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.

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 Optimization of the energy for Breast monochromatic absorption X-ray Computed Tomography

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Pasquale Delogu ◽  
Vittorio Di Trapani ◽  
Luca Brombal ◽  
Giovanni Mettivier ◽  
Angelo Taibi ◽  
...  
Keyword(s):  
Computed Tomography ◽  
Imaging Techniques ◽  
Fixed Dose ◽  
X Rays ◽  
Reconstruction Algorithms ◽  
Contrast Resolution ◽  
X Ray ◽  
X Ray Imaging ◽  
X Ray Computed ◽  
Dose Levels

Abstract The limits of mammography have led to an increasing interest on possible alternatives such as the breast Computed Tomography (bCT). The common goal of all X-ray imaging techniques is to achieve the optimal contrast resolution, measured through the Contrast to Noise Ratio (CNR), while minimizing the radiological risks, quantified by the dose. Both dose and CNR depend on the energy and the intensity of the X-rays employed for the specific imaging technique. Some attempts to determine an optimal energy for bCT have suggested the range 22 keV–34 keV, some others instead suggested the range 50 keV–60 keV depending on the parameters considered in the study. Recent experimental works, based on the use of monochromatic radiation and breast specimens, show that energies around 32 keV give better image quality respect to setups based on higher energies. In this paper we report a systematic study aiming at defining the range of energies that maximizes the CNR at fixed dose in bCT. The study evaluates several compositions and diameters of the breast and includes various reconstruction algorithms as well as different dose levels. The results show that a good compromise between CNR and dose is obtained using energies around 28 keV.

Absorption and secondary scattering of X-rays with an off-axis small beam for a cylindrical sample geometry

2019 ◽  
Vol 75 (2) ◽  
pp. 362-369
Author(s):  
Daniel C. Van Hoesen ◽  
James C. Bendert ◽  
Kenneth F. Kelton
Keyword(s):  
Multiple Scattering ◽  
Incident Beam ◽  
Cylindrical Sample ◽  
X Rays ◽  
Beam Size ◽  
X Ray ◽  
Sample Geometry ◽  
Integral Forms ◽  
Secondary Scattering ◽  
X Ray Absorption

Expressions for X-ray absorption and secondary scattering are developed for cylindrical sample geometries. The incident-beam size is assumed to be smaller than the sample and in general directed off-axis onto the cylindrical sample. It is shown that an offset beam has a non-negligible effect on both the absorption and multiple scattering terms, resulting in an asymmetric correction that must be applied to the measured scattering intensities. The integral forms of the corrections are first presented. A small-beam limit is then developed for easier computation.

scholarly journals Magnetic X-Ray Circular Dichroism in Spin-Polarized Photoelectron Diffraction

1994 ◽  
Vol 375 ◽  
Author(s):  
G. D. Waddill ◽  
J. G. Tobin ◽  
X. Guo ◽  
S. Y. Tong
Keyword(s):  
Magnetic Structure ◽  
Multiple Scattering ◽  
Analytical Procedure ◽  
Structural Determination ◽  
X Rays ◽  
Circularly Polarized ◽  
X Ray ◽  
Photoelectron Diffraction ◽  
Spin Polarized ◽  
Energy Dependent

AbstractThe first structural determination with spin-polarized, energy-dependent photoelectron diffraction using circularly-polarized x-rays is reported for Fe films on Cu(001). Circularly-polarized x-rays produce spin-polarized photoelectrons from the Fe 2p doublet, and intensity asymmetries in the 2p3/2 level are observed. Fully spin-specific multiple scattering calculations reproduce the experimentally-determined energy and angular dependences. A new analytical procedure which focuses upon intensity variations due to spin-dependent diffraction is introduced. A sensitivity to local geometric and magnetic structure is demonstrated.

scholarly journals Timing Analysis with INTEGRAL: Comparing Different Reconstruction Algorithms

10.14311/1312 ◽  
2011 ◽  
Vol 51 (1) ◽  
Author(s):  
V. Grinberg ◽  
I. Kreykenbohm ◽  
F. Fürst ◽  
J. Wilms ◽  
K. Pottschmidt ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Time Resolution ◽  
Timing Analysis ◽  
Light Curves ◽  
X Rays ◽  
Reconstruction Algorithms ◽  
X Ray ◽  
Coded Mask

