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At least 127 records · Page 7

Surface wave diffraction by a truncated dielectric slab recessed in a perfectly conducting surface

The diffraction of a TM sub 0 surface wave by a terminated dielectric slab which is flush mounted in a perfectly conducting surface is studied. The incident surface wave gives rise to waves reflected and diffracted by the termination; these reflected and diffracted fields may be expressed in terms of the geometrical theory of diffraction by introducing surface wave reflection and diffraction coefficients which are associated with the termination. In this investigation the surface wave reflection and diffraction coefficients have been deduced from a formally exact solution to this canonical problem. The solution is obtained via a combination of the generalized scattering matrix technique and the Wiener-Hopf procedure. Expressions for the reflection and diffraction coefficients contain integrals which can be evaluated numerically.

Pathak, P. H.↗

Radar cross section of an open-ended circular waveguide Calculation of second-order diffraction terms

The radar cross section of an open-ended, semi-infinite circular waveguide is calculated by the geometrical theory of diffraction and the equivalent-current (EC) method. Both single- and double-diffraction terms are included. It is found that the double-diffraction term is stronger than the single-diffraction term for the horizontal polarization at wide-angle incidence. Its inclusion is necessary in order to check with experimental data and the asymptotic expansion of the exact Wiener-Hopf solution. The EC method is used for the single diffraction. On the other hand the double-diffraction term is obtained by using the EC method for axial incidence and geometrical theory of diffraction for wide-angle incidence. These two solutions are matched with a proper matching function. This technique is computationally more efficient than the matching technique of integration over the equivalent currents.

Lee, C. S.↗

Wavelength-division multiplexed optical integrated circuit with vertical diffraction grating

A semiconductor optical integrated circuit for wave division multiplexing has a semiconductor waveguide layer, a succession of diffraction grating points in the waveguide layer along a predetermined diffraction grating contour, a semiconductor diode array in the waveguide layer having plural optical ports facing the succession of diffraction grating points along a first direction, respective semiconductor diodes in the array corresponding to respective ones of a predetermined succession of wavelengths, an optical fiber having one end thereof terminated at the waveguide layer, the one end of the optical fiber facing the succession of diffraction grating points along a second direction, wherein the diffraction grating points are spatially distributed along the predetermined contour in such a manner that the succession of diffraction grating points diffracts light of respective ones of the succession of wavelengths between the one end of the optical fiber and corresponding ones of the optical ports.

Lang, Robert J.↗

MANN: A program to transfer designs for diffractive optical elements to a MANN photolithographic mask generator

There are two basic areas of interest for diffractive optics. In the first, the property of wavefront division is exploited for achieving optical fanout, analogous to the more familiar electrical fanout of electronic circuitry. The basic problem here is that when using a simple uniform diffraction grating the energy input is divided unevenly among the output beams. The other area of interest is the use of diffractive elements to replace or supplement standard refractive elements such as lenses. Again, local grating variations can be used to control the amount of bending imparted to optical rays, and the efficiency of the diffractive element will depend on how closely the element can be matched to the design requirements. In general, production restrictions limit how closely the element approaches the design, and for the common case of photolithographic production, a series of binary masks is required to achieve high efficiency. The actual design process is much more involved than in the case of elements for optical fanout, as the desired phase of the optical wavefront over some reference plane must be specified and the phase alteration to be introduced at each point by the diffraction element must be known. This generally requires the utilization of a standard optical design program. Two approaches are possible. In the first approach, the diffractive element is treated as a special type of lens and the ordinary optical design equations are used. Optical design programs tend to follow a second approach, namely, using the equations of optical interference derived from holographic theory and then allowing the introduction of phase front corrections in the form of polynomial equations. By using either of these two methods, diffractive elements can be used not only to compensate for distortions such as chromatic or spherical aberration, but also to perform the work of a variety of other optical elements such as null correctors, beam shapers, etc. The main focus of the project described in this report is how the design information from the lens design program is incorporated into the photolithographic process. It is shown that the MANN program, a photolithographic mask generator, fills the need for a link between lens design programs and mask generation controllers.The generated masks can be used to expose a resist-coated substrate which is etched and then must be re-coated, re-exposed, and re-etched for making copies, just as in the electronics industry.

