Diffraction

2002 ◽  
Author(s):  
David Blow
Keyword(s):  
Red Light ◽  
Three Dimensional ◽  
Three Dimensions ◽  
X Rays ◽  
X Ray ◽  
Original Direction ◽  
Computational Procedures ◽  
Scattering Material ◽  
Opaque Object ◽  
Diffraction Effects

Diffraction refers to the effects observed when light is scattered into directions other than the original direction of the light, without change of wavelength. An X-ray photon may interact with an electron and set the electron oscillating with the X-ray frequency. The oscillating electron may radiate an X-ray photon of the same wavelength, in a random direction, when it returns to its unexcited state. Other processes may also occur, akin to fluorescence, which emit X-rays of longer wavelengths, but these processes do not give diffraction effects. Just as we see a red card because red light is scattered off the card into our eyes, objects are observed with X-rays because an illuminating X-ray beam is scattered into the X-ray detector. Our eye can analyse details of the card because its lens forms an image on the retina. Since no X-ray lens is available, the scattered X-ray beam cannot be converted directly into an image. Indirect computational procedures have to be used instead. X-rays are penetrating radiation, and can be scattered from electrons throughout the whole scattering object, while light only shows the external shape of an opaque object like a red card. This allows X-rays to provide a truly three-dimensional image. When X-rays pass near an atom, only a tiny fraction of them is scattered: most of the X-rays pass further into the object, and usually most of them come straight out the other side of the whole object. In forming an image, these ‘straight through’ X-rays tell us nothing about the structure, and they are usually captured by a beam stop and ignored. This chapter begins by explaining that the diffraction of light or X-rays can provide a precise physical realization of Fourier’s method of analysing a regularly repeating function. This method may be used to study regularly repeating distributions of scattering material. Beginning in one dimension, examples will be used to bring out some fundamental features of diffraction analysis. Graphic examples of two-dimensional diffraction provide further demonstrations. Although the analysis in three dimensions depends on exactly the same principles, diffraction by a three-dimensional crystal raises additional complications.

scholarly journals Three dimensions, two microscopes, one code: Automatic differentiation for x-ray nanotomography beyond the depth of focus limit

2020 ◽  
Vol 6 (13) ◽  
pp. eaay3700 ◽  
Author(s):  
Ming Du ◽  
Youssef S. G. Nashed ◽  
Saugat Kandel ◽  
Doğa Gürsoy ◽  
Chris Jacobsen
Keyword(s):  
Multiple Scattering ◽  
Automatic Differentiation ◽  
Optimization Problems ◽  
Three Dimensions ◽  
Reconstruction Method ◽  
X Rays ◽  
Reconstruction Algorithms ◽  
Depth Of Focus ◽  
X Ray ◽  
Diffraction Effects

Conventional tomographic reconstruction algorithms assume that one has obtained pure projection images, involving no within-specimen diffraction effects nor multiple scattering. Advances in x-ray nanotomography are leading toward the violation of these assumptions, by combining the high penetration power of x-rays, which enables thick specimens to be imaged, with improved spatial resolution that decreases the depth of focus of the imaging system. We describe a reconstruction method where multiple scattering and diffraction effects in thick samples are modeled by multislice propagation and the 3D object function is retrieved through iterative optimization. We show that the same proposed method works for both full-field microscopy and for coherent scanning techniques like ptychography. Our implementation uses the optimization toolbox and the automatic differentiation capability of the open-source deep learning package TensorFlow, demonstrating a straightforward way to solve optimization problems in computational imaging with flexibility and portability.

scholarly journals Utilizing broadband X-rays in a Bragg coherent X-ray diffraction imaging experiment

2016 ◽  
Vol 23 (5) ◽  
pp. 1241-1244 ◽  
Author(s):  
Wonsuk Cha ◽  
Wenjun Liu ◽  
Ross Harder ◽  
Ruqing Xu ◽  
Paul H. Fuoss ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Three Dimensions ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Individual Crystal ◽  
Sample Motion ◽  
Diffraction Imaging ◽  
Individual Grains

A method is presented to simplify Bragg coherent X-ray diffraction imaging studies of complex heterogeneous crystalline materials with a two-stage screening/imaging process that utilizes polychromatic and monochromatic coherent X-rays and is compatible within situsample environments. Coherent white-beam diffraction is used to identify an individual crystal particle or grain that displays desired properties within a larger population. A three-dimensional reciprocal-space map suitable for diffraction imaging is then measured for the Bragg peak of interest using a monochromatic beam energy scan that requires no sample motion, thus simplifyingin situchamber design. This approach was demonstrated with Au nanoparticles and will enable, for example, individual grains in a polycrystalline material of specific orientation to be selected, then imaged in three dimensions while under load.

scholarly journals Is Micro X-ray Computer Tomography a Suitable Non-Destructive Method for the Characterisation of Dental Materials?

