Showing papers on "Diffraction published in 2009"

Theory of Reflectance and Emittance Spectroscopy

Abstract: Acknowledgements 1. Introduction 2. Electromagnetic wave propagation 3. The absorption of light 4. Specular reflection 5. Single particle scattering: perfect spheres 6. Single particle scattering: irregular particles 7. Propagation in a nonuniform medium: the equation of radiative transfer 8. The bidirectional reflectance of a semi-infinite medium 9. The opposition effect 10. A miscellany of bidirectional reflectances and related quantities 11. Integrated reflectances and planetary photometry 12. Photometric effects of large scale roughness 13. Polarization 14. Reflectance spectroscopy 15. Thermal emission and emittance spectroscopy 16. Simultaneous transport of energy by radiation and conduction Appendix A. A brief review of vector calculus Appendix B. Functions of a complex variable Appendix C. The wave equation in spherical coordinates Appendix D. Fraunhoffer diffraction by a circular hole Appendix E. Table of symbols Bibliography Index.

Optics and interferometry with atoms and molecules

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

X-ray diffraction of III-nitrides

Abstract: The III-nitrides include the semiconductors AlN, GaN and InN, which have band gaps spanning the entire UV and visible ranges. Thin films of III-nitrides are used to make UV, violet, blue and green light-emitting diodes and lasers, as well as solar cells, high-electron mobility transistors (HEMTs) and other devices. However, the film growth process gives rise to unusually high strain and high defect densities, which can affect the device performance. X-ray diffraction is a popular, non-destructive technique used to characterize films and device structures, allowing improvements in device efficiencies to be made. It provides information on crystalline lattice parameters (from which strain and composition are determined), misorientation (from which defect types and densities may be deduced), crystallite size and microstrain, wafer bowing, residual stress, alloy ordering, phase separation (if present) along with film thicknesses and superlattice (quantum well) thicknesses, compositions and non-uniformities. These topics are reviewed, along with the basic principles of x-ray diffraction of thin films and areas of special current interest, such as analysis of non-polar, semipolar and cubic III-nitrides. A summary of useful values needed in calculations, including elastic constants and lattice parameters, is also given. Such topics are also likely to be relevant to other highly lattice-mismatched wurtzite-structure materials such as heteroepitaxial ZnO and ZnSe.

Three-dimensional single-molecule fluorescence imaging beyond the diffraction limit using a double-helix point spread function

Abstract: Embodiments of the present invention can resolve molecules beyond the optical diffraction limit in three dimensions. A double-helix point spread function can be used to in conjunction with a microscope to provide dual-lobed images of a molecule. Based on the rotation of the dual-lobed image, the axial position of the molecule can be estimated or determined. In some embodiments, the angular rotation of the dual-lobed imaged can be determined using a centroid fit calculation or by finding the midpoints of the centers of the two lobes. Regardless of the technique, the correspondence between the rotation and axial position can be utilized. A double-helix point spread function can also be used to determine the lateral positions of molecules and hence their three-dimensional location.

Plasmonics for near-field nano-imaging and superlensing

Abstract: Diffraction of light prevents optical microscopes from having spatial resolution beyond a value comparable to the wavelength of the probing light. This essentially means that visible light cannot image nanomaterials. Here we review the mechanism for going beyond this diffraction limit and discuss how manipulation of light by means of surface plasmons propagating along the metal surface can help to achieve this. The interesting behaviour of light under the influence of plasmons not only allows superlensing, in which perfect imaging is possible through a flat thin metal film, but can also provide nano-imaging of practical samples by using a localized surface plasmon mode at the tip of a metallic nanoprobe. We also discuss the current research status and some intriguing future possibilities.

