observed for the first time with the maximum reflectivity close to 80%. The structure factor of the 002 reflection in Si was experimentally determined as zero.
X-ray multiple diffraction; silicon; high resolution; forbidden reflections
The spatial structure of an X-ray beam focused by a planar refractive lens and Bragg diffracted from perfect silicon crystals has been studied experimentally and theoretically.
The spatial structure of a beam focused by a planar refractive lens and Bragg diffracted from perfect silicon crystals was experimentally studied at the focal plane using a knife-edge scan and a high-resolution CCD camera. The use of refractive lenses allowed for a detailed comparison with theory. It was shown that diffraction leads to broadening of the focused beam owing to the extinction effect and, for a sufficiently thin crystal, to the appearance of a second peak owing to reflection from the back surface. It was found that the spatial structure of the diffracted beam depends on whether the crystal diffracts strongly (dynamically) or weakly (kinematically). The results help to understand the physical origin of the diffracted intensity recorded in a typical microbeam diffraction experiment.
X-rays; focusing; refractive lenses; X-ray diffraction; extinction effect
Computer control of beam tilt and image capture allows the collection of electron diffraction patterns over a large angular range, without any overlap in diffraction data and from a region limited only by the size of the electron beam. This results in a significant improvement in data volumes and ease of interpretation.
The advantages of convergent-beam electron diffraction for symmetry determination at the scale of a few nm are well known. In practice, the approach is often limited due to the restriction on the angular range of the electron beam imposed by the small Bragg angle for high-energy electron diffraction, i.e. a large convergence angle of the incident beam results in overlapping information in the diffraction pattern. Techniques have been generally available since the 1980s which overcome this restriction for individual diffracted beams, by making a compromise between illuminated area and beam convergence. Here a simple technique is described which overcomes all of these problems using computer control, giving electron diffraction data over a large angular range for many diffracted beams from the volume given by a focused electron beam (typically a few nm or less). The increase in the amount of information significantly improves the ease of interpretation and widens the applicability of the technique, particularly for thin materials or those with larger lattice parameters.
electron diffraction; symmetry determination; CBED; LACBED; computer control
Recently developed microscopy techniques, such as 4Pi, break the Abbe diffraction limit and allow for imaging at unprecedented resolution. The effective focal volume is also reduced, leading to more sensitive measurements in fluorescence microphotolysis or correlation spectroscopy. In 4Pi microscopy, the improvement is due to the utilization of two interfering laser beams for illumination, rather than a single one as in conventional microscopy. We study theoretically the possibility of further reduction of the focal volume with employment of three or more interfering beams, including the limiting case of an inifinite number of beams. The volume is indeed reduced, but reaches a limit quickly as beams are added. The volume obtained in the setups with three or four beams is about half of that in the 4Pi case and is close to the volume computed for the limit of an infinite number of beams. The setups suggested employ purely optical principles, and, thus, the considered limiting case arguably represents the maximal reduction in focal volume possible for a purely optical far-field setup.
To test the efficacy of phase-sensitive x-ray imaging for intact synovial joints, whereby refraction effects, along with the attenuation of conventional radiography, can be exploited.
Intact cadaveric human knee joints were imaged, in the computed tomographic mode, using an analyzer based x-ray system at the National Synchrotron Light Source, Brookhaven National Laboratory. A collimated fan beam of 51 keV X-rays was prepared by a silicon [1,1,1 reflection] double-crystal monochromator. The x-ray beam transmitted through the specimen was imaged after diffraction in the vertical plane by means of the analyzer crystal with the analyzer crystal tuned to its half-reflectivity point (6.5 microradians). A two-dimensional filtered backprojection (FBP) algorithm was used for reconstructing transverse slices of images.
The resulting images demonstrate simultaneous soft-tissue and bone contrast at a level that has not been achieved previously. Identifiable structures include articular cartilage, cruciate ligaments, loose connective tissue, menisci, and chondrocalcinosis.
Phase-sensitive x-ray imaging using an analyzer-based system renders exceptionally high quality images of soft and hard tissues within synovial joints, with high contrast and resolution, and thus holds promise for the eventual clinical utility.
A three-dimensional Bragg diffraction imaging technique, which combines rocking curve imaging with ‘pinhole’ and ‘section’ diffraction topography in the transmission case, allows three-dimensional lattice distortion in the bulk of an ice crystal under compression to be measured.
