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Showing papers on "Diffraction published in 2010"


Journal ArticleDOI
TL;DR: In this article, the authors summarized the basic principles and major achievements of plasmon guiding, and details the current state-of-the-art in subwavelength PLASmonic waveguides, passive and active nanoplasmonic components for the generation, manipulation and detection of radiation, and configurations for the nanofocusing of light.
Abstract: Recent years have seen a rapid expansion of research into nanophotonics based on surface plasmon–polaritons. These electromagnetic waves propagate along metal–dielectric interfaces and can be guided by metallic nanostructures beyond the diffraction limit. This remarkable capability has unique prospects for the design of highly integrated photonic signal-processing systems, nanoresolution optical imaging techniques and sensors. This Review summarizes the basic principles and major achievements of plasmon guiding, and details the current state-of-the-art in subwavelength plasmonic waveguides, passive and active nanoplasmonic components for the generation, manipulation and detection of radiation, and configurations for the nanofocusing of light. Potential future developments and applications of nanophotonic devices and circuits are also discussed, such as in optical signals processing, nanoscale optical devices and near-field microscopy with nanoscale resolution.

3,481 citations


Journal ArticleDOI
23 Dec 2010-Cell
TL;DR: This Primer explains the principles of various super-resolution approaches, such as STED, (S)SIM, and STORM/(F)PALM, and demonstrates how these approaches are beginning to provide new insights into cell biology, microbiology, and neurobiology.

1,056 citations


Journal ArticleDOI
TL;DR: A global approach has been developed to analyze complex thin film structures by X-ray diffraction as mentioned in this paper, which is based on the fitting of multiple data, diffraction pattern and/or images collected at different orientation of the sample to obtain all the information needed.
Abstract: A global approach has been developed to analyze complex thin film structures by X-ray diffraction The method is based on the fitting of multiple data, diffraction pattern and/or images, collected at different orientation of the sample to obtain all the information needed It requires the knowledge of the crystal structure for the phases present in the film, or if the amount/film thickness is sufficient, the crystal structure can be also determined or refined Reflectivity patterns can be added to the global refinement to improve the accuracy of the thickness determination and when coupled with total X-ray fluorescence can give the in depth chemical concentrations In addition, it constraints the solution for the quantitative phase analysis obtained from the diffraction patterns The principles of the analysis with the main methods will be presented from the theoretical point of view These cover the models from crystal structure to texture, residual strain/stresses, crystallite sizes and microstrains To make the method more effective, some specific models have been developed in the past few years Then some experimental/analysis examples will be given to enlighten how the method works and what kind of information can be obtained Not every model suits every analysis or kind of thin film and the examples will cover different cases from multiple phases to strong texture, epitaxial thin films or multilayers

866 citations


Journal ArticleDOI
TL;DR: In this article, the authors used spatial wavefront shaping to improve the focusing resolution of a lens by using wave front shaping to compensate for scattering in an inhomogeneous medium between the lens and the focal plane.
Abstract: Optical microscopy and manipulation methods rely on the ability to focus light to a small volume. However, in inhomogeneous media such as biological tissue, light is scattered out of the focusing beam. Disordered scattering is thought to fundamentally limit the resolution and penetration depth of optical methods1,2,3. Here we demonstrate, in an optical experiment, that scattering can be used to improve, rather than deteriorate, the sharpness of the focus. The resulting focus is even sharper than that in a transparent medium. By using scattering in the medium behind a lens, light was focused to a spot ten times smaller than the diffraction limit of that lens. Our method is the optical equivalent of highly successful methods for improving the resolution and communication bandwidth of ultrasound, radio waves and microwaves4,5,6. Our results, obtained using spatial wavefront shaping, apply to all coherent methods for focusing through scattering matter, including phase conjugation7 and time-reversal4. Light is scattered out of a focusing beam when an inhomogeneous medium is placed between the lens and the focal plane. Now, scientists experimentally demonstrate that scattering can be exploited to improve, rather than deteriorate, the focusing resolution of a lens by using wavefront shaping to compensate for scattering.