Matthys, Donald R.↗

Transmissive Diffractive Optical Element Solar Concentrators

Solar-thermal-radiation concentrators in the form of transmissive diffractive optical elements (DOEs) have been proposed as alternatives to mirror-type solar concentrators now in use. In comparison with functionally equivalent mirror-type solar concentrators, the transmissive, diffractive solar concentrators would weigh and cost less, and would be subject to relaxed mechanical tolerances. A DOE concentrator would be made from a thin, flat disk or membrane of a transmissive material having a suitable index of refraction. By virtue of its thinness, the DOE concentrator would have an areal mass density significantly less than that of a functionally equivalent conventional mirror. The DOE concentrator would have a relatively wide aperture--characterized by a focal-length/aperture-diameter ratio ('f number') on the order of 1. A kinoform (a surface-relief phase hologram) of high diffractive order would be microfabricated onto one face of the disk. The kinoform (see figure) would be designed to both diffract and refract incident solar radiation onto a desired focal region, without concern for forming an image of the Sun. The high diffractive order of this kinoform (in contradistinction to the low diffractive orders of some other kinoforms) would be necessary to obtain the desired f number of 1, which, in turn, would be necessary for obtaining a desired concentration ratio of 2,500 or greater. The design process of optimizing the concentration ratio of a proposed DOE solar concentrator includes computing convolutions of the optical bandwidth of the Sun with the optical transmission of the diffractive medium. Because, as in the cases of other non-imaging, light-concentrating optics, image quality is not a design requirement, the process also includes trading image quality against concentration ratio. A baseline design for one example calls for an aperture diameter of 1 m. This baseline design would be scalable to a diameter as large as 10 m, or to a smaller diameter for a laboratory test article. Initial calculations have indicated that the characteristics of the test article would be readily scalable to a full-size unit.

Baron, Richard↗

Suppressing Ghost Diffraction in E-Beam-Written Gratings

A modified scheme for electron-beam (E-beam) writing used in the fabrication of convex or concave diffraction gratings makes it possible to suppress the ghost diffraction heretofore exhibited by such gratings. Ghost diffraction is a spurious component of diffraction caused by a spurious component of grating periodicity as described below. The ghost diffraction orders appear between the main diffraction orders and are typically more intense than is the diffuse scattering from the grating. At such high intensity, ghost diffraction is the dominant source of degradation of grating performance. The pattern of a convex or concave grating is established by electron-beam writing in a resist material coating a substrate that has the desired convex or concave shape. Unfortunately, as a result of the characteristics of electrostatic deflectors used to control the electron beam, it is possible to expose only a small field - typically between 0.5 and 1.0 mm wide - at a given fixed position of the electron gun relative to the substrate. To make a grating larger than the field size, it is necessary to move the substrate to make it possible to write fields centered at different positions, so that the larger area is synthesized by "stitching" the exposed fields.

Wilson, Daniel↗

Amorphous Phase Characterization Through X-Ray Diffraction Profile Modeling: Implications for Amorphous Phases in Gale Crater Rocks and Soils

The CheMin X-ray diffraction instrument on the Mars Science Laboratory rover has analyzed 18 rock and soil samples in Gale crater. Diffraction data allow for the identification of major crystalline phases based on the positions and intensities of well-defined peaks and also provides information regarding amorphous and poorly-ordered materials based on the shape and positions of broad scattering humps. The combination of diffraction data, elemental chemistry from APXS (Alpha Particle X-ray Spectrometer) and evolved gas analyses (EGA) from SAM (Sample Analysis at Mars) help constrain possible amorphous materials present in each sample (e.g., glass, opal, iron oxides, sulfates) but are model dependent. We present a novel method to characterize amorphous material in diffraction data and, through this approach, aim to characterize the phases collectively producing the amorphous profiles in CheMin diffraction data. This method may be applied to any diffraction data from samples containing X-ray amorphous materials, not just CheMin datasets, but we re-strict our discussion to Martian-relevant amorphous phases and diffraction data measured by CheMin or CheMin-like instruments.

Achilles, C. N.↗

Multispectral Quantitative Phase Imaging Using a Diffractive Optical Network

As a label‐free imaging technique, quantitative phase imaging (QPI) provides optical path length information of transparent specimens for various applications in biology, materials science, and engineering. Multispectral QPI measures quantitative phase information across multiple spectral bands, permitting the examination of wavelength‐specific phase and dispersion characteristics of samples. Herein, the design of a diffractive processor is presented that can all‐optically perform multispectral quantitative phase imaging of transparent phase‐only objects within a snapshot. The design utilizes spatially engineered diffractive layers, optimized through deep learning, to encode the phase profile of the input object at a predetermined set of wavelengths into spatial intensity variations at the output plane, allowing multispectral QPI using a monochrome focal plane array. Through numerical simulations, diffractive multispectral processors are demonstrated to simultaneously perform quantitative phase imaging at 9 and 16 target spectral bands in the visible spectrum. The generalization of these diffractive processor designs is validated through numerical tests on unseen objects, including thin Pap smear images. Due to its all‐optical processing capability using passive dielectric diffractive materials, this diffractive multispectral QPI processor offers a compact and power‐efficient solution for high‐throughput quantitative phase microscopy and spectroscopy.