Rocking curve imaging (RCI) is a quantitative version of monochromatic beam diffraction topography that involves using a two-dimensional detector, each pixel of which records its own ‘local’ rocking curve. From these local rocking curves one can reconstruct maps of particularly relevant quantities (e.g. integrated intensity, angular position of the centre of gravity, FWHM). Up to now RCI images have been exploited in the reflection case, giving a quantitative picture of the features present in a several-micrometre-thick subsurface layer. Recently, a three-dimensional Bragg diffraction imaging technique, which combines RCI with ‘pinhole’ and ‘section’ diffraction topography in the transmission case, was implemented. It allows three-dimensional images of defects to be obtained and measurement of three-dimensional distortions within a 50 × 50 × 50 µm elementary volume inside the crystal with angular misorientations down to 10−5–10−6 rad. In the present paper, this three-dimensional-RCI (3D-RCI) technique is used to study one of the grains of a three-grained ice polycrystal. The inception of the deformation process is followed by reconstructing virtual slices in the crystal bulk. 3D-RCI capabilities allow the effective distortion in the bulk of the crystal to be investigated, and the predictions of diffraction theories to be checked, well beyond what has been possible up to now.
rocking curve imaging (RCI); 3D-RCI; ice crystals; crystal distortion; crystal defects
Three-wave diffraction has been experimentally studied for a set of III–nitride and ZnO epitaxial films differing in thickness and structural perfection. Properties of the multiple diffraction pattern in highly distorted layers are analyzed.
Three-wave diffraction has been measured for a set of GaN, AlN, AlGaN and ZnO epitaxial layers grown on c-sapphire. A Renninger scan for the primary forbidden 0001 reflection was used. For each of the three-wave combinations, θ-scan curves were measured. The intensity and angular width of both ϕ- and θ-scan three-wave peaks were analyzed. The experimental data were used to determine properties of the multiple diffraction pattern in highly distorted layers. It is shown that the FWHM of θ scans is highly sensitive to the structural perfection and strongly depends on the type of three-wave combination. The narrowest peaks are observed for multiple combinations with the largest l index of the secondary hkl reflection. An influence of the type of the dislocation structure on the θ-scan broadening was revealed. These experimental facts are interpreted by considering the scanning geometry in the reciprocal space and taking into account the disc-shaped reciprocal-lattice points. The total integrated intensities of all the three-wave combinations were determined and their ratios were found to be in only a qualitative agreement with the theory. For AlGaN layers, the presence of the nonzero 0001 reflection was revealed, in contrast to AlN and GaN films.
X-ray diffraction; multiple diffraction; epitaxial layers; structural defects; wurtzite structure
The crystalline structure of single free-standing GaAs nanowires, grown by molecular beam epitaxy on a GaAs substrate at specific positions defined by focused ion beams, and the substrate regions close to the Au-implanted regions are investigated through grazing-incidence X-ray diffraction.
Grazing-incidence X-ray diffraction measurements on single GaAs nanowires (NWs) grown on a (111)-oriented GaAs substrate by molecular beam epitaxy are reported. The positions of the NWs are intentionally determined by a direct implantation of Au with focused ion beams. This controlled arrangement in combination with a nanofocused X-ray beam allows the in-plane lattice parameter of single NWs to be probed, which is not possible for randomly grown NWs. Reciprocal space maps were collected at different heights along the NW to investigate the crystal structure. Simultaneously, substrate areas with different distances from the Au-implantation spots below the NWs were probed. Around the NWs, the data revealed a 0.4% decrease in the lattice spacing in the substrate compared with the expected unstrained value. This suggests the presence of a compressed region due to Au implantation.
semiconductor nanowires; growth; grazing-incidence X-ray diffraction; GaAs
X-ray computed tomography (XCT) has become a very important method for non-destructive 3D-characterization and evaluation of materials. Due to measurement speed and quality, XCT systems with cone beam geometry and matrix detectors have gained general acceptance. Continuous improvements in the quality and performance of X-ray tubes and XCT devices have led to cone beam CT systems that can now achieve spatial resolutions down to 1 μm and even below. However, the polychromatic nature of the source, limited photon flux and cone beam artefacts mean that there are limits to the quality of the CT-data achievable; these limits are particularly pronounced with materials of higher density like metals. Synchrotron radiation offers significant advantages by its monochromatic and parallel beam of high brilliance. These advantages usually cause fewer artefacts, improved contrast and resolution.