716 citations


Journal ArticleDOI
TL;DR: The results suggest that, although the diffusion of bulky alkene and oxidant reagents can be a rate-limiting factor in MOF-catalyzed asymmetric reactions, the catalytic activity of the CMOFs with large open channels is limited by the intrinsic reactivity of the catalytical molecular building blocks.
Abstract: A family of isoreticular chiral metal−organic frameworks (CMOFs) of the primitive cubic network topology was constructed from [Zn4(μ4-O)(O2CR)6] secondary building units and systematically elongated dicarboxylate struts that are derived from chiral Mn-Salen catalytic subunits. CMOFs 1−5 were synthesized by directly incorporating three different chiral Mn-Salen struts into the frameworks under solvothermal conditions, and they were characterized by a variety of methods, including single-crystal X-ray diffraction, PXRD, TGA, and 1H NMR. Although the CMOFs 1 vs 2 and CMOFs 3 vs 4 pairs were constructed from the same building blocks, they exhibit two-fold interpenetrated or non-interpenetrated structures, respectively, depending on the steric sizes of the solvents that were used to grow the MOF crystals. For CMOF-5, only a three-fold interpenetrated structure was obtained due to the extreme length of the Mn-Salen-derived dicarboxylate strut. The open channel and pore sizes of the CMOF series vary systematical...

614 citations


Journal ArticleDOI
TL;DR: In this paper, the first observation of a class of versatile three-dimensional linear light "bullets" was reported, where Bessel beams in the transverse plane with temporal Airy pulses were used to generate spatiotemporal optical wave packets resistant to both dispersion and diffraction.
Abstract: The generation of spatiotemporal optical wave packets that are resistant to both dispersion and diffraction are attractive for bioimaging applications and plasma physics. By combining Bessel beams in the transverse plane with temporal Airy pulses, scientists now report the first observation of a class of versatile three-dimensional linear light ‘bullets’.

568 citations


Book
05 Aug 2010
TL;DR: Numerical Simulation of Optical Wave Propagation is solely dedicated to wave-optics simulations and discusses digital Fourier transforms, FT-based operations, and sampling requirements, and simulations in atmospheric turbulence.
Abstract: Foundations of Scalar Diffraction Theory Digital Fourier Transforms Simple Computations Using Fourier Transforms Fraunhofer Diffraction and Lenses Imaging Systems and Aberrations Fresnel Diffraction in Vacuum Sampling Requirements for Fresnel Diffraction Relaxed Sampling Constraints with Partial Propagations Propagation Through Atmospheric Turbulence Appendix A: Function Definitions Appendix B: MATLAB Code Listings References Index

540 citations


Journal ArticleDOI
TL;DR: A new classes of waves that tend to autofocus in an abrupt fashion are introduced that can be generated through the use of radially symmetric Airy waves.
Abstract: We introduce a new class of (2+1)D spatial and (3+1)D spatiotemporal waves that tend to autofocus in an abrupt fashion. While the maximum intensity of such a radial wave remains almost constant during propagation, it suddenly increases by orders of magnitude right before its focal point. These waves can be generated through the use of radially symmetric Airy waves or by appropriately superimposing Airy wave packets. Possible applications of such abruptly focusing beams are also discussed.

439 citations


Journal ArticleDOI
TL;DR: The spherical hyperlens is designed with flat hyperbolic dispersion that supports wave propagation with very large spatial frequency and yet same phase speed, which allows it to resolve features down to 160 nm, much smaller than the diffraction limit at visible wavelengths.
Abstract: Hyperlenses have generated much interest recently, not only because of their intriguing physics but also for their ability to achieve sub-diffraction imaging in the far field in real time. All previous efforts have been limited to sub-wavelength confinement in one dimension only and at ultraviolet frequencies, hindering the use of hyperlenses in practical applications. Here, we report the first experimental demonstration of far-field imaging at a visible wavelength, with resolution beyond the diffraction limit in two lateral dimensions. The spherical hyperlens is designed with flat hyperbolic dispersion that supports wave propagation with very large spatial frequency and yet same phase speed. This allows us to resolve features down to 160 nm, much smaller than the diffraction limit at visible wavelengths, that is, 410 nm. The hyperlens can be integrated into conventional microscopes, expanding their capabilities beyond the diffraction limit and opening a new realm in real-time nanoscopic optical imaging.