36 MATERIALS SCIENCE↗

In situ synchrotron X-ray diffraction analysis of ultrasonically assisted microstructure refinement during laser melting process

This work investigates the effect of ultrasonic treatment (UST) on the microstructure of AA4043 alloy during laser melting process. Here, the study utilizes in situ synchrotron X-ray diffraction (SXRD) and postmortem electron backscatter diffraction (EBSD) techniques to examine the ultrasonic grain refinement mechanism. The SXRD diffraction patterns exhibit higher continuity of major diffraction rings in the UST-test pattern, indicating a more refined grain structure. The presence of new diffraction spots in the post-test diffraction pattern with UST suggests the breakdown of epitaxial growth of columnar dendrites during solidification. Thermal profiles determined by analyzing the lattice parameter evolution show a faster cooling rate with UST. The inverse pole figures and aspect ratio distribution from EBSD reveal that the UST samples exhibit a refined, more equiaxed grain structure along the weld centerline. UST sample also develops more fine-sized low angle grain boundaries (LAGBs). These features offer better hot-cracking resistance in aluminum alloys.

36 MATERIALS SCIENCE↗

Complex-valued universal linear transformations and image encryption using spatially incoherent diffractive networks

As an optical processor, a diffractive deep neural network (D2NN) utilizes engineered diffractive surfaces designed through machine learning to perform all-optical information processing, completing its tasks at the speed of light propagation through thin optical layers. With sufficient degrees of freedom, D2NNs can perform arbitrary complex-valued linear transformations using spatially coherent light. Similarly, D2NNs can also perform arbitrary linear intensity transformations with spatially incoherent illumination; however, under spatially incoherent light, these transformations are nonnegative, acting on diffraction-limited optical intensity patterns at the input field of view. Here, we expand the use of spatially incoherent D2NNs to complex-valued information processing for executing arbitrary complex-valued linear transformations using spatially incoherent light. Through simulations, we show that as the number of optimized diffractive features increases beyond a threshold dictated by the multiplication of the input and output space-bandwidth products, a spatially incoherent diffractive visual processor can approximate any complex-valued linear transformation and be used for all-optical image encryption using incoherent illumination. The findings are important for the all-optical processing of information under natural light using various forms of diffractive surface-based optical processors.

36 MATERIALS SCIENCE↗

Synchrotron X-ray diffraction analysis of constituent phases in transition joint between nickel alloy 738LC and a MnFeCoNiCu alloy

Synchrotron x-ray diffraction (XRD) analysis was performed on transition joints between a single-phase MnFeCoNiCu alloy and Ni-base Alloy 738LC to efficiently identify the constituent phases across the interface, with different levels of material intermixing generated by laser-welding with variable power. Here, the intermixing extent was quantified by postmortem energy dispersive x-ray spectroscopy mapping. Diffraction-based analyses on complex composition spaces with limited prior data present significant challenges because elemental substitution in both disordered and ordered phases is more extensive than in conventional alloy spaces, which may effectuate relatively large shifts in the observed lattice parameters that convolute the analysis. Therefore, thermodynamic simulations and crystallographic literature data were employed to construct a system-specific diffraction library of twelve prospective phases for the composition space investigated. Subsequently, for predicted disordered cubic phases, statistical hard-sphere models were established to estimate the lattice parameters and predict diffraction peak positions for inclusion in the library. The library was then employed to analyze diffraction profiles measured from the variably intermixed transition joints, with focus on accounting for both high and low-intensity peaks. 99.0 % of diffraction peaks with relative intensity greater than 0.001 were assigned to phases from the system-specific library, exemplifying rigorous peak accounting and indicating that no unexpected phases were present. Up to six of the twelve library phases were experimentally found in the transition joints. The lattice parameters predicted by the statistical hard-sphere model based upon thermodynamic simulations agree reasonably well with the measured values for the disordered FCC matrix phase.