Optical diffraction tomography for high resolution live cell imaging

Abstract: We report the experimental implementation of optical diffraction tomography for quantitative 3D mapping of refractive index in live biological cells. Using a heterodyne Mach-Zehnder interferometer, we record complex field images of light transmitted through a sample with varying directions of illumination. To quantitatively reconstruct the 3D map of complex refractive index in live cells, we apply optical diffraction tomography based on the Rytov approximation. In this way, the effect of diffraction is taken into account in the reconstruction process and diffraction-free high resolution 3D images are obtained throughout the entire sample volume. The quantitative refractive index map can potentially serve as an intrinsic assay to provide the molecular concentrations without the addition of exogenous agents and also to provide a method for studying the light scattering properties of single cells.

Achieving λ/20 Resolution by One-Color Initiation and Deactivation of Polymerization

Abstract: In conventional photolithography, diffraction limits the resolution to about one-quarter of the wavelength of the light used. We introduce an approach to photolithography in which multiphoton absorption of pulsed 800-nanometer (nm) light is used to initiate cross-linking in a polymer photoresist and one-photon absorption of continuous-wave 800-nm light is used simultaneously to deactivate the photopolymerization. By employing spatial phase-shaping of the deactivation beam, we demonstrate the fabrication of features with scalable resolution along the beam axis, down to a 40-nm minimum feature size. We anticipate application of this technique for the fabrication of diverse two- and three-dimensional structures with a feature size that is a small fraction of the wavelength of the light employed.

Two-Dimensional X-Ray Diffraction

Abstract: Preface. 1. Introduction. 1.1 X-Ray Technology and Its Brief History. 1.2 Geometry of Crystals. 1.3 Principles of X-Ray Diffraction. 1.4 Reciprocal Space and Diffraction. 1.5 Two-Dimensional X-Ray Diffraction. 2. Geometry Conventions. 2.1 Introduction. 2.2 Diffraction Space and Laboratory Coordinates. 2.3 Detector Space and Detector Geometry. 2.4 Sample Space and Goniometer Geometry. 2.5 Transformation from Diffraction Space to Sample Space. 2.6 Summary of XRD2 Geometry. References. 3. X-Ray Source and Optics. 3.1 X-Ray Generation and Characteristics. 3.2 X-Ray Optics. References. 4. X-Ray Detectors. 4.1 History of X-Ray Detection Technology. 4.2 Point Detectors in Conventional Diffractometers. 4.3 Characteristics of Point Detectors. 4.4 Line Detectors. 4.5 Characteristics of Area Detectors. 4.6 Types of Area Detectors. 5. Goniometer and Sample Stages. 5.1 Goniometer and Sample Position. 5.2 Goniometer Accuracy. 5.3 Sample Alignment and Visualization Systems. 5.4 Environment Stages. References. 6. Data Treatment. 6.1 Introduction. 6.2 Nonuniform Response Correction. 6.3 Spatial Correction. 6.4 Detector Position Accuracy and Calibration. 6.5 Frame Integration. 6.6 Lorentz, Polarization, and Absorption Corrections. 7. Phase Identification. 7.1 Introduction. 7.2 Relative Intensity. 7.3 Geometry and Resolution. 7.4 Sampling Statistics. 7.5 Preferred Orientation Effect. References. 8. Texture Analysis. 8.1 Introduction. 8.2 Pole Density and Pole Figure. 8.3 Fundamental Equations. 8.4 Data Collection Strategy. 8.5 Texture Data Process. 8.6 Orientation Distribution Function. 8.7 Fiber Texture. 8.8 Other Advantages of XRD2 for Texture. References. 9. Stress Measurement. 9.1 Introduction. 9.2 Principle of X-Ray Stress Analysis. 9.3 Theory of Stress Analysis with XRD2. 9.4 Process of Stress Measurement with XRD2. 9.5 Experimental Examples. Appendix 9.A Calculation of Principal Stresses from the General Stress Tensor. Appendix 9.B Parameters for Stress Measurement. References. 10. Small-Angle X-Ray Scattering. 10.1 Introduction. 10.2 2D SAXS Systems. 10.3 Application Examples. 10.4 Some Innovations in 2D SAXS. References. 11. Combinatorial Screening. 11.1 Introduction. 11.2 XRD2 Systems for Combinatorial Screening. 11.3 Combined Screening with XRD2 and Raman. 12. Quantitative Analysis. 12.1 Percent Crystallinity. 12.2 Crystal Size. 12.3 Retained Austenite. References. 13. Innovation and Future Development. 13.1 Introduction. 13.2 Scanning Line Detector for XRD2. 13.3 Three-Dimensional Detector. 13.4 Pixel Direct Diffraction Analysis. References. Appendix A. Values of Commonly Used Parameters. Appendix B. Symbols. Index.

Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields.

Abstract: A novel method is proposed for simulating free-space propagation. This method is an improvement of the angular spectrum method (AS). The AS does not include any approximation of the propagation distance, because the formula thereof is derived directly from the Rayleigh-Sommerfeld equation. However, the AS is not an all-round method, because it produces severe numerical errors due to a sampling problem of the transfer function even in Fresnel regions. The proposed method resolves this problem by limiting the bandwidth of the propagation field and also expands the region in which exact fields can be calculated by the AS. A discussion on the validity of limiting the bandwidth is also presented.

Near-field focusing and magnification through self-assembled nanoscale spherical lenses

Abstract: The performance of a light microscope is intrinsically constrained by the Abbe diffraction limit. No matter how close to optical perfection it is, an imaging system cannot resolve two objects that are beyond this natural limit, which is dependent on the wavelength of the observed light and its angular distribution. Several methods have been devised to beat the diffraction limit, but these have generally required esoteric excitation schemes, so remain impractical. Lee et al. are working on a new way of beating the limit, using nanoscale spherical lenses that self-assemble by bottom-up integration of cup-shaped organic molecules called calixarenes. Lenses produced in this way have very short focal lengths that can generate near-field magnification beyond the diffraction limit, enabling the resolution of features of the order of 200 nm. The lenses can be placed at will on a surface and, among other things, can be used to reduce the size of deep-ultraviolet lithography features. Cup-shaped molecules of calix[4]hydroquinone self-assemble on a surface into a lens shape; these lenses are shown to generate near-field magnification beyond the diffraction limit, enabling the resolution of features of the order of 200 nanometres. Such spherical nanolenses provide new pathways for lens-based near-field focusing and high-resolution optical imaging at very low intensities, which are useful for, among other things, bio-imaging and near-field lithography. It is well known that a lens-based far-field optical microscope cannot resolve two objects beyond Abbe’s diffraction limit. Recently, it has been demonstrated that this limit can be overcome by lensing effects driven by surface-plasmon excitation1,2,3, and by fluorescence microscopy driven by molecular excitation4. However, the resolution obtained using geometrical lens-based optics without such excitation schemes remains limited by Abbe’s law even when using the immersion technique5, which enhances the resolution by increasing the refractive indices of immersion liquids. As for submicrometre-scale or nanoscale objects, standard geometrical optics fails for visible light because the interactions of such objects with light waves are described inevitably by near-field optics6. Here we report near-field high resolution by nanoscale spherical lenses that are self-assembled by bottom-up integration7 of organic molecules. These nanolenses, in contrast to geometrical optics lenses, exhibit curvilinear trajectories of light, resulting in remarkably short near-field focal lengths. This in turn results in near-field magnification that is able to resolve features beyond the diffraction limit. Such spherical nanolenses provide new pathways for lens-based near-field focusing and high-resolution optical imaging at very low intensities, which are useful for bio-imaging, near-field lithography, optical memory storage, light harvesting, spectral signal enhancing, and optical nano-sensing.