INTEGRAL is one of the few instruments capable of detecting X-rays above 20 keV. It is therefore in principle well suited for studying X-ray variability in this regime. Because INTEGRAL uses coded mask instruments for imaging, the reconstruction of light curves of X-ray sources is highly non-trivial. We present results from a comparison of two commonly employed algorithms, which primarily measure flux from mask deconvolution (ii_lc_extract) and from calculating the pixel illuminated fraction (ii_light). Both methods agree well for timescales above about 10 s, the highest time resolution for which image reconstruction is possible. For higher time resolution, ii light produces meaningful results, although the overall variance of the lightcurves is not preserved.

scholarly journals A comparative study of the method of Williamson Hall and the pattern of cadmium oxide nanoparticles for X-rays

2021 ◽  
Vol 12 (4) ◽  
pp. 881-889
Author(s):  
Esraa Ahmed Mohammed
Keyword(s):  
Texture Coefficient ◽  
Cadmium Oxide ◽  
Physical Parameters ◽  
X Rays ◽  
Nano Structure ◽  
Crystalline Materials ◽  
X Ray ◽  
Cdo Nanoparticles ◽  
Special Area ◽  
Diffraction Effects

X-ray difraction (XRD) is an effective non-destructive instrument used in the determination and analysis of amorphous and crystalline materials. Three basic elements are the X-ray diffractometers: the X-ray tube, a retention of samples and an X-ray detector. In many industries such as diodes, transistors, detectors, solar and photovoltaic cells, cadmium oxide CdO nanoparticles are used. For this analysis, CdO nanoparticles are semi-conductors (type) and band-gaps of 2.5 eV and 1.98 eV in direct and indirect bands using cadmium oxide. Several temperatures, effects and parameters such as texture coefficient (TC), dislocation density(μ), special area (SSA), and micro strain were measured and determined (S). The peaks of the analysis were the extension of the nano structure, crystal size and grid pressure of the CdO and were measured using the Size Train Plot of Williamson-Hall (SSP). The composition of the particle is the cubic fluorite and spatial group Fm-3m (225). In the peaks resulting from the calcination process, strain enlargement was observed. Accordingly, the above procedure determined all physical parameters as a result of the diffraction effects.

Development of a High-Speed Optical Microscope Auto-Focus Control System for EPMA

1996 ◽  
Vol 54 ◽  
pp. 442-443
Author(s):  
S. Notoya ◽  
M. Saito ◽  
M. Matsuya ◽  
T. Ishii ◽  
K. Murakami ◽  
...  
Keyword(s):  
Control System ◽  
High Speed ◽  
Optical Microscope ◽  
X Rays ◽  
Depth Of Focus ◽  
X Ray ◽  
Simultaneous Acquisition ◽  
New Development ◽  
Electron Probe Microanalyser ◽  
Dimensional Element

This paper reports the new development of an optical microscope automatic focus control system (OMAFD) for the JXA-8800/8900 series Electron Probe Microanalyser (EPMA). In recent years, a method called “wide area mapping” has been increasingly used with EPMA for measurement of X-rays by moving the specimen to obtain 2-dimensional element distributions over large analysis areas. In mapping, the simultaneous acquisition of multiple elements is required. Using an optical microscope, which has a very small (about ±1 μm) depth of focus, the specimen surface needs to be vertically adjusted to the Rowland circle of a wavelength dispersive X-ray spectrometer. Even with flat specimens, actual analysis points often show some inclination. Specimens are often inclined accidentally during sample preparation and mounting. Moreover, requirements of specimen analysis with curved or irregular surfaces have been increasing.

scholarly journals Observation of correlated X-ray scattering at atomic resolution

2014 ◽  
Vol 369 (1647) ◽  
pp. 20130315 ◽  
Author(s):  
Derek Mendez ◽  
Thomas J. Lane ◽  
Jongmin Sung ◽  
Jonas Sellberg ◽  
Clément Levard ◽  
...  
Keyword(s):  
Disordered Systems ◽  
Rational Drug Design ◽  
Three Dimensions ◽  
Atomic Resolution ◽  
Synchrotron Radiation Beam ◽  
X Rays ◽  
Radiation Beam ◽  
X Ray ◽  
X Ray Scattering ◽  
Ray Scattering

