scholarly journals X-ray focusing by bent crystals: focal positions as predicted by the crystal lens equation and the dynamical diffraction theory

2022 ◽  
Vol 29 (1) ◽  
Author(s):  
Jean-Pierre Guigay ◽  
Manuel Sanchez del Rio
Keyword(s):  
Diffraction Theory ◽  
Dynamical Theory ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Focusing Effect ◽  
Bent Crystal ◽  
Symmetrical Case ◽  
Bent Crystals ◽  
Laue Geometry

The location of the beam focus when monochromatic X-ray radiation is diffracted by a thin bent crystal is predicted by the `crystal lens equation'. This equation is derived in a general form valid for Bragg and Laue geometries. It has little utility for diffraction in Laue geometry. The focusing effect in the Laue symmetrical case is discussed using concepts of dynamical theory and an extension of the lens equation is proposed. The existence of polychromatic focusing is considered and the feasibility of matching the polychromatic and monochromatic focal positions is discussed.

Experimental verification of dynamical diffraction focusing by a bent crystal wedge in Laue geometry

2008 ◽  
Vol 41 (4) ◽  
pp. 695-700 ◽  
Author(s):  
V. Mocella ◽  
C. Ferrero ◽  
J. Hrdý ◽  
J. Wright ◽  
S. Pascarelli ◽  
...  
Keyword(s):  
Experimental Verification ◽  
Theoretical Work ◽  
Suitable Choice ◽  
Crystal Thickness ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Bent Crystal ◽  
Bent Crystals ◽  
Laue Geometry

Recent X-ray optical experiments have validated previous theoretical work on focusing by bent crystals in Laue geometry. It was shown that a suitable choice of the crystal thickness significantly improves the focusing performance of the crystal by combining the dynamical focusing of the Borrmann triangle with the geometrical focusing obtained by the crystal bending. The best focus size achieved during the experiments was less than 5 µm and is in practice limited by the source demagnification for the considered setup.

X-ray interferometer using wavefront division

2003 ◽  
Vol 36 (2) ◽  
pp. 213-219 ◽  
Author(s):  
Hiroshi Yamazaki ◽  
Tetsuya Ishikawa
Keyword(s):  
Interference Pattern ◽  
Coherence Length ◽  
Coherence Function ◽  
Diffraction Theory ◽  
Dynamical Theory ◽  
Time Dependent ◽  
X Rays ◽  
Fringe Spacing ◽  
Dynamical Diffraction ◽  
X Ray

The properties of an X-ray Laue-case wavefront-dividing interferometer have been analysed using time-dependent dynamical diffraction theory. The visibility and the fringe spacing of the interference pattern depend both on the coherence function of the isochronous wavefields on the entrance surface of the interferometer and the spreads of the wavefields into Borrmann fans in the Laue plates. Interference patterns for partially coherent incident X-rays were observed experimentally. The changes of the visibility and of the fringe spacing with respect to the coherence length of the incident X-rays agreed well with the results of the calculations from the dynamical theory.

Dynamical focusing by bent, asymmetrically cut perfect crystals in Laue geometry

2016 ◽  
Vol 72 (4) ◽  
pp. 489-499 ◽  
Author(s):  
J. P. Guigay ◽  
C. Ferrero
Keyword(s):  
Point Source ◽  
Strain Gradient ◽  
Analytical Approach ◽  
Crystal Surface ◽  
Influence Functions ◽  
X Ray ◽  
Bent Crystal ◽  
Straightforward Method ◽  
Bent Crystals ◽  
Laue Geometry

A semi-analytical approach based on the influence functions of a point source located on the crystal surface has been adopted to show that the focusing ability of cylindrically bent Laue crystals may be strongly enhanced by replacing symmetrically cut crystals with asymmetrically cut crystals. This approach is generally applicable to any distance between the X-ray source and the focusing bent crystal. A mathematically straightforward method to simplify the derivation of the already known expression of the influence functions in the case of deformed crystals with a constant strain gradient (e.g.cylindrically bent crystals) is also presented.

X-ray diffraction properties of curved crystal diffractors

1992 ◽  
Vol 50 (2) ◽  
pp. 1734-1735
Author(s):  
W. Z. Chang ◽  
D. B. Wittry
Keyword(s):  
Diffraction Theory ◽  
X Rays ◽  
Diffraction Image ◽  
X Ray Diffraction ◽  
Rocking Curve ◽  
X Ray ◽  
Bent Crystal ◽  
Diffraction Geometry ◽  
Crystal Parameter ◽  
Quantitative Procedure

Since Du Mond and Kirkpatrick first discussed the principle of a bent crystal spectrograph in 1930, curved single crystals have been widely utilized as spectrometric monochromators as well as diffractors for focusing x rays diverging from a point. Curved crystal diffraction theory predicts that the diffraction parameters - the rocking curve width w, and the peak reflection coefficient r of curved crystals will certainly deviate from those of their flat form. Due to a lack of curved crystal parameter data in current literature and the need for optimizing the choice of diffraction geometry and crystal materials for various applications, we have continued the investigation of our technique presented at the last conference. In the present abstract, we describe a more rigorous and quantitative procedure for measuring the parameters of curved crystals.The diffraction image of a singly bent crystal under study can be obtained by using the Johann geometry with an x-ray point source.