Structural color films with lotus effects, superhydrophilicity, and tunable stop-bands

Abstract: The structural blue color of a Morpho butterfly originates from the diffraction of light and interference effects due to the presence of the microstructures on the wing of the butterfly. Structural color on the surface of a damselfish reversibly changes between green and blue. Inspired by these creatures, we have been trying to prepare high-quality and functional structural color films. We describe our efforts in this Account. A useful technique to prepare such structural color films in colloidal solution is a “lifting” method, which allows us to quickly fabricate brilliant colloidal crystal films. The thicknesses of the films can be controlled by precisely adjusting the particle concentration and the lifting speed. Moreover, in order to prepare a complicated structure, we have used template methods. Indeed, we have successfully prepared the inverse structure of the wing of a Morpho butterfly with this technique. Initially, however, our structural color films had a whitish appearance due to the scattering...

Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of Friedel pairs in diffraction data analysis.

Abstract: X-ray diffraction contrast tomography (DCT) is a technique for mapping grain shape and orientation in plastically undeformed polycrystals. In this paper, we describe a modified DCT data acquisition strategy which permits the incorporation of an innovative Friedel pair method for analyzing diffraction data. Diffraction spots are acquired during a 360 degrees rotation of the sample and are analyzed in terms of the Friedel pairs ((hkl) and (hkl) reflections, observed 180 degrees apart in rotation). The resulting increase in the accuracy with which the diffraction vectors are determined allows the use of improved algorithms for grain indexing (assigning diffraction spots to the grains from which they arise) and reconstruction. The accuracy of the resulting grain maps is quantified with reference to synchrotron microtomography data for a specimen made from a beta titanium system in which a second phase can be precipitated at grain boundaries, thereby revealing the grain shapes. The simple changes introduced to the DCT methodology are equally applicable to other variants of grain mapping.

Complete modal decomposition for optical fibers using CGH-based correlation filters.

Abstract: The description of optical fields in terms of their eigenmodes is an intuitive approach for beam characterization. However, there is a lack of unambiguous, pure experimental methods in contrast to numerical phase-retrieval routines, mainly because of the difficulty to characterize the phase structure properly, e.g. if it contains singularities. This paper presents novel results for the complete modal decomposition of optical fields by using computer-generated holographic filters. The suitability of this method is proven by reconstructing various fields emerging from a weakly multi-mode fiber (V ≈ 5) with arbitrary mode contents. Advantages of this approach are its mathematical uniqueness and its experimental simplicity. The method constitutes a promising technique for real-time beam characterization, even for singular beam profiles.

Three-dimensional visualization of a human chromosome using coherent X-ray diffraction.

Abstract: Coherent x-ray diffraction microscopy is a lensless phase-contrast imaging technique with high image contrast. Although electron tomography allows intensive study of the three-dimensional structure of cellular organelles, it has inherent difficulty with thick objects. X rays have the unique benefit of allowing noninvasive analysis of thicker objects and high spatial resolution. We observed an unstained human chromosome using coherent x-ray diffraction. The reconstructed images in two or three dimensions show an axial structure, which has not been observed under unstained conditions.

Single-shot diffractive imaging with a table-top femtosecond soft x-ray laser-harmonics source.

Abstract: Coherent x-ray diffractive imaging is a powerful method for studies on nonperiodic structures on the nanoscale. Access to femtosecond dynamics in major physical, chemical, and biological processes requires single-shot diffraction data. Up to now, this has been limited to intense coherent pulses from a free electron laser. Here we show that laser-driven ultrashort x-ray sources offer a comparatively inexpensive alternative. We present measurements of single-shot diffraction patterns from isolated nano-objects with a single 20 fs pulse from a table-top high-harmonic x-ray laser. Images were reconstructed with a resolution of 119 nm from the single shot and 62 nm from multiple shots.