36 MATERIALS SCIENCE↗

Quantitative agreement between dynamical rocking curves in ultrafast electron diffraction for x-ray lasers

Electron diffraction through a thin patterned silicon membrane can be used to create complex spatial modulations in electron distributions. By precisely varying parameters such as crystallographic orientation and wafer thickness, the intensity of reflections in the diffraction plane can be controlled and by placing an aperture to block all but one spot, we can form an image with different parts of the patterned membrane, as is done for bright-field imaging in microscopy. The patterned electron beams can then be used to control phase and amplitude of subsequent x-ray emission, enabling novel coherent x-ray methods. Furthermore, the electrons themselves can also be used for femtosecond time resolved diffraction and microscopy. As a first step toward patterned beams, we demonstrate experimentally and through simulation the ability to accurately predict and control diffraction spot intensities. We simulate MeV transmission electron diffraction patterns using the multislice method for various crystallographic orientations of a single crystal Si(001) membrane near beam normal. The resulting intensity maps of the Bragg reflections are compared to experimental results obtained at the Accelerator Structure Test Area Ultrafast Electron Diffraction (ASTA UED) facility at SLAC. Furthermore, the fraction of inelastic and elastic scattering of the initial charge is estimated along with the absorption of the membrane to determine the contrast that would be seen in a patterned version of the Si(001) membrane.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Data-driven analysis of neutron diffraction line profiles: application to plastically deformed Ta

Abstract Non-destructive evaluation of plastically deformed metals, particularly diffraction line profile analysis (DLPA), is valuable both to estimate dislocation densities and arrangements and to validate microstructure-aware constitutive models. To date, the interpretation of whole line diffraction profiles relies on the use of semi-analytical models such as the extended convolutional multiple whole profile (eCMWP) method. This study introduces and validates two data-driven DLPA models to extract dislocation densities from experimentally gathered whole line diffraction profiles. Using two distinct virtual diffraction models accounting for both strain and instrument induced broadening, a database of virtual diffraction whole line profiles of Ta single crystals is generated using discrete dislocation dynamics. The databases are mined to create Gaussian process regression-based surrogate models, allowing dislocation densities to be extracted from experimental profiles. The method is validated against 11 experimentally gathered whole line diffraction profiles from plastically deformed Ta polycrystals. The newly proposed model predicts dislocation densities consistent with estimates from eCMWP. Advantageously, this data driven LPA model can distinguish broadening originating from the instrument and from the dislocation content even at low dislocation densities. Finally, the data-driven model is used to explore the effect of heterogeneous dislocation densities in microstructures containing grains, which may lead to more accurate data-driven predictions of dislocation density in plastically deformed polycrystals.

36 MATERIALS SCIENCE↗

X-ray diffraction strains in laser-ablated aluminum, nickel, sodium, and invar: Pressures to 475 GPa

Dynamically compressed materials in longitudinal waves are described by two physical models: hydrostatic pressure, with equal, normal, principal stresses or material uniaxially strained in the wave propagation direction. These models are disparate, so experimental comparisons and evaluations are important. Polycrystalline material in a state of hydrostatic pressure will have no eccentricity of x-ray-diffracted Debye–Scherrer rings. A general three-dimensional solution of Bragg diffracted x rays based on principal crystallographic strains in the compression wave was found. The distortion of x-ray diffraction beams has been used for strain measurements; the analysis developed incorporates a strained reciprocal lattice and the incident x-ray beam. Strain-distorted Polanyi surfaces form an annulus of compression with an ellipsoid of revolution in reciprocal space, which is intersected by Ewald's sphere for Bragg diffraction. The in situ measurements for strain describe nanosecond diffraction evaluated using two planes, (hkl) and (h′k′l′), both in the same crystallographic phase. Diffraction from Al, Ni, Na, and Invar quantifies the compression axial strains in these materials: The compression axial ratios are 0.65, 1.05, 0.88, and 1.58 at pressures of 291, 402, 409, and 367 GPa for the respective materials. Crystal structure transformations with homogeneous pressurized stresses, mandating equal normal strains, should not be anticipated to agree with heterogeneous, uniaxially strained, and sheared crystalline phases. Measurements support in-plane strains increasing with pressure, p , in fcc and hcp aluminum as ε 22 = −0.21 p /TPa.

Alloys↗

Combined computed tomography and position-resolved X-ray diffraction of an intact Roman-era Egyptian portrait mummy

Hawara Portrait Mummy 4, a Roman-era Egyptian portrait mummy, was studied with computed tomography (CT) and with CT-guided synchrotron X-ray diffraction mapping. These are the first X-ray diffraction results obtained non-invasively from objects within a mummy. The CT data showed human remains of a 5-year-old child, consistent with the female (but not the age) depicted on the portrait. Physical trauma was not evident in the skeleton. Diffraction at two different mummy-to-detector separations allowed volumetric mapping of features including wires and inclusions within the wrappings and the skull and femora. Additionally, the largest uncertainty in origin determination was approximately 1.5 mm along the X-ray beam direction, and diffraction- and CT-determined positions matched. Diffraction showed that the wires were a modern dual-phase steel and showed that the 7 × 5 × 3 mm inclusion ventral of the abdomen was calcite. Tracing the 00.2 and 00.4 carbonated apatite (bone's crystalline phase) reflections back to their origins produced cross-sectional maps of the skull and of femora; these maps agreed with transverse CT slices within approximately 1 mm. Coupling CT and position-resolved X-ray diffraction, therefore, offers considerable promise for non-invasive studies of mummies.