Tomography data of a steel sample and of two multi-phase Al-samples (AlSi12Ni1, AlMg5Si7) are recorded by advanced cone beam XCT-systems with a μ-focus (μXCT) and a sub-μm (nano-focus, sub-μXCT) X-ray source with voxel dimensions between 0.4 and 3.5 μm and are compared with synchrotron computed tomography (sXCT) with 0.3 μm/voxel. CT data features like beam hardening and ring artefacts, detection of details, sharpness, contrast, signal-to-noise ratio and the grey value histogram are systematically compared. In all cases μXCT displayed the lowest performance. Sub-μXCT gives excellent results in the detection of details, spatial and contrast resolution, which are comparable to synchrotron-XCT recordings. The signal-to-noise ratio is usually significantly lower for sub-μXCT compared with the two other methods. With regard to measurement costs “for industrial users”, scanning volume, accessibility and user-friendliness sub-μXCT has significant advantages in comparison to synchrotron-XCT.
X-ray computed tomography; Synchrotron tomography; High resolution tomography; 3D-characterization
Crystallization of human membrane proteins in lipidic cubic phase often results in very small but highly ordered crystals. Advent of the sub-10 µm minibeam at the APS GM/CA CAT has enabled the collection of high quality diffraction data from such microcrystals. Herein we describe the challenges and solutions related to growing, manipulating and collecting data from optically invisible microcrystals embedded in an opaque frozen in meso material. Of critical importance is the use of the intense and small synchrotron beam to raster through and locate the crystal sample in an efficient and reliable manner. The resulting diffraction patterns have a significant reduction in background, with strong intensity and improvement in diffraction resolution compared with larger beam sizes. Three high-resolution structures of human G protein-coupled receptors serve as evidence of the utility of these techniques that will likely be useful for future structural determination efforts. We anticipate that further innovations of the technologies applied to microcrystallography will enable the solving of structures of ever more challenging targets.
lipidic cubic phase; G protein-coupled receptor; minibeam; microcrystallography
Characterization of PILATUS single-photon-counting X-ray detector modules regarding charge sharing, energy resolution and rate capability is presented. The performance of the detector was tested with surface diffraction experiments at the synchrotron.
PILATUS is a silicon hybrid pixel detector system, operating in single-photon-counting mode, that has been developed at the Paul Scherrer Institut for the needs of macromolecular crystallography at the Swiss Light Source (SLS). A calibrated PILATUS module has been characterized with monochromatic synchrotron radiation. The influence of charge sharing on the count rate and the overall energy resolution of the detector were investigated. The dead-time of the system was determined using the attenuated direct synchrotron beam. A single module detector was also tested in surface diffraction experiments at the SLS, whereby its performance regarding fluorescence suppression and saturation tolerance were evaluated, and have shown to greatly improve the sensitivity, reliability and speed of surface diffraction data acquisition.
hybrid pixel detector; single photon counting; energy resolution; charge sharing; dead-time; surface X-ray diffraction
Although fiber-optical two-photon endoscopy has been recognized as a potential high-resolution diagnostic and therapeutic procedure in vivo, its resolution is limited by the optical diffraction nature to a few micrometers due to the low numerical aperture of an endoscopic objective. On the other hand, stimulated emission depletion (STED) achieved by a circularly-polarized vortex beam has been used to break the diffraction-limited resolution barrier in a bulky microscope. It has been a challenge to apply the STED principle to a fiber-optical two-photon endoscope as a circular polarization state cannot be maintained due to the birefringence of a fiber. Here, we demonstrate the first fiber-optical STED two-photon endoscope using an azimuthally-polarized beam directly generated from a double-clad fiber. As such, the diffraction-limited resolution barrier of fiber-optical two-photon endoscopy can be broken by a factor of three. Our new accomplishment has paved a robust way for high-resolution in vivo biomedical studies.
