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At least 271 records · Page 15

Mathmatical modeling for diffractive optics

We consider a 'diffractive optic' to be a biperiodic surface separating two half-spaces, each having constant constitutive parameters; within a unit cell of the periodic surface and across the transition zone between the two half-spaces, the constitutive parameters can be a continuous, complex-valued function. Mathematical models for diffractive optics have been developed, and implemented as numerical codes, both for the 'direct' problem and for the 'inverse' problem. In problems of the 'direct' class, the diffractive optic is specified, and the full set of Maxwell's equations is cast in a variational form and solved numerically by a finite element approach. This approach is well-posed in the sense that existence and uniqueness of the solution can be proved and specific convergence conditions can be derived. An example of a metallic grating at a Wood anomaly is presented as a case where other approaches are known to have convergence problems. In problems of the 'inverse' class, some information about the diffracted field (e.g., the far-field intensity) is given, and the problem is to find the periodic structure in some optimal sense. Two approaches are described: phase reconstruction in the far-field approximation; and relaxed optimal design based on the Helmholtz equation. Practical examples are discussed for each approach to the inverse problem, including array generators in the far-field case and antireflective structures for the relaxed optimal design.

Dobson, David↗

Note on use of slope diffraction coefficients for aperture antennas on finite ground planes

The use of slope diffraction coefficients along with regular diffraction coefficients for calculating the radiation patterns of aperture antennas in a finite ground plane is investigated. Explicit expressions for regular diffraction coefficients and slope diffraction coefficients are presented. The expressions for the incident magnetic field in terms of the magnetic current in the aperture are given. The slope of the incident magnetic field is calculated and closed form expressions are presented.

Cockrell, C. R.↗

X-Ray Diffraction Apparatus

An x-ray diffraction apparatus for use in analyzing the x-ray diffraction pattern of a sample is introduced. The apparatus includes a beam source for generating a collimated x-ray beam having one or more discrete x-ray energies, a holder for holding the sample to be analyzed in the path of the beam, and a charge-coupled device having an array of pixels for detecting, in one or more selected photon energy ranges, x-ray diffraction photons produced by irradiating such a sample with said beam. The CCD is coupled to an output unit which receives input information relating to the energies of photons striking each pixel in the CCD, and constructs the diffraction pattern of photons within a selected energy range striking the CCD.

Blake, David F.↗

A Homing Missile Control System to Reduce the Effects of Radome Diffraction

The problem of radome diffraction in radar-controlled homing missiles at high speeds and high altitudes is considered from the point of view of developing a control system configuration which will alleviate the deleterious effects of the diffraction. It is shown that radome diffraction is in essence a kinematic feedback of body angular velocities which causes the radar to sense large apparent line-of-sight angular velocities. The normal control system cannot distinguish between the erroneous and actual line-of-sight rates, and entirely wrong maneuvers are produced which result in large miss distances. The problem is resolved by adding to the control system a special-purpose computer which utilizes measured body angular velocity to extract from the radar output true line-of-sight information for use in steering the missile. The computer operates on the principle of sampling and storing the radar output at instants when the body angular velocity is low and using this stored information for maneuvering commands. In addition, when the angular velocity is not low the computer determines a radome diffraction compensation which is subtracted from the radar output to reduce the error in the sampled information. Analog simulation results for the proposed control system operating in a coplanar (vertical plane) attack indicate a potential decrease in miss distance to an order of magnitude below that for a conventional system. Effects of glint noise, random target maneuvers, initial heading errors, and missile maneuverability are considered in the investigation.

Smith, Gerald L.↗

Rectangular Relief Diffraction Gratings for Coherent Lidar Beam Scanning

The application of specialized rectangular relief transmission gratings to coherent lidar beam scanning is presented. Two types of surface relief transmission grating approaches are studied with an eye toward potential insertion of a constant thickness, diffractive scanner where refractive wedges now exist. The first diffractive approach uses vertically oriented relief structure in the surface of an optical flat; illumination of the diffractive scanner is off-normal in nature. The second grating design case describes rectangular relief structure slanted at a prescribed angle with respect to the surface. In this case, illumination is normal to the diffractive scanner. In both cases, performance predictions for 2.0 micron, circularly polarized light at beam deflection angles of 30 or 45 degrees are presented.