391 citations


Journal ArticleDOI
09 Dec 2010-Nature
TL;DR: Effectively, the atomic motions that result from the optically induced change in the electronic spatial distribution are directly observed and the degree of cooperativity in the observed structural dynamics is remarkable and illustrates the importance of obtaining atomic-level perspectives of the processes directing the physics of strongly correlated systems.
Abstract: The development of tabletop femtosecond electron diffraction sources has provided an alternative way of observing atomic motions in crystalline materials. This technique has now been applied to the charge-density-wave material 1T-TaS2, in which modulation of the electron density is accompanied by a periodic lattice distortion. Previous time-resolved studies have revealed the dynamics of the electronic charge density wave, but until now the dynamics of the lattice system has been only indirectly inferred. In this new experiment, atomic motions were observed in response to a 140 femtosecond optical pulse. Periodic lattice distortion was seen to collapse on an exceptionally fast timescale (about 250 fs), indicative of an electronically driven process involving a high degree of cooperativity. The surprisingly high degree of cooperation in the observed structural dynamics between the electronic and lattice system illustrates the potential for the technique in studies of strongly correlated systems.

390 citations


Journal ArticleDOI
TL;DR: In this article, an aging and re-poling induced enhancement of piezoelectricity is found in (K,Na)NbO3 (KNN)-based lead-free PPE ceramics.
Abstract: Aging and re-poling induced enhancement of piezoelectricity are found in (K,Na)NbO3 (KNN)-based lead-free piezoelectric ceramics. For a compositionally optimized Li-doped composition, its piezoelectric coefficient d33 can be increased up to 324 pC N−1 even from a considerably high value (190 pC N−1) by means of a re-poling treatment after room-temperature aging. Such a high d33 value is only reachable in KNN ceramics with complicated modifications using Ta and Sb dopants. High-angle X-ray diffraction analysis reveals apparent changes in the crystallographic orientations related to a 90° domain switching before and after the aging and re-poling process. A possible mechanism considering both defect migration and rotation of spontaneous polarization explains the experimental results. The present study provides a general approach towards piezoelectric response enhancement in KNN-based piezoelectric ceramics.

Journal ArticleDOI
TL;DR: It is shown that the Airy(3) light bullets are robust up to the high intensity regime, since they are capable of healing the nonlinearly induced distortions of their spatiotemporal profile.
Abstract: We demonstrate the realization of intense Airy-Airy-Airy (Airy(3)) light bullets by combining a spatial Airy beam with an Airy pulse in time. The Airy(3) light bullets belong to a family of linear spatiotemporal wave packets that do not require any specific tuning of the material optical properties for their formation and withstand both diffraction and dispersion during their propagation. We show that the Airy(3) light bullets are robust up to the high intensity regime, since they are capable of healing the nonlinearly induced distortions of their spatiotemporal profile.

Journal ArticleDOI
TL;DR: In this article, the basic properties of Floquet-Bloch (FB) modes in parity-time symmetric optical lattices are examined in detail, and the conjugate pairs of these FB modes are obtained by reflecting both the spatial coordinate and the Bloch momentum number itself.
Abstract: The basic properties of Floquet-Bloch (FB) modes in parity-time ($\mathcal{PT}$)-symmetric optical lattices are examined in detail. Due to the parity-time symmetry of such complex periodic potentials, the corresponding FB modes are skewed (nonorthogonal) and nonreciprocal. The conjugate pairs of these FB modes are obtained by reflecting both the spatial coordinate and the Bloch momentum number itself. The orthogonality conditions are analytically derived for a single cell, for both a finite and an infinite lattice. Some of the peculiarities associated with the diffraction dynamics in $\mathcal{PT}$ lattices such as nonreciprocity, power oscillations, and phase dislocations, are also examined.

Journal ArticleDOI
TL;DR: Key advances in fabrication and experimental techniques have enabled diffraction patterns to be obtained from six Bragg reflections of the same ZnO nanocrystal for the first time, and all three Cartesian components of the ion displacement field, and in turn the full nine-component strain tensor, have thereby been imaged in three dimensions.
Abstract: Nanoscale structures can be highly strained because of confinement effects and the strong influence of their external boundaries. This results in dramatically different electronic, magnetic and optical material properties of considerable utility. Third-generation synchrotron-based coherent X-ray diffraction has emerged as a non-destructive tool for three-dimensional (3D) imaging of strain and defects in crystals that are smaller than the coherence volume, typically a few cubic micrometres, of the available beams that have sufficient flux to reveal the material's structure(1). Until now, measurements have been possible only at a single Bragg point of a given crystal because of the limited ability to maintain alignment(2); it has therefore been possible to determine only one component of displacement and not the full strain tensor. Here we report key advances in our fabrication and experimental techniques, which have enabled diffraction patterns to be obtained from six Bragg reflections of the same ZnO nanocrystal for the first time. All three Cartesian components of the ion displacement field, and in turn the full nine-component strain tensor, have thereby been imaged in three dimensions.