Polymers ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1271
Author(s):  
Andreas Koenig ◽  
Leonie Schmohl ◽  
Johannes Scheffler ◽  
Florian Fuchs ◽  
Michaela Schulz-Siegmund ◽  
...  
Keyword(s):  
Flexural Strength ◽  
Computer Tomography ◽  
Mechanical Performance ◽  
Dental Materials ◽  
Three Dimensional ◽  
X Rays ◽  
Scanning Calorimetry ◽  
X Ray ◽  
Multiple Measurements ◽  
High Doses

The aim of the study was to investigate the effect of X-rays used in micro X-ray computer tomography (µXCT) on the mechanical performance and microstructure of a variety of dental materials. Standardised bending beams (2 × 2 × 25 mm3) were forwarded to irradiation with an industrial tomograph. Using three-dimensional datasets, the porosity of the materials was quantified and flexural strength was investigated prior to and after irradiation. The thermal properties of irradiated and unirradiated materials were analysed and compared by means of differential scanning calorimetry (DSC). Single µXCT measurements led to a significant decrease in flexural strength of polycarbonate with acrylnitril-butadien-styrol (PC-ABS). No significant influence in flexural strength was identified for resin-based composites (RBCs), poly(methyl methacrylate) (PMMA), and zinc phosphate cement (HAR) after a single irradiation by measurement. However, DSC results suggest that changes in the microstructure of PMMA are possible with increasing radiation doses (multiple measurements, longer measurements, higher output power from the X-ray tube). In summary, it must be assumed that X-ray radiation during µXCT measurement at high doses can lead to changes in the structure and properties of certain polymers.

Visualizing Fluid Flows With X-Rays

2007 ◽  
Author(s):  
Theodore J. Heindel ◽  
Terrence C. Jensen ◽  
Joseph N. Gray
Keyword(s):  
Computed Tomography ◽  
Flow Visualization ◽  
Three Dimensional ◽  
Fluid Flows ◽  
X Rays ◽  
Radiographic Images ◽  
Optical Access ◽  
X Ray ◽  
X Ray Computed ◽  
Density Map

There are several methods available to visualize fluid flows when one has optical access. However, when optical access is limited to near the boundaries or not available at all, alternative visualization methods are required. This paper will describe flow visualization using an X-ray system that is capable of digital X-ray radiography, digital X-ray stereography, and digital X-ray computed tomography (CT). The unique X-ray flow visualization facility will be briefly described, and then flow visualization of various systems will be shown. Radiographs provide a two-dimensional density map of a three dimensional process or object. Radiographic images of various multiphase flows will be presented. When two X-ray sources and detectors simultaneously acquire images of the same process or object from different orientations, stereographic imaging can be completed; this type of imaging will be demonstrated by trickling water through packed columns and by absorbing water in a porous medium. Finally, local time-averaged phase distributions can be determined from X-ray computed tomography (CT) imaging, and this will be shown by comparing CT images from two different gas-liquid sparged columns.

Recent Developments In Monochromatic Microprobe X-Ray Fluorescence (MMXRF)

1998 ◽  
Vol 4 (S2) ◽  
pp. 378-379
Author(s):  
Z. W. Chen ◽  
D. B. Wittry
Keyword(s):  
Materials Science ◽  
High Vacuum ◽  
Three Dimensional ◽  
High Sensitivity ◽  
X Rays ◽  
Fluorescence Excitation ◽  
X Ray ◽  
Quantitative Microanalysis ◽  
Recent Developments ◽  
Fifth Order

A monochromatic x-ray microprobe based on a laboratory source has recently been developed in our laboratory and used for fluorescence excitation. This technique provides high sensitivity (ppm to ppb), nondestructive, quantitative microanalysis with minimum sample preparation and does not require a high vacuum specimen chamber. It is expected that this technique (MMXRF) will have important applications in materials science, geological sciences and biological science.Three-dimensional focusing of x-rays can be obtained by using diffraction from doubly curved crystals. In our MMXRF setup, a small x-ray source was produced by the bombardment of a selected target with a focused electron beam and a toroidal mica diffractor with Johann pointfocusing geometry was used to focus characteristic x-rays from the source. In the previous work ∼ 108 photons/s were obtained in a Cu Kα probe of 75 μm × 43 μm in the specimen plane using the fifth order reflection of the (002) planes of mica.