Cole, H. J.↗

Application of Powder Diffraction Methods to the Analysis of Short- and Long-Range Atomic Order in Nanocrystalline Diamond and SiC: The Concept of the Apparent Lattice Parameter (alp)

Two methods of the analysis of powder diffraction patterns of diamond and SiC nanocrystals are presented: (a) examination of changes of the lattice parameters with diffraction vector Q ('apparent lattice parameter', alp) which refers to Bragg scattering, and (b), examination of changes of inter-atomic distances based on the analysis of the atomic Pair Distribution Function, PDF. Application of these methods was studied based on the theoretical diffraction patterns computed for models of nanocrystals having (i) a perfect crystal lattice, and (ii), a core-shell structure, i.e. constituting a two-phase system. The models are defined by the lattice parameter of the grain core, thickness of the surface shell, and the magnitude and distribution of the strain field in the shell. X-ray and neutron experimental diffraction data of nanocrystalline SiC and diamond powders of the grain diameter from 4 nm up to micrometers were used. The effects of the internal pressure and strain at the grain surface on the structure are discussed based on the experimentally determined dependence of the alp values on the Q-vector, and changes of the interatomic distances with the grain size determined experimentally by the atomic Pair Distribution Function (PDF) analysis. The experimental results lend a strong support to the concept of a two-phase, core and the surface shell structure of nanocrystalline diamond and SiC.

Palosz, B.↗

Diffraction and Imaging Study of Imperfections of Protein Crystals with Coherent X-rays

High angular-resolution x-ray diffraction and phase contrast x-ray imaging were combined to study defects and perfection of protein crystals. Imperfections including line defects, inclusions and other microdefects were observed in the diffraction images of a uniformly grown lysozyme crystal. The observed line defects carry distinct dislocation features running approximately along the <110> growth front and have been found to originate mostly in a central growth area and occasionally in outer growth regions. Slow dehydration led to the broadening of a fairly symmetric 4 4 0 rocking curve by a factor of approximately 2.6, which was primarily attributed to the dehydration-induced microscopic effects that are clearly shown in diffraction images. X-ray imaging and diffraction characterization of the quality of apoferritin crystals will also be discussed in the presentation.

Hu, Z. W.↗

Diffraction and imaging study of imperfections of crystallized lysozyme with coherent X-rays

Phase-contrast X-ray diffraction imaging and high-angular-resolution diffraction combined with phase-contrast radiographic imaging were employed to characterize defects and perfection of a uniformly grown tetragonal lysozyme crystal in the symmetric Laue case. The full-width at half-maximum (FWHM) of a 4 4 0 rocking curve measured from the original crystal was approximately 16.7 arcsec and imperfections including line defects, inclusions and other microdefects were observed in the diffraction images of the crystal. The observed line defects carry distinct dislocation features running approximately along the <1 1 0> growth front and have been found to originate mostly in a central growth area and occasionally in outer growth regions. Inclusions of impurities or formations of foreign particles in the central growth region are resolved in the images with high sensitivity to defects. Slow dehydration led to the broadening of a fairly symmetric 4 4 0 rocking curve by a factor of approximately 2.6, which was primarily attributed to the dehydration-induced microscopic effects that are clearly shown in X-ray diffraction images. The details of the observed defects and the significant change in the revealed microstructures with drying provide insight into the nature of imperfections, nucleation and growth, and the properties of protein crystals.