scholarly journals Improving the energy resolution of bent crystal X-ray spectrometers with position-sensitive detectors

2014 ◽  
Vol 21 (4) ◽  
pp. 762-767 ◽  
Author(s):  
Ari-Pekka Honkanen ◽  
Roberto Verbeni ◽  
Laura Simonelli ◽  
Marco Moretti Sala ◽  
Ali Al-Zein ◽  
...  
Keyword(s):  
High Resolution ◽  
Internal Stress ◽  
Photon Energy ◽  
Energy Resolution ◽  
Preceding Paper ◽  
X Ray ◽  
Bent Crystal ◽  
Position Sensitive ◽  
Position Sensitive Detectors ◽  
Bent Crystals

Wavelength-dispersive high-resolution X-ray spectrometers often employ elastically bent crystals for the wavelength analysis. In a preceding paper [Honkanenet al.(2014).J. Synchrotron Rad.21, 104–110] a theory for quantifying the internal stress of a macroscopically large spherically curved analyser crystal was presented. Here the theory is applied to compensate for the corresponding decrease of the energy resolution. The technique is demonstrated with a Johann-type spectrometer using a spherically bent Si(660) analyser in near-backscattering geometry, where an improvement in the energy resolution from 1.0 eV down to 0.5 eV at 9.7 keV incident photon energy was observed.

Dynamical Diffraction Effect on Fluorescent X-Ray Emission in Absorbing Perfect Germanium Crystals in the Laue Geometry

1993 ◽  
Vol 62 (2) ◽  
pp. 455-458 ◽  
Author(s):  
Katsuhiro Kaneko ◽  
Yasuji Kashiwase ◽  
Motokazu Kogiso ◽  
Masahiro Mori ◽  
Masayuki Minoura
Keyword(s):  
Diffraction Effect ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Laue Geometry

scholarly journals X-ray microscopy of laser-produced plasmas with the use of bent crystals

1991 ◽  
Vol 9 (1) ◽  
pp. 135-148 ◽  
Author(s):  
E. Förster ◽  
K. Gäbel ◽  
I. Uschmann
Keyword(s):  
Dynamical Theory ◽  
High Luminosity ◽  
Spectral Window ◽  
X Ray ◽  
Lyman Alpha ◽  
Laser Facility ◽  
Spectral Ranges ◽  
Bent Crystals ◽  
Intercombination Line

X-ray spectroscopical and microscopical methods are used for the determination of the spectral and spatial distribution of X-ray intensity of laser-produced plasmas. The use of Bragg reflections of two-dimensionally bent crystals enables the X-ray microscopical imaging in narrow spectral ranges (Δλ/λ = 10−4 to 10−2) with wavelengths 0.1 nm < λ > 2.6 nm. It is possible to adapt, in the X-ray microscope, the distances, magnification, position, and width of the spectral window to the special conditions of the laser facility. Manufacturing and testing of the two-dimensionally bent crystals requires a great deal of effort. It was demonstrated that a spatial resolution of about 5 μm was achieved, and that the experimentally determined reflectivity was found to be in close agreement with the dynamical theory of X-ray interferences. Due to high luminosity of the X-ray microscope, in experiments with laser-produced plasmas it was necessary to attenuate the radiation with aperture-limiting diaphragms or filters down to 0.01–1% of the original intensity in the case of a magnification of about one. Emission of the resonance line W 1–2, the intercombination line of helium-like ions, and Lyman alpha line were imaged simultaneously with a three-channel microscope. Such images form the foundation for establishing the Ne(r), Tz(r) maps.

scholarly journals Spatial displacement of forward-diffracted X-ray beams by perfect crystals

2018 ◽  
Vol 74 (2) ◽  
pp. 75-87
Author(s):  
A. Rodriguez-Fernandez ◽  
V. Esposito ◽  
D. F. Sanchez ◽  
K. D. Finkelstein ◽  
P. Juranic ◽  
...  
Keyword(s):  
Free Electron ◽  
Bragg Reflection ◽  
Diffraction Theory ◽  
Bragg Diffraction ◽  
Transverse Displacement ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Theoretical Predictions ◽  
Thin Crystal ◽  
Good Agreement

Time-delayed, narrow-band echoes generated by forward Bragg diffraction of an X-ray pulse by a perfect thin crystal are exploited for self-seeding at hard X-ray free-electron lasers. Theoretical predictions indicate that the retardation is strictly correlated to a transverse displacement of the echo pulses. This article reports the first experimental observation of the displaced echoes. The displacements are in good agreement with simulations relying on the dynamical diffraction theory. The echo signals are characteristic for a given Bragg reflection, the structure factor and the probed interplane distance. The reported results pave the way to exploiting the signals as an online diagnostic tool for hard X-ray free-electron laser seeding and for dynamical diffraction investigations of strain at the femtosecond timescale.

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