New opportunities for 3D materials science of polycrystalline materials at the micrometre lengthscale by combined use of X-ray diffraction and X-ray imaging

Abstract: Non-destructive, three-dimensional (3D) characterization of the grain structure in mono-phase polycrystalline materials is an open challenge in material science. Recent advances in synchrotron based X-ray imaging and diffraction techniques offer interesting possibilities for mapping 3D grain shapes and crystallographic orientations for certain categories of polycrystalline materials. Direct visualisation of the three-dimensional grain boundary network or of two-phase (duplex) grain structures by means of absorption and/or phase contrast techniques may be possible, but is restricted to specific material systems. A recent extension of this methodology, termed X-ray diffraction contrast tomography (DCT), combines the principles of X-ray diffraction imaging, three-dimensional X-ray diffraction microscopy (3DXRD) and image reconstruction from projections. DCT provides simultaneous access to 3D grain shape, crystallographic orientation and local attenuation coefficient distribution. The technique applies to the larger range of plastically undeformed, polycrystalline mono-phase materials, provided some conditions on grain size and texture are fulfilled. The straightforward combination with high-resolution microtomography opens interesting new possibilities for the observation of microstructure related damage and deformation mechanisms in these materials.

Evanescent Bloch waves and the complex band structure of phononic crystals

Abstract: The complex band structure of a phononic crystal is composed of both propagating and evanescent Bloch waves. Evanescent Bloch waves are involved in the diffraction of acoustic phonons at the interfaces of finite phononic crystal structures. They are shown to arise both because of band gaps, where they directly measure the exponential decrease upon transmission, and because of the frustrated nature of higher-order diffracted waves at low frequencies. These diffracted evanescent Bloch waves become propagative as the frequency increases thus populating higher frequency bands. These results should apply as well to any periodic medium supporting the propagation of waves.

A dedicated superbend x-ray microdiffraction beamline for materials, geo-, and environmental sciences at the advanced light source.

Abstract: A new facility for microdiffraction strain measurements and microfluorescence mapping has been built on beamline 12.3.2 at the advanced light source of the Lawrence Berkeley National Laboratory. This beamline benefits from the hard x-radiation generated by a 6 T superconducting bending magnet (superbend). This provides a hard x-ray spectrum from 5 to 22 keV and a flux within a 1 microm spot of approximately 5x10(9) photons/s (0.1% bandwidth at 8 keV). The radiation is relayed from the superbend source to a focus in the experimental hutch by a toroidal mirror. The focus spot is tailored by two pairs of adjustable slits, which serve as secondary source point. Inside the lead hutch, a pair of Kirkpatrick-Baez (KB) mirrors placed in a vacuum tank refocuses the secondary slit source onto the sample position. A new KB-bending mechanism with active temperature stabilization allows for more reproducible and stable mirror bending and thus mirror focusing. Focus spots around 1 microm are routinely achieved and allow a variety of experiments, which have in common the need of spatial resolution. The effective spatial resolution (approximately 0.2 microm) is limited by a convolution of beam size, scan-stage resolution, and stage stability. A four-bounce monochromator consisting of two channel-cut Si(111) crystals placed between the secondary source and KB-mirrors allows for easy changes between white-beam and monochromatic experiments while maintaining a fixed beam position. High resolution stage scans are performed while recording a fluorescence emission signal or an x-ray diffraction signal coming from either a monochromatic or a white focused beam. The former allows for elemental mapping, whereas the latter is used to produce two-dimensional maps of crystal-phases, -orientation, -texture, and -strain/stress. Typically achieved strain resolution is in the order of 5x10(-5) strain units. Accurate sample positioning in the x-ray focus spot is achieved with a commercial laser-triangulation unit. A Si-drift detector serves as a high-energy-resolution (approximately 150 eV full width at half maximum) fluorescence detector. Fluorescence scans can be collected in continuous scan mode with up to 300 pixels/s scan speed. A charge coupled device area detector is utilized as diffraction detector. Diffraction can be performed in reflecting or transmitting geometry. Diffraction data are processed using XMAS, an in-house written software package for Laue and monochromatic microdiffraction analysis.