Muramidase/chemistry↗

Synchrotron X-Ray Diffraction Studies of Olivine from Comet Wild 2

We have analyzed a collection of the Comet Wild 2 coma grains returned by the NASA Stardust Mission, using micro-area Laue diffraction equipment. The purpose of the diffraction experiment is to permit the structure refinement of olivine including site occupancies. In addition to the intrinsic importance of the olivine structures for revealing the thermal history of Wild 2 materials, we wish to test reports that olivine recovered after hypervelocity capture in silica aerogel has undergone a basic structural change due to capture heating [1]. The diffraction equipment placed at beam line BL- 4B1 of PF, KEK was developed with a micropinhole and an imaging plate (Fuji Co. Ltd.) using the Laue method combined with polychromatic X-ray of synchrotron radiation operated at energy of 2.5 GeV. The incident beam is limited to 1.6 m in diameter by a micropinhole set just upstream of the sample [2, 3]. It is essential to apply a microbeam to obtain diffracted intensities with high signal to noise ratios. This equipment has been successfully applied to various extraterrestrial materials, including meteorites and interplanetary dust particles [4]. The Laue pattern of the sample C2067,1,111,4 (Fig. 1) was successfully taken on an imaging plate after a 120 minute exposure (Fig. 2).

Source record↗

Focusing Diffraction Grating Element with Aberration Control

Diffraction gratings are optical components with regular patterns of grooves, which angularly disperse incoming light by wavelength in a single plane, called dispersion plane. Traditional gratings on flat substrates do not perform wavefront transformation in the plane perpendicular to the dispersion plane. The device proposed here exhibits regular diffraction grating behavior, dispersing light. In addition, it performs wavelength transformation (focusing or defocusing) of diffracted light in a direction perpendicular to the dispersion plane (called sagittal plane). The device is composed of a diffraction grating with the grooves in the form of equidistant arcs. It may be formed by defining a single arc or an arc approximation, then translating it along a certain direction by a distance equal to a multiple of a fixed distance ("grating period") to obtain other groove positions. Such groove layout is nearly impossible to obtain using traditional ruling methods, such as mechanical ruling or holographic scribing, but is trivial for lithographically scribed gratings. Lithographic scribing is the newly developed method first commercially introduced by LightSmyth Technologies, which produces gratings with the highest performance and arbitrary groove shape/spacing for advanced aberration control. Unlike other types of focusing gratings, the grating is formed on a flat substrate. In a plane perpendicular to the substrate and parallel to the translation direction, the period of the grating and, therefore, the projection of its k-vector onto the plane is the same for any location on the grating surface. In that plane, no waveform transformation by the grating k-vector occurs, except of simple redirection.

Iazikov, Dmitri↗

Transmission X-ray Diffraction (XRD) Patterns Relevant to the MSL Chemin Amorphous Component: Sulfates And Silicates

The Mars Science Laboratory (MSL) CheMin instrument on the Curiosity rover is a transmission X-ray diffractometer (Co-Kalpha radiation source and a approx.5deg to approx.52deg 2theta range) where the analyzed powder samples are constrained to have discrete particle diameters <150 microns by a sieve. To date, diffraction patterns have been obtained for one basaltic soil (Rocknest (RN)) and four drill fines of coherent rock (John Klein (JK), Cumberland (CB), Windjana (WJ), and Confidence Hills (CH)). The CheMin instrument has detected and quantified the abundance of both primary igneous (e.g., feldspar, olivine, and pyroxene) and secondary (e.g., Ca-sulfates, hematite, akaganeite, and Fe-saponite) minerals. The diffraction patterns of all CheMin samples are also characterized by a broad diffraction band centered near 30deg 2theta and by increasing diffraction intensity (scattering continuum) from approx.15deg to approx.5deg, the 2theta minimum. Both the broad band and the scattering continuum are attributed to the presence of an XRD amorphous component. Estimates of amorphous component abundance, based on the XRD data itself and on mass-balance calculations using APXS data crystalline component chemistry derived from XRD data, martian meteorites, and/or stoichiometry [e.g., 6-9], range from approx.20 wt.% to approx.50 wt.% of bulk sample. The APXSbased calculations show that the amorphous component is rich in volatile elements (esp. SO3) and is not simply primary basaltic glass, which was used as a surrogate to model the broad band in the RN CheMin pattern. For RN, the entire volatile inventory (except minor anhydrite) is assigned to the amorphous component because no volatile-bearing crystalline phases were reported within detection limits [2]. For JK and CB, Fesaponite, basanite, and akaganeite are volatile-bearing crystalline components. Here we report transmission XRD patterns for sulfate and silicate phases relevant to interpretation of MSL-CheMin XRD amorphous components.