Journal ArticleDOI
TL;DR: In this paper, the authors demonstrate the compression of 95 keV, space-charge-dominated electron bunches to sub-100 fs durations by means of velocity bunching by inverting the positive space charge-induced velocity chirp.
Abstract: We demonstrate the compression of 95 keV, space-charge-dominated electron bunches to sub-100 fs durations. These bunches have sufficient charge (200 fC) and are of sufficient quality to capture a diffraction pattern with a single shot, which we demonstrate by a diffraction experiment on a polycrystalline gold foil. Compression is realized by means of velocity bunching by inverting the positive space-charge-induced velocity chirp. This inversion is induced by the oscillatory longitudinal electric field of a 3 GHz radio-frequency cavity. The arrival time jitter is measured to be 80 fs.

Journal ArticleDOI
TL;DR: Pd−Ag bimetallic dendrites have been synthesized via a galvanic replacement reaction of Ag dendrite in a Na2PdCl4 solution as discussed by the authors, which showed up to four times higher catalytic activity toward the reduction of 4-nitrophenol (4-NP) by sodium borohydride (NaBH4) than the best recently reported catalysts.
Abstract: Pd−Ag bimetallic dendrites have been synthesized via a galvanic replacement reaction of Ag dendrites in a Na2PdCl4 solution. Scanning and transmission electron microscopy (SEM and TEM), energy dispersive X-ray spectrometry (EDX), X-ray diffraction (XRD), and X-ray photoelectron spectroscopy (XPS) analysis reveal that the resulting product is composed of partially depleted Ag dendrites covered with a rough surface with many Pd granules protruding by up to about 20 nm. High-solution TEM combined with EDX and selected area electron diffraction (SAED) confirms the formation of bimetallic interfaces between Pd and Ag. These Pd−Ag dendrites show up to four times higher catalytic activity toward the reduction of 4-nitrophenol (4-NP) by sodium borohydride (NaBH4) than the best recently reported catalysts. This further enhancement over the already strong performance of similarly synthesized Au−Ag dendrites is explained by the presence of Pd, adding a hydrogen relay mechanism on top of the very effective electron r...

Journal ArticleDOI
TL;DR: In this article, a new method for collecting complete three-dimensional electron diffraction data is described, which is collected by combining electron beam tilt at many very small steps, with rotation of the crystal in a few but large steps.
Abstract: A new method for collecting complete three-dimensional electron diffraction data is described. Diffraction data is collected by combining electron beam tilt at many very small steps, with rotation of the crystal in a few but large steps. A number of practical considerations are discussed, as well as advantages and disadvantages compared to other methods of collecting electron diffraction data.

Journal ArticleDOI
TL;DR: A report on the characterization, calibration and performances of the MYTHEN photon-counting silicon microstrip detector at the powder diffraction station at the Swiss Light Source is given.
Abstract: The MYTHEN single-photon-counting silicon microstrip detector has been developed at the Swiss Light Source for time-resolved powder diffraction experiments. An upgraded version of the detector has been installed at the SLS powder diffraction station allowing the acquisition of diffraction patterns over 120° in 2θ in fractions of seconds. Thanks to the outstanding performance of the detector and to the calibration procedures developed, the quality of the data obtained is now comparable with that of traditional high-resolution point detectors in terms of FWHM resolution and peak profile shape, with the additional advantage of fast and simultaneous acquisition of the full diffraction pattern. MYTHEN is therefore optimal for time-resolved or dose-critical measurements. The characteristics of the MYTHEN detector together with the calibration procedures implemented for the optimization of the data are described in detail. The refinements of two known standard powders are discussed together with a remarkable application of MYTHEN to organic compounds in relation to the problem of radiation damage.

Patent
05 Mar 2010
TL;DR: In this paper, the simultaneous measurement of four separately polarized beams upon diffraction from a substrate is used to determine properties of the substrate, where the plurality of polarizing beamsplitters replaces the use of a phase modulator.
Abstract: The simultaneous measurement of four separately polarized beams upon diffraction from a substrate is used to determine properties of the substrate. Circularly or elliptically polarized light sources are passed via up to three polarizing elements. This polarizes the light sources by 0, 45, 90 and 135°. The plurality of polarizing beamsplitters replaces the use of a phase modulator, but enables the measurement of the intensity of all four beams and thus the measurement of the phase modulation and amplitude of the combined beams to give the features of the substrate.