Acoustical and optical non-diffracting beams are potentially useful for manipulating particles
and larger objects. An extended optical theorem for a non-diffracting beam was given recently in the
context of acoustics. The theorem relates the extinction by an object to the scattering at the
forward direction of the beam’s plane wave components. Here we use this theorem to examine
the extinction cross section of a sphere centered on the axis of the beam, with a non-diffracting
Bessel beam as an example. The results are applied to recover the axial radiation force and torque
on the sphere by the Bessel beam.
(350.4855) Optical tweezers or optical manipulation; (290.2200) Extinction; (290.4020) Mie theory; (290.5850) Scattering, particles
Diamond transmission-mode white-beam position monitors installed at undulator beamline X25 at the National Synchrotron Light Source are described.
Two transmission-mode diamond X-ray beam position monitors installed at National Synchrotron Light Source (NSLS) beamline X25 are described. Each diamond beam position monitor is constructed around two horizontally tiled electronic-grade (p.p.b. nitrogen impurity) single-crystal (001) CVD synthetic diamonds. The position, angle and flux of the white X-ray beam can be monitored in real time with a position resolution of 500 nm in the horizontal direction and 100 nm in the vertical direction for a 3 mm × 1 mm beam. The first diamond beam position monitor has been in operation in the white beam for more than one year without any observable degradation in performance. The installation of a second, more compact, diamond beam position monitor followed about six months later, adding the ability to measure the angular trajectory of the photon beam.
diamond; detector; monitor; position-sensitive; quadrant; white beam; BPM; photon; undulator
Polarized total internal reflection fluorescence microscopy (polTIRFM) can be used to detect the spatial orientation and rotational dynamics of single molecules. polTIRFM determines the three-dimensional angular orientation and the extent of wobble of a fluorescent probe bound to the macromolecule of interest. This protocol describes how to acquire polTIRFM data and then calibrate the setup. Calibration corrects for any systematic variations in beam intensity and unequal detector sensitivities and is performed for each slide after experimental data are recorded. To convert the intensities into angles, one set of (θ, φ, δs, δf, κ) is then determined from one complete cycle of the incident intensities. This process is repeated for every cycle in the trace to measure the time dependence of rotational motions. The collection and analysis of data is similar for the processive motility assay for myosin V and for the twirling filament assay, in which a sparsely labeled actin filament is translocated by a field of unlabeled myosin V.
A scanning X-ray strain microscopy technique using a micro-focused beam is demonstrated.
Strained semiconductors are ubiquitous in microelectronics and microelectromechanical systems, where high local stress levels can either be detrimental for their integrity or enhance their performance. Consequently, local probes for elastic strain are essential in analyzing such devices. Here, a scanning X-ray sub-microprobe experiment for the direct measurement of deformation over large areas in single-crystal thin films with a spatial resolution close to the focused X-ray beam size is presented. By scanning regions of interest of several tens of micrometers at different rocking angles of the sample in the vicinity of two Bragg reflections, reciprocal space is effectively mapped in three dimensions at each scanning position, obtaining the bending, as well as the in-plane and out-of-plane strain components. Highly strained large-area Ge structures with applications in optoelectronics are used to demonstrate the potential of this technique and the results are compared with finite-element-method models for validation.
X-ray diffraction; local probe X-ray diffraction; strain
A new powder diffractometer operating in transmission mode is described. It can work as a rapid very compact instrument or as a high-resolution instrument, and the sample preparation is simplified.
A new powder diffractometer operating in transmission mode is described. It can work as a rapid very compact instrument or as a high-resolution instrument, and the sample preparation is simplified. The incident beam optics create pure Cu Kα1 radiation, giving rise to peak widths of ∼0.1° in 2θ in compact form with a sample-to-detector minimum radius of 55 mm, reducing to peak widths of <0.05° in high-resolution mode by increasing the detector radius to 240 mm. The resolution of the diffractometer is shown to be governed by a complex mixture of angular divergence, sample size, diffraction effects and the dimensions of the detector pixels. The data can be collected instantaneously, which combined with trivial sample preparation and no sample alignment, makes it a suitable method for very rapid phase identification. As the detector is moved further from the sample, the angular step from the pixel dimension is reduced and the resolution improves significantly for very detailed studies, including structure determination and analysis of the microstructure. The advantage of this geometry is that the resolution of the diffractometer can be calculated precisely and the instrumental artefacts can be analysed easily without a sample present. The performance is demonstrated with LaB6 and paracetamol, and a critical appraisal of the uncertainties in the measurements is presented. The instantaneous data collection offers possibilities in dynamic experiments.