Morris, R. V.↗

Light Diffraction by Large Amplitude Ultrasonic Waves in Liquids

Light diffraction from ultrasound, which can be used to investigate nonlinear acoustic phenomena in liquids, is reported for wave amplitudes larger than that typically reported in the literature. Large amplitude waves result in waveform distortion due to the nonlinearity of the medium that generates harmonics and produces asymmetries in the light diffraction pattern. For standing waves with amplitudes above a threshold value, subharmonics are generated in addition to the harmonics and produce additional diffraction orders of the incident light. With increasing drive amplitude above the threshold a cascade of period-doubling subharmonics are generated, terminating in a region characterized by a random, incoherent (chaotic) diffraction pattern. To explain the experimental results a toy model is introduced, which is derived from traveling wave solutions of the nonlinear wave equation corresponding to the fundamental and second harmonic standing waves. The toy model reduces the nonlinear partial differential equation to a mathematically more tractable nonlinear ordinary differential equation. The model predicts the experimentally observed cascade of period-doubling subharmonics terminating in chaos that occurs with increasing drive amplitudes above the threshold value. The calculated threshold amplitude is consistent with the value estimated from the experimental data.

Adler, Laszlo↗

Sound Diffraction Modeling of Rotorcraft Noise Around Terrain

A new computational technique, Wave Confinement (WC), is extended here to account for sound diffraction around arbitrary terrain. While diffraction around elementary scattering objects, such as a knife edge, single slit, disc, sphere, etc. has been studied for several decades, realistic environments still pose significant problems. This new technique is first validated against Sommerfeld's classical problem of diffraction due to a knife edge. This is followed by comparisons with diffraction over three-dimensional smooth obstacles, such as a disc and Gaussian hill. Finally, comparisons with flight test acoustics data measured behind a hill are also shown. Comparison between experiment and Wave Confinement prediction demonstrates that a Poisson spot occurred behind the isolated hill, resulting in significantly increased sound intensity near the center of the shadowed region.

Stephenson, James H.↗

Diffraction by Sharp Edges of Noncanonical Shape with Mean Flow and Surface Impedance

This paper presents a study on diffraction by sharp edges of noncanonical edge shape in the presence of mean flow and surface impedance, which are important features for aircraft noise but have not been accounted for in previous studies on sharp-edge diffraction. An analytical formula for the diffracted pressure is derived by applying asymptotic analysis to the integral representation of the total pressure scattered by a geometry that contains sharp edges. The asymptotic analysis is presented as a systematic process that can be carried out to any order, if needed. An illustration is given to use a higher-order result to eliminate the singularity in the first-order result to make the solution regular in the entire parameter domain. The formula for the diffracted pressure is validated by experimental data and is applied to parametric studies to reveal the effects of noncanonical edge shape, mean flow and surface impedance, as well as the impact of these effects on the total scattered pressure in the presence of other scattering components.

Yueping Guo↗

3D Reconstruction of a High-Energy Diffraction Microscopy Sample Using Multi-modal Serial Sectioning with High-Precision EBSD and Surface Profilometry

High-energy diffraction microscopy (HEDM) combined with in situ mechanical testing is a powerful nondestructive technique for tracking the evolving microstructure within polycrystalline materials during deformation. This technique relies on a sophisticated analysis of X-ray diffraction patterns to produce a three-dimensional reconstruction of grains and other microstructural features within the interrogated volume. However, it is known that HEDM can fail to identify certain microstructural features, particularly smaller grains or twinned regions. Characterization of the identical sample volume using high-resolution surface-specific techniques, particularly electron backscatter diffraction (EBSD), can not only provide additional microstructure information about the interrogated volume but also highlight opportunities for improvement of the HEDM reconstruction algorithms. In this study, a sample fabricated from undeformed “low solvus, high refractory” nickel-based superalloy was scanned using HEDM. The volume interrogated by HEDM was then carefully characterized using a combination of surface-specific techniques, including epi-illumination optical microscopy, zero-tilt secondary and backscattered electron imaging, scanning white light interferometry, and high-precision EBSD. Custom data fusion protocols were developed to integrate and align the microstructure maps captured by these surface-specific techniques and HEDM. The raw and processed data from HEDM and serial sectioning have been made available via the Materials Data Facility (MDF) at https://doi.org/10.18126/4y0p-v604 for further investigation.

