scholarly journals Spherical-wave X-ray dynamical diffraction Talbot effect inside a crystal

2020 ◽  
Vol 76 (4) ◽  
pp. 494-502
Author(s):  
Minas K. Balyan ◽  
Levon V. Levonyan ◽  
Karapet G. Trouni
Keyword(s):  
Spherical Wave ◽  
Transmission Function ◽  
Talbot Effect ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Focusing Effect ◽  
Wave Effects ◽  
Focus Point ◽  
Amplitude Transmission

Two-wave dynamical diffraction of an X-ray spherical wave in a crystal, when the wave passes through an object with a periodic amplitude transmission function, is considered. The behavior of the diffracted wave (spherical-wave Talbot effect) in the crystal is investigated. The Talbot effect inside the crystal is accompanied by the focusing effect and the pendulum effect. Peculiarities of the effect before the focus point, in the focusing plane and in the region after the focus point inside the crystal are revealed. An expression is found for the Talbot depth and the spherical-wave Talbot effect in these three regions is investigated. The spherical-wave dynamical diffraction Talbot effect in a crystal is compared with the classical spherical-wave Talbot effect and also with spherical-wave effects inside the crystal without a periodic object.

Numerical reconstruction of an object image using an X-ray dynamical diffraction Fraunhofer hologram

2013 ◽  
Vol 21 (1) ◽  
pp. 127-130 ◽  
Author(s):  
Minas K. Balyan
Keyword(s):  
Transmission Coefficient ◽  