scholarly journals Hard X-ray polarizer to enable simultaneous three-dimensional nanoscale imaging of magnetic structure and lattice strain

2016 ◽  
Vol 23 (5) ◽  
pp. 1210-1215 ◽  
Author(s):  
Jonathan Logan ◽  
Ross Harder ◽  
Luxi Li ◽  
Daniel Haskel ◽  
Pice Chen ◽  
...  
Keyword(s):  
Magnetic Circular Dichroism ◽  
Three Dimensional ◽  
Control Sample ◽  
Magnetic Ordering ◽  
X Rays ◽  
Diffractive Imaging ◽  
X Ray ◽  
Coherent Diffractive Imaging ◽  
Diffraction Patterns ◽  
A New Technique

Recent progress in the development of dichroic Bragg coherent diffractive imaging, a new technique for simultaneous three-dimensional imaging of strain and magnetization at the nanoscale, is reported. This progress includes the installation of a diamond X-ray phase retarder at beamline 34-ID-C of the Advanced Photon Source. The performance of the phase retarder for tuning X-ray polarization is demonstrated with temperature-dependent X-ray magnetic circular dichroism measurements on a gadolinium foil in transmission and on a Gd5Si2Ge2crystal in diffraction geometry with a partially coherent, focused X-ray beam. Feasibility tests for dichroic Bragg coherent diffractive imaging are presented. These tests include (1) using conventional Bragg coherent diffractive imaging to determine whether the phase retarder introduces aberrations using a nonmagnetic gold nanocrystal as a control sample, and (2) collecting coherent diffraction patterns of a magnetic Gd5Si2Ge2nanocrystal with left- and right-circularly polarized X-rays. Future applications of dichroic Bragg coherent diffractive imaging for the correlation of strain and lattice defects with magnetic ordering and inhomogeneities are considered.

scholarly journals Synchrotron radiation X-ray tomographic microscopy (SRXTM) of brachiopod shell interiors for taxonomy: Preliminary report

2010 ◽  
pp. 109-117 ◽  
Author(s):  
Neda Motchurova-Dekova ◽  
David Harper
Keyword(s):  
Synchrotron Radiation ◽  
Three Dimensional ◽  
X Rays ◽  
X Ray ◽  
Fine Grained ◽  
Internal Structures ◽  
Efficient Alternative ◽  
Micro Tomography ◽  
Light Beams ◽  
Non Destructive

Synchrotron radiation X-ray tomographic microscopy (SRXTM) is a non-destructive technique for the investigation and visualization of the internal features of solid opaque objects, which allows reconstruction of a complete three-dimensional image of internal structures by recording of the differences in the effects on the passage of waves of energy reacting with those structures. Contrary to X-rays, produced in a conventional X-ray tube, the intense synchrotron light beams are sharply focused like a laser beam. We report encouraging results from the use of SRXTM for purely taxonomic purposes in brachiopods: an attempt to find a non-destructive and more efficient alternative to serial sectioning and several other methods of dissection together with the non-destructive method of X-ray computerised micro-tomography. Two brachiopod samples were investigated using SRXTM. In ?Rhynchonella? flustracea it was possible to visualise the 3D shape of the crura and dental plates. In Terebratulina imbricata it was possible to reveal the form of the brachidium. It is encouraging that we have obtained such promising results using SRXTM with our very first two fortuitous samples, which had respectively fine-grained limestone and marl as infilling sediment, in contrast to the discouraging results communicated to us by some colleagues who have tested specimens with such infillings using X-ray micro-tomography. In future the holotypes, rare museum specimens or delicate Recent material may be preferentially subjected to this mode of analysis.

scholarly journals Three-dimensional propagation in near-field tomographic X-ray phase retrieval

2016 ◽  
Vol 72 (2) ◽  
pp. 215-221 ◽  
Author(s):  
Aike Ruhlandt ◽  
Tim Salditt
Keyword(s):  
Phase Retrieval ◽  
Near Field ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Current Phase ◽  
Computationally Efficient ◽  
X Ray ◽  
Reconstruction Quality ◽  
Consistency Constraints

This paper presents an extension of phase retrieval algorithms for near-field X-ray (propagation) imaging to three dimensions, enhancing the quality of the reconstruction by exploiting previously unused three-dimensional consistency constraints. The approach is based on a novel three-dimensional propagator and is derived for the case of optically weak objects. It can be easily implemented in current phase retrieval architectures, is computationally efficient and reduces the need for restrictive prior assumptions, resulting in superior reconstruction quality.