Super‐Resolution Reactivity Mapping of Nanostructured Catalyst Particles

Abstract: For almost a century, heterogeneous catalysts have been at the heart of countless industrial chemical processes, but their operation at the molecular level is generally much less understood than that of homogeneous catalysts or enzymes. The principal reason is that despite the macroscopic dimensions of solid catalyst particles, their activity seems to be governed by compositional heterogeneities and structural features at the nanoscale. Progress in understanding heterogeneous catalysis thus requires that the nanoscale compositional and structural data be linked with local catalytic activity data, recorded in the same small spatial domains and under in situ reaction conditions. Light microscopy is a recent addition to the toolbox for in situ study of solid catalytic materials. It combines high temporal resolution and sensitivity with considerable specificity in distinguishing reaction products from reagents. However, lens-based microscopes are subjected to light diffraction which limits the optical resolution to 250 nm in the image plane. This resolution is far too limited to resolve the nanosized domains on solid catalysts. Nanometer-accurate localization of single emitters can be achieved by fitting a Gaussian distribution function to the intensity of the observed fluorescence spot (point-spread function, PSF). This method has been used to map out diffusion pathways in mesoporous or clay materials under highly dilute conditions. However, for more concentrated systems, several molecules simultaneously located within a diffraction-limited area cannot be distinguished. Separating the emission of the different fluorescent labels in time, for example by selective photoactivation, solves the problem for imaging of static systems, 13–18] but not when looking at the dynamics of a working catalyst. Herein, we used single catalytic conversions of small fluorogenic reactants, which occurred stochastically on the densely packed active sites of the catalyst, to reconstruct diffraction-unlimited reactivity maps of catalyst particles. As successive catalytic reactions do not overlap in time, one can precisely determine the location of reaction sites that show turnovers at different moments in time, even if the distance between them is only 10 nm (or less, depending on the signal-to-noise ratio), and reconstruct images of catalytically active zones with super-resolution. Although fluorogenic substrates are widely used in singlemolecule enzymology, so far only a few studies have reported single-turnover counting using fluorescence microscopy on solid chemocatalysts. 24, 25] Such studies typically use large polycyclic substrates, which cannot enter the micropores of many heterogeneous catalysts. Hence, similar experiments on microporous materials critically depend on identifying a small reagent that is converted to a product detectable at the single-molecule level. Surprisingly, furfuryl alcohol is such a reagent, and it appears that after acid-catalyzed reaction (see the Supporting Information), the pore-entrapped products are sufficiently fluorescent to be individually observed using a standard microscope equipped with a single excitation source (532 nm diode laser) and sensitive CCD camera (for experimental details, see the Supporting Information). We refer to this novel high-resolution reconstruction method based on catalytic conversion of fluorogenic substrates as NASCA microscopy, or nanometer accuracy by stochastic catalytic reactions microscopy. Figure 1a and b show the concept of NASCA microscopy and a 2D fluorescence intensity image of individual product molecules formed by an acid zeolite crystal, respectively. The fluorescence intensity plot of Figure 1c proves how well the intensity of the individual product molecules allows them to be distinguished from background signals, caused by scatter[*] Dr. M. B. J. Roeffaers, Dr. P. Dedecker, Prof. Dr. J. Hofkens Department of Chemistry, Katholieke Universiteit Leuven Celestijnenlaan 200F, 3001 Heverlee (Belgium) Fax: (+ 32)163-2799 E-mail: johan.hofkens@chem.kuleuven.be

Growth of high-quality SrTiO3 films using a hybrid molecular beam epitaxy approach