36 MATERIALS SCIENCE↗

New perspectives on materials and device dynamics using time-resolved full-field diffraction X-ray imaging

Understanding how materials evolve during synthesis, processing, or device operation requires experimental access to structural dynamics across wide ranges of length and time scales, often in bulk samples or even within packaged devices. Time-resolved full-field diffraction X-ray microscopy has recently emerged as a powerful way to meet this need by combining the penetration and structural sensitivity of X-ray diffraction with objective-lens-based magnification, sensitive high-resolution X-ray imaging detectors, and pump-probe and real-time imaging strategies. Advances in full-field X-ray diffraction microscopy, often termed dark-field X-ray microscopy (DFXM), enable simultaneous imaging of extended fields of view while retaining crystallographic selectivity. Time-resolved DFXM promises to enable advances in materials processing and dynamics, electrochemical and photochemical processes, and the design of electronic devices. This Perspective summarizes the key instrumental concepts that define the performance of these methods, including the choice of imaging optics, detector considerations, and the impact of source time structure at synchrotron light sources and X-ray free-electron lasers (XFELs). We discuss the simultaneous use of complementary imaging modes that are increasingly used in practice. The early demonstrations of the potential of time-resolved DFXM include real-time defect and grain-boundary dynamics during metal annealing, stroboscopic imaging of functional devices with high strain sensitivity, and ultrafast pump-probe implementations at XFELs that directly visualize acoustic-wave propagation and energy dissipation in bulk crystals.

Dark-field X-ray microscopy↗

Signatures of electronic and nuclear coherences in ultrafast molecular x-ray and electron diffraction

Femtosecond x-ray and electron diffraction hold promise to image the evolving structures of single molecules. We present a unified quantum-electrodynamical formulation of diffraction signals, based on the exact many-body nuclear + electronic wavefunction that can be extracted from quantum chemistry simulations. This gives a framework for analyzing various approximate molecular dynamics simulations. We show that the complete description of ultrafast diffraction signals contains interesting contributions involving mixed elastic and inelastic scattered photons that are usually masked by other larger contributions and are neglected. These terms include overlaps of nuclear wavepackets between different electronic states that provide an electronic decoherence mechanism and are important for the time-resolved imaging of conical intersections.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Strength of tantalum to 276 GPa determined by two x-ray diffraction techniques using diamond anvil cells

Tantalum (Ta) is a metal that has useful properties that make it useful in extreme environments. It is therefore important to understand how Ta performs in such extreme conditions by accurately measuring its properties. In this work, the yield strength of tantalum has been measured at pressures up to 276 GPa using axial and radial x-ray diffraction (XRD) methods in diamond anvil cells (DAC). We measured strength using XRD in a radial DAC to 50 GPa, in an axial DAC to 60 GPa using diamonds with standard flat culets, and in a final experiment to 276 GPa using toroidal diamond anvils. The radial XRD data were refined using the Material Analysis Using Diffraction (MAUD) Rietveld software package to extract lattice strain and the yield strength. The axial data were refined using the General Structure Analysis System (GSAS) II and a linewidth method was used to calculate the yield strength. The yield strength measured near ambient pressure was found to be 0.5 GPa and increased with pressure up to 50 GPa, where the yield strength plateaued at a value of 2.4 GPa. At pressures above 60 GPa, the strength increased again to a maximum value of 9 GPa at the highest pressure of 276 GPa. Here, the data from the three experiments show good agreement between the methods and previously reported experimental data. This agreement illustrates the value of axial diffraction data for material strength determination and allows for measurements at multihundreds of GPa using toroidal DACs.

36 MATERIALS SCIENCE↗