60 APPLIED LIFE SCIENCES↗

One-dimensional neutron diffraction from layered graphite: Reciprocal space structure and grating behavior

In this work we report observations of one-dimensional neutron diffraction from highly oriented pyrolytic graphite (HOPG), where the scattering angle varies continuously with incident angle following classical grating-like behavior. The 2D polycrystalline structure of HOPG—with highly aligned layers along the 𝑐 axis but random in-plane rotations—creates planes of scattering intensity in reciprocal space at 𝑄 𝑐 =𝑛⁢(2⁢𝜋/𝑑) where 𝑑=3.35Å is the interlayer spacing. As the Ewald sphere sweeps through reciprocal space during sample rotation, it continuously intersects these planes, producing the observed angular dispersion. We observe both first-order (𝑛=1) and second-order (𝑛=2) diffraction at conventional scattering angles (25°–70°), with peak positions that remain temperature-independent between 10 K and 294 K and follow quantitative agreement with momentum conservation 𝑄 𝑐 =𝑘⁢[sin⁡𝜓−sin⁡𝜓 𝑓 ]=𝑛⁢(2⁢𝜋/𝑑). X-ray diffraction under similar conditions shows no comparable behavior, confirming that sharp nuclear-vacuum contrast is essential. While diffraction intensities are weak (∼10 −6 of Bragg peaks), the observations demonstrate how the interplay of atomic-scale periodicity, nuclear contrast, and structural disorder enables observation of continuous diffraction curves at thermal neutron wavelengths, illustrating how HOPG's unique microstructure determines its scattering properties beyond conventional Bragg diffraction.

2-dimensional systems↗

Detector Tilt Considerations in Bragg Coherent Diffraction Imaging: A Simulation Study

This paper addresses the three-dimensional signal distortion and image reconstruction issues in X-ray Bragg coherent diffraction imaging (BCDI) in the event of a general non-orthogonal orientation of the area detector with respect to the diffracted beam. Growing interest in novel BCDI adaptations at fourth-generation synchrotron light sources has necessitated improvisations in the experimental configuration and the subsequent data analysis. One such possibly unavoidable improvisation that is envisioned in this paper is a photon-counting area detector whose face is tilted away from the perpendicular to the Bragg-diffracted beam during the acquisition of the coherent diffraction signal. We describe a likely circumstance in which one would require such a detector configuration, along with the experimental precedent at third-generation synchrotrons. Using physically accurate diffraction simulations from synthetic scatterers in the presence of such tilted detectors, we analyze the general nature of the observed signal distortion qualitatively and quantitatively and provide a prescription to correct for it during image reconstruction. Our simulations and reconstructions are based on an adaptation of the known theory of BCDI sampling geometry, as well as the recently developed projection-based methods of wavefield propagation. Such configurational modifications and their numerical remedies are potentially valuable in realizing unconventional coherent diffraction measurement geometries, eventually paving the way for the integration of BCDI into new material characterization experiments at next-generation light sources.

36 MATERIALS SCIENCE↗

Modeling and experimental validation of dynamical effects in Bragg coherent x-ray diffractive imaging of finite crystals

Bragg coherent diffractive imaging (BCDI) is a noninvasive microscopy technique that can visualize the shape and internal lattice deviations of crystals with nanoscale spatial resolution and picometer deformation sensitivity. Its strain imaging capability relies on Fourier transform–based iterative phase retrieval algorithms, which are mostly developed under the kinematical approximation. Such approximation prohibits the application of BCDI on larger crystals, which are commonly seen in most emerging functional materials. Understanding the dynamical effect in BCDI, as well as developing a validated method for modeling BCDI at the dynamical diffraction limit, is crucial for applying BCDI to hierarchical systems that contain micron-sized crystals and grains. Thus we report a comparative study on the impact of dynamical diffraction effects by comparing the reconstruction results from two measurements of the same crystal. Forward simulation is implemented to show subtle changes of interference fringes in the diffraction pattern due to the dynamical diffraction, and is compared directly with the experimental data.

36 MATERIALS SCIENCE↗