Abstract: A hybrid molecular beam epitaxy approach for atomic-layer controlled growth of high-quality SrTiO3 films with scalable growth rates was developed. The approach uses an effusion cell for Sr, a plasma source for oxygen, and a metal-organic source (titanium tetra isopropoxide) for Ti. SrTiO3 films were investigated as a function of cation flux ratio on (001) SrTiO3 and (LaAlO3)0.3(Sr2AlTaO6)0.7 (LSAT) substrates. Growth conditions for stoichiometric insulating films were identified. Persistent (>180 oscillations) reflection high-energy electron diffraction oscillation characteristic of layer-by-layer growth were observed. The full widths at half maximum of x-ray diffraction rocking curves were similar to those of the substrates, i.e., 34 arc sec on LSAT. The film surfaces were nearly ideal with root mean square surface roughness values of less than 0.1 nm. The relationship between surface reconstructions, growth modes, and stoichiometry is discussed.

Apparatus and Method of Measuring a Property of a Substrate

Abstract: The present invention makes the use of measurement of a diffraction spectrum in or near an image plane in order to determine a property of an exposed substrate. In particular, the positive and negative first diffraction orders are separated or diverged, detected and their intensity measured to determine overlay (or other properties) of exposed layers on the substrate.

Structure from fleeting illumination of faint spinning objects in flight

Abstract: Moves are afoot to illuminate particles in flight with powerful X-ray bursts, to determine the structure of single molecules, viruses and nanoparticles. This would circumvent important limitations of current techniques, including the need to condense molecules into pure crystals. Proposals to reconstruct the molecular structure from diffraction ‘snapshots’ of unknown orientation, however, require ∼1,000 times more signal than available from next-generation sources. Using a new approach, we demonstrate the recovery of the structure of a weakly scattering macromolecule at the anticipated next-generation X-ray source intensities. Our work closes a critical gap in determining the structure of single molecules and nanoparticles by X-ray methods, and opens the way to reconstructing the structure of spinning, or randomly oriented objects at extremely low signal levels. An algorithm that reconstructs the structure of an object in flight from the diffraction pattern generated by exposing it to an ultrashort burst of X-rays should enhance the potential of free-electron lasers for studying individual molecules, virus and nanoparticles.

Diffractive Imaging Using Partially Coherent X Rays

Abstract: The measured spatial coherence characteristics of the illumination used in a diffractive imaging experiment are incorporated in an algorithm that reconstructs the complex transmission function of an object from experimental x-ray diffraction data using 1.4 keV x rays. Conventional coherent diffractive imaging, which assumes full spatial coherence, is a limiting case of our approach. Even in cases in which the deviation from full spatial coherence is small, we demonstrate a significant improvement in the quality of wave field reconstructions. Our formulation is applicable to x-ray and electron diffraction imaging techniques provided that the spatial coherence properties of the illumination are known or can be measured.

Surface plasmon Fourier optics

Abstract: Surface plasmons are usually described as surface waves with either a complex wave vector or a complex frequency. When discussing their merits in terms of field confinement or enhancement of the local density of states, controversies have arisen as the results depend on the choice of a complex wave vector or a complex frequency. In particular, the shape of the dispersion curves depends on this choice. In this work, we derive two equivalent vectorial representations of a surface plasmon field using an expansion over surface waves with either a complex wave vector or a complex frequency. These representations can be used to discuss the issue of field confinement and local density of states as they have a nonambiguous relation with the two dispersion relations. They can also be used to account for propagation and diffraction of surface waves. They generalize the scalar approximation often used when discussing surface plasmon diffraction.

Improved precision in strain measurement using nanobeam electron diffraction

Abstract: Improvements in transmission electron microscopy have transformed nanobeam electron diffraction into a simple and powerful technique to measure strain. A Si0.69Ge0.31 layer, grown onto a Si substrate has been used to evaluate the precision and accuracy of the technique. Diffraction patterns have been acquired along a ⟨110⟩ zone axis using a FEI-Titan microscope and have been analyzed using dedicated software. A strain precision of 6×10−4 using a probe size of 2.7 nm with a convergence angle of 0.5 mrad has been reached. The bidimensional distortion tensor in the plane perpendicular to the electron beam has been obtained.