Three-dimensional X-ray diffraction imaging of process-induced dislocation loops in silicon

2011 ◽  
Vol 44 (3) ◽  
pp. 526-531 ◽  
Author(s):  
David Allen ◽  
Jochen Wittge ◽  
Jennifer Stopford ◽  
Andreas Danilewsky ◽  
Patrick McNally
Keyword(s):  
Semiconductor Industry ◽  
Three Dimensional ◽  
Crystal Defects ◽  
Three Dimensions ◽  
Dimensional Structure ◽  
Dislocation Loops ◽  
X Ray Diffraction ◽  
X Ray ◽  
Diffraction Imaging ◽  
Relationship Of

In the semiconductor industry, wafer handling introduces micro-cracks at the wafer edge and the causal relationship of these cracks to wafer breakage is a difficult task. By way of understanding the wafer breakage process, a series of nano-indents were introduced both into 20 × 20 mm (100) wafer pieces and into whole wafers as a means of introducing controlled strain. Visualization of the three-dimensional structure of crystal defects has been demonstrated. The silicon samples were then treated by various thermal anneal processes to initiate the formation of dislocation loops around the indents. This article reports the three-dimensional X-ray diffraction imaging and visualization of the structure of these dislocations. A series of X-ray section topographs of both the indents and the dislocation loops were taken at the ANKA Synchrotron, Karlsruhe, Germany. The topographs were recorded on a CCD system combined with a high-resolution scintillator crystal and were measured by repeated cycles of exposure and sample translation along a direction perpendicular to the beam. The resulting images were then rendered into three dimensions utilizing open-source three-dimensional medical tomography algorithms that show the dislocation loops formed. Furthermore this technique allows for the production of a video (avi) file showing the rotation of the rendered topographs around any defined axis. The software also has the capability of splitting the image along a segmentation line and viewing the internal structure of the strain fields.

Diffraction by crystals

2002 ◽  
Author(s):  
David Blow
Keyword(s):  
Fourier Transform ◽  
Three Dimensional ◽  
Incident Beam ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Dimensional Structure ◽  
Angle Of Incidence ◽  
X Ray ◽  
Max Von Laue ◽  
The Fourier Transform

In Chapter 4 many two-dimensional examples were shown, in which a diffraction pattern represents the Fourier transform of the scattering object. When a diffracting object is three-dimensional, a new effect arises. In diffraction by a repetitive object, rays are scattered in many directions. Each unit of the lattice scatters, but a diffracted beam arises only if the scattered rays from each unit are all in phase. Otherwise the scattering from one unit is cancelled out by another. In two dimensions, there is always a direction where the scattered rays are in phase for any order of diffraction (just as shown for a one-dimensional scatterer in Fig. 4.1). In three dimensions, it is only possible for all the points of a lattice to scatter in phase if the crystal is correctly oriented in the incident beam. The amplitudes and phases of all the scattered beams from a three-dimensional crystal still provide the Fourier transform of the three-dimensional structure. But when a crystal is at a particular angular orientation to the X-ray beam, the scattering of a monochromatic beam provides only a tiny sample of the total Fourier transform of its structure. In the next section, we are going to find what is needed to allow a diffracted beam to be generated. We shall follow a treatment invented by Lawrence Bragg in 1913. Max von Laue, who discovered X-ray diffraction in 1912, used a different scheme of analysis; and Paul Ewald introduced a new way of looking at it in 1921. These three methods are referred to as the Laue equations, Bragg’s law and the Ewald construction, and they give identical results. All three are described in many crystallographic text books. Bragg’s method is straightforward, understandable, and suffices for present needs. I had heard J.J. Thomson lecture about…X-rays as very short pulses of radiation. I worked out that such pulses…should be reflected at any angle of incidence by the sheets of atoms in the crystal as if these sheets were mirrors.…It remained to explain why certain of the atomic mirrors in the zinc blende [ZnS] crystal reflected more powerfully than others.

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