Journal ArticleDOI
TL;DR: The resonant metalens is introduced, a cluster of coupled subwavelength resonators that is realizable at any frequency where subwa wavelength resonators can be designed and experimentally demonstrates imaging and focusing from the far field with resolutions far below the diffraction limit.
Abstract: We introduce the resonant metalens, a cluster of coupled subwavelength resonators. Dispersion allows the conversion of subwavelength wave fields into temporal signatures while the Purcell effect permits an efficient radiation of this information in the far field. The study of an array of resonant wires using microwaves provides a physical understanding of the underlying mechanism. We experimentally demonstrate imaging and focusing from the far field with resolutions far below the diffraction limit. This concept is realizable at any frequency where subwavelength resonators can be designed.

Journal ArticleDOI
TL;DR: In this article, a low-loss three-dimensional metamaterial nanolens consisting of aligned gold nanowires embedded in a porous alumina matrix was used for super-resolution imaging.
Abstract: Super-resolution imaging beyond Abbe’s diffraction limit can be achieved by utilizing an optical medium or “metamaterial” that can either amplify or transport the decaying near-field evanescent waves that carry subwavelength features of objects. Earlier approaches at optical frequencies mostly utilized the amplification of evanescent waves in thin metallic films or metal-dielectric multilayers, but were restricted to very small thicknesses (⪡λ, wavelength) and accordingly short object-image distances, due to losses in the material. Here, we present an experimental demonstration of super-resolution imaging by a low-loss three-dimensional metamaterial nanolens consisting of aligned gold nanowires embedded in a porous alumina matrix. This composite medium possesses strongly anisotropic optical properties with negative permittivity in the nanowire axis direction, which enables the transport of both far-field and near-field components with low-loss over significant distances (>6λ), and over a broad spectral range. We demonstrate the imaging of large objects, having subwavelength features, with a resolution of at least λ/4 at near-infrared wavelengths. The results are in good agreement with a theoretical model of wave propagation in anisotropic media.

Journal ArticleDOI
TL;DR: The effect of emission dipole orientation in conjunction with optical aberrations on the localization accuracy of position estimators based on a gaussian model PSF is studied.
Abstract: The Gaussian function is simple and easy to implement as Point Spread Function (PSF) model for fitting the position of fluorescent emitters in localization microscopy. Despite its attractiveness the appropriateness of the Gaussian is questionable as it is not based on the laws of optics. Here we study the effect of emission dipole orientation in conjunction with optical aberrations on the localization accuracy of position estimators based on a Gaussian model PSF. Simulated image spots, calculated with all effects of high numerical aperture, interfaces between media, polarization, dipole orientation and aberrations taken into account, were fitted with a Gaussian PSF based Maximum Likelihood Estimator. For freely rotating dipole emitters it is found that the Gaussian works fine. The same, theoretically optimum, localization accuracy is found as if the true PSF were a Gaussian, even for aberrations within the usual tolerance limit of high-end optical imaging systems such as microscopes (Marechal’s diffraction limit). For emitters with a fixed dipole orientation this is not the case. Localization errors are found that reach up to 40 nm for typical system parameters and aberration levels at the diffraction limit. These are systematic errors that are independent of the total photon count in the image. The Gaussian function is therefore inappropriate, and more sophisticated PSF models are a practical necessity.

Journal ArticleDOI
TL;DR: In this article, two software, IPAnalyzer and PDIndexer, were developed to convert a two-dimensional Debye-ring pattern to one-dimensional (Bragg-Brentano) geometry.
Abstract: Angle dispersive powder X-ray diffraction experiments using a flat imaging plate (IP) are one of the most popular methods in high-pressure material science. In order to support such experiments, we developed two software, IPAnalyzer and PDIndexer. IPAnalyzer can convert a two-dimensional Debye-ring pattern to one-dimensional (Bragg-Brentano) geometry. IPAnalyzer can also calibrate experimental parameters (wave length, camera length, and so on) automatically. PDIndexer can display the converted pattern(s) and diffraction peaks calculated for any crystals.

Journal ArticleDOI
TL;DR: In this paper, the synthesis of hydroxyapatatite (HAp) from recycled eggshell was described by using mechanochemical activation method (ball milling and attrition milling).