Tools to study disordered systems with local structural order, such as proteins in solution, remain limited. Such understanding is essential for e.g. rational drug design. Correlated X-ray scattering (CXS) has recently attracted new interest as a way to leverage next-generation light sources to study such disordered matter. The CXS experiment measures angular correlations of the intensity caused by the scattering of X-rays from an ensemble of identical particles, with disordered orientation and position. Averaging over 15 496 snapshot images obtained by exposing a sample of silver nanoparticles in solution to a micro-focused synchrotron radiation beam, we report on experimental efforts to obtain CXS signal from an ensemble in three dimensions. A correlation function was measured at wide angles corresponding to atomic resolution that matches theoretical predictions. These preliminary results suggest that other CXS experiments on disordered ensembles—such as proteins in solution—may be feasible in the future.

scholarly journals Phase-Contrast and Dark-Field Imaging

2018 ◽  
Vol 4 (10) ◽  
pp. 113
Author(s):  
Simon Zabler
Keyword(s):  
Phase Contrast ◽  
Dark Field ◽  
X Rays ◽  
Reconstruction Algorithms ◽  
Contrast Imaging ◽  
Full Field ◽  
X Ray ◽  
Dark Field Imaging ◽  
Contrast Mechanisms ◽  
Field Imaging

Very early, in 1896, Wilhelm Conrad Röntgen, the founding father of X-rays, attempted to measure diffraction and refraction by this new kind of radiation, in vain. Only 70 years later, these effects were measured by Ulrich Bonse and Michael Hart who used them to make full-field images of biological specimen, coining the term phase-contrast imaging. Yet, another 30 years passed until the Talbot effect was rediscovered for X-radiation, giving rise to a micrograting based interferometer, replacing the Bonse–Hart interferometer, which relied on a set of four Laue-crystals for beam splitting and interference. By merging the Lau-interferometer with this Talbot-interferometer, another ten years later, measuring X-ray refraction and X-ray scattering full-field and in cm-sized objects (as Röntgen had attempted 110 years earlier) became feasible in every X-ray laboratory around the world. Today, now that another twelve years have passed and we are approaching the 125th jubilee of Röntgen’s discovery, neither Laue-crystals nor microgratings are a necessity for sensing refraction and scattering by X-rays. Cardboard, steel wool, and sandpaper are sufficient for extracting these contrasts from transmission images, using the latest image reconstruction algorithms. This advancement and the ever rising number of applications for phase-contrast and dark-field imaging prove to what degree our understanding of imaging physics as well as signal processing have advanced since the advent of X-ray physics, in particular during the past two decades. The discovery of the electron, as well as the development of electron imaging technology, has accompanied X-ray physics closely along its path, both modalities exploring the applications of new dark-field contrast mechanisms these days. Materials science, life science, archeology, non-destructive testing, and medicine are the key faculties which have already integrated these new imaging devices, using their contrast mechanisms in full. This special issue “Phase-Contrast and Dark-field Imaging” gives us a broad yet very to-the-point glimpse of research and development which are currently taking place in this very active field. We find reviews, applications reports, and methodological papers of very high quality from various groups, most of which operate X-ray scanners which comprise these new imaging modalities.

scholarly journals Simultaneous cryo X-ray ptychographic and fluorescence microscopy of green algae

2015 ◽  
Vol 112 (8) ◽  
pp. 2314-2319 ◽  
Author(s):  
Junjing Deng ◽  
David J. Vine ◽  
Si Chen ◽  
Youssef S. G. Nashed ◽  
Qiaoling Jin ◽  
...  
Keyword(s):  
Trace Elements ◽  
Fluorescence Microscopy ◽  
Green Algae ◽  
Element Distribution ◽  
Trace Element Distribution ◽  
X Rays ◽  
Binding Affinities ◽  
Reconstruction Algorithms ◽  
X Ray

Trace metals play important roles in normal and in disease-causing biological functions. X-ray fluorescence microscopy reveals trace elements with no dependence on binding affinities (unlike with visible light fluorophores) and with improved sensitivity relative to electron probes. However, X-ray fluorescence is not very sensitive for showing the light elements that comprise the majority of cellular material. Here we show that X-ray ptychography can be combined with fluorescence to image both cellular structure and trace element distribution in frozen-hydrated cells at cryogenic temperatures, with high structural and chemical fidelity. Ptychographic reconstruction algorithms deliver phase and absorption contrast images at a resolution beyond that of the illuminating lens or beam size. Using 5.2-keV X-rays, we have obtained sub–30-nm resolution structural images and ∼90-nm–resolution fluorescence images of several elements in frozen-hydrated green algae. This combined approach offers a way to study the role of trace elements in their structural context.

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