high-resolution powder diffaction; transmission geometry; monochromatization
A dual modality computed mammotomography (CmT) and single photon emission computed tomography (SPECT) system for dedicated 3D breast imaging is in development. Using heavy K-edge filtration, the CmT component narrows the energy spectrum of the cone-shaped x-ray beam incident on the patient’s pendant, uncompressed breast. This quasi-monochromatic beam is expected to improve discrimination of tissue with similar attenuation coefficients while restraining absorbed dose to below that of dual view mammography. Previous simulation studies showed the optimal energy that maximizes dose efficiency for a 50/50% adipose/glandular breast is between 30 and 40 keV. This study experimentally validates these results using pre-breast and post-breast spectral measurements made under tungsten tube voltages between 40 and 100 kVp using filter materials with K-edge values ranging from 15 to 70 keV. Different filter material thicknesses are used, approximately equivalent to the 200th and 500th attenuating value layer (VL) thickness. Cerium (K = 40.4 keV) filtered post-breast spectra for 8–18 cm breasts are measured for a range of breast compositions. Figures of merit include mean beam energy, spectral full-width at tenth-maximum, beam hardening and dose for the range of breast sizes. Measurements corroborate simulation results, indicating that for a given dose, a 200th VL of cerium filtration may have optimal performance in the dedicated mammotomography paradigm.
Small-angle X-ray scattering (SAXS) is an X-ray diffraction-based technique where a narrow collimated beam of X-rays is focused onto a sample and the scattered X-rays recorded by a detector. The pattern of the scattered X-rays carries information on the molecular structure of the material. As breast cancer is the most widespread cancer in women and differentiation among its tumors is important, this project compared the results of coherent X-ray scattering measurements obtained from benign and malignant breast tissues. The energy-dispersive method with a setup including X-ray tube, primary collimator, sample holder, secondary collimator and high-purity germanium (HpGe) detector was used. One hundred thirty-one breast-tissue samples, including normal, fibrocystic changes and carcinoma, were studied at the 6° scattering angle. Diffraction profiles (corrected scattered intensity versus momentum transfer) of normal, fibrocystic changes and carcinoma were obtained. These profiles showed a few peak positions for adipose (1.15 ± 0.06 nm−1), mixed normal (1.15 ± 0.06 nm−1 and 1.4 ± 0.04 nm−1), fibrocystic changes (1.46 ± 0.05 nm−1 and 1.74 ± 0.04 nm−1) and carcinoma (1.55 ± 0.04 nm−1, 1.73 ± 0.06 nm−1, 1.85 ± 0.05 nm−1). We were able to differentiate between normal, fibrocystic changes (benign) and carcinoma (malignant) breast tissues by SAXS. However, we were unable to differentiate between different types of carcinoma.
Breast tumor; coherent scattering; small-angle X-ray scattering
The parasitoid fly Ormia ochracea shows an astonishing localization ability with its tiny hearing organ. A novel MEMS biomimetic acoustic pressure gradient sensitive structure was designed and fabricated by mimicking the mechanically coupled tympana of the fly. Firstly, the analytic representation formulas of the resultant force and resultant moment of the incoming plane wave acting on the structure were derived. After that, structure modal analysis was performed and the results show that the structure has out-of-phase and in-phase vibration modes, and the corresponding eigenfrequency is decided by the stiffness of vertical torsional beam and horizontal beam respectively. Acoustic-structural coupled analysis was performed and the results show that phase difference and amplitude difference between the responses of the two square diaphragms of the sensitive structure are effectively enlarged through mechanical coupling beam. The phase difference and amplitude difference increase with increasing incident angle and can be used to distinguish the direction of sound arrival. At last, the fabrication process and results of the device is also presented.