Journal ArticleDOI
TL;DR: The number of shots needed for a required accuracy in structure factor measurement and resolution is determined, the convergence of the Monte-Carlo integration method is investigated, and X-ray diffraction patterns for Photosystem I nanocrystals are developed.
Abstract: X-ray diffraction patterns may be obtained from individual submicron protein nanocrystals using a femtosecond pulse from a free-electron X-ray laser. Many “single-shot” patterns are read out every second from a stream of nanocrystals lying in random orientations. The short pulse terminates before significant atomic (or electronic) motion commences, minimizing radiation damage. Simulated patterns for Photosystem I nanocrystals are used to develop a method for recovering structure factors from tens of thousands of snapshot patterns from nanocrystals varying in size, shape and orientation. We determine the number of shots needed for a required accuracy in structure factor measurement and resolution, and investigate the convergence of our Monte-Carlo integration method.

Journal ArticleDOI
TL;DR: In this paper, the first experimental observation of three-dimensional light bullets, excited by femtosecond pulses in a system featuring quasi-instantaneous cubic nonlinearity and a periodic, transversally modulated refractive index was reported.
Abstract: We report the first experimental observation of three-dimensional light bullets, excited by femtosecond pulses in a system featuring quasi-instantaneous cubic nonlinearity and a periodic, transversally modulated refractive index. Stringent evidence of the excitation of light bullets is based on time-gated images and spectra which perfectly match our numerical simulations. Furthermore, we reveal a novel evolution mechanism forcing the light bullets to follow varying dispersion or diffraction conditions, until they leave their existence range and decay.

Journal ArticleDOI
TL;DR: It is demonstrated that the absorptive model is appropriate for measuring thickness and other specimen parameters even for relatively thick samples (>50nm).

Journal ArticleDOI
TL;DR: In this article, a robust 12-parameter per-grain fit of the centre-of-mass grain positions, orientations and stress tensors including error estimation and outlier rejection is presented.
Abstract: An algorithm is presented for characterization of the grain resolved (type II) stress states in a polycrystalline sample based on monochromatic X-ray diffraction data. The algorithm is a robust 12-parameter-per-grain fit of the centre-of-mass grain positions, orientations and stress tensors including error estimation and outlier rejection. The algorithm is validated by simulations and by two experiments on interstitial free steel. In the first experiment, using only a far-field detector and a rotation range of 2 × 110°, 96 grains in one layer were monitored during elastic loading and unloading. Very consistent results were obtained, with mean resolutions for each grain of approximately 10 µm in position, 0.05° in orientation, and 8, 20 and 13 × 10−5 in the axial, normal and shear components of the strain, respectively. The corresponding mean deviations in stress are 30, 50 and 15 MPa in the axial, normal and shear components, respectively, though some grains may have larger errors. In the second experiment, where a near-field detector was added, ∼2000 grains were characterized with a positional accuracy of 3 µm.

Journal ArticleDOI
TL;DR: The experimental demonstration of what are to the authors' knowledge the first two-dimensional planar plasmonic lenses formed by an array of spatially varying cross-shaped apertures in a metallic film for Fresnel-region focusing is presented.
Abstract: We present the experimental demonstration of what are to our knowledge the first two-dimensional planar plasmonic lenses formed by an array of spatially varying cross-shaped apertures in a metallic film for Fresnel-region focusing. The design utilizes localized surface plasmon resonances occurring inside the apertures, accompanied by an aperture geometry dependent phase shift, to achieve the desired spatial phase modulation in the transmitted field. The performance of lenses with different design configurations was evaluated using a confocal scanning optical microscope, and the effects of diffraction on the optical response of these microscale devices are discussed.

Journal ArticleDOI
TL;DR: An x-ray differential phase-contrast imaging method based on two-dimensional transmission gratings that are directly resolved by an x-rays that obviates the need for multiple exposures and separate measurements for different directions and thereby accelerates imaging speed.
Abstract: We describe an x-ray differential phase-contrast imaging method based on two-dimensional transmission gratings that are directly resolved by an x-ray camera. X-ray refraction and diffraction in the sample lead to variations of the positions and amplitudes of the grating fringes on the camera. These effects can be quantified through spatial harmonic analysis. The use of 2D gratings allows differential phase contrast in several directions to be obtained from a single image. When compared to previous grating-based interferometry methods, this approach obviates the need for multiple exposures and separate measurements for different directions and thereby accelerates imaging speed.