MEMS; biomimetic; parasitoid fly; pressure gradient; sound source localization
A novel design is described for an aperture that blocks a half-plane of the electron diffraction pattern out to a desired scattering angle, and then – except for a narrow support beam – transmits all of the scattered electrons beyond that angle. Our proposed tulip-shaped design is thus a hybrid between the single-sideband (ssb) aperture, which blocks a full half-plane of the diffraction pattern, and the conventional (i.e. fully open) double-sideband (dsb) aperture. The benefits of this hybrid design include the fact that such an aperture allows one to obtain high-contrast images of weak-phase objects with the objective lens set to Scherzer defocus. We further demonstrate that such apertures can be fabricated from thin-foil materials by milling with a focused ion beam (FIB), and that such apertures are fully compatible with the requirements of imaging out to a resolution of at least 0.34 nm. As is known from earlier work with single-sideband apertures, however, the edge of such an aperture can introduce unwanted, electrostatic phase shifts due to charging. The principal requirement for using such an aperture in a routine data-collection mode is thus to discover appropriate materials, protocols for fabrication and processing, and conditions of use such that the hybrid aperture remains free of charging over long periods of time.
Phase contrast; single-sideband aperture; charging
The focal field distribution of tightly focused laser beams in turbid media is sensitive to optical scattering and therefore of direct relevance to image quality in confocal and nonlinear microscopy. A model that considers both the influence of scattering and diffraction on the amplitude and phase of the electric field in focused beam geometries is required to describe these distorted focal fields. We combine an electric field Monte Carlo approach that simulates the electric field propagation in turbid media with an angular-spectrum representation of diffraction theory to analyze the effect of tissue scattering properties on the focal field. In particular, we examine the impact of variations in the scattering coefficient (µs), single-scattering anisotropy (g), of the turbid medium and the numerical aperture of the focusing lens on the focal volume at various depths. The model predicts a scattering-induced broadening, amplitude loss, and depolarization of the focal field that corroborates experimental results. We find that both the width and the amplitude of the focal field are dictated primarily by µs with little influence from g. In addition, our model confirms that the depolarization rate is small compared to the amplitude loss of the tightly focused field.
(170.0180) Microscopy; (260.1960) Diffraction theory; (290.7050) Scattering in turbid media
Dose-compatible measurements of a mammography phantom demonstrate an increase in contrast attainable through differential phase and dark-field imaging over conventional absorption-based projections. All measurements have been performed at 21 keV using a monochromatic laser-driven miniature synchrotron X-ray source (Compact Light Source).
The Compact Light Source is a miniature synchrotron producing X-rays at the interaction point of a counter-propagating laser pulse and electron bunch through the process of inverse Compton scattering. The small transverse size of the luminous region yields a highly coherent beam with an angular divergence of a few milliradians. The intrinsic monochromaticity and coherence of the produced X-rays can be exploited in high-sensitivity differential phase-contrast imaging with a grating-based interferometer. Here, the first multimodal X-ray imaging experiments at the Compact Light Source at a clinically compatible X-ray energy of 21 keV are reported. Dose-compatible measurements of a mammography phantom clearly demonstrate an increase in contrast attainable through differential phase and dark-field imaging over conventional attenuation-based projections.
medical X-ray imaging; phase contrast; inverse Compton X-rays
The nonlinear continuum equation of thin-film growth is applicable to simulate the surface of multilayer gratings with large boundary profile heights and/or gradient jumps. The integrated approach to the calculation of boundary profiles and the intensity of short-wave scattering by multilayer gratings is a way of performing studies comparable in accuracy to measurements with synchrotron radiation for known materials and growth techniques.
It is shown that taking into proper account certain terms in the nonlinear continuum equation of thin-film growth makes it applicable to the simulation of the surface of multilayer gratings with large boundary profile heights and/or gradient jumps. The proposed model describes smoothing and displacement of Mo/Si and Al/Zr boundaries of gratings grown on Si substrates with a blazed groove profile by magnetron sputtering and ion-beam deposition. Computer simulation of the growth of multilayer Mo/Si and Al/Zr gratings has been conducted. Absolute diffraction efficiencies of Mo/Si and Al/Zr gratings in the extreme UV range have been found within the framework of boundary integral equations applied to the calculated boundary profiles. It has been demonstrated that the integrated approach to the calculation of boundary profiles and of the intensity of short-wave scattering by multilayer gratings developed here opens up a way to perform studies comparable in accuracy to measurements with synchrotron radiation, at least for known materials and growth techniques.
continuum growth model; boundary profiles; boundary integral equation method; scattering intensity; diffraction grating efficiency; multilayer relief gratings; soft-X-ray and extreme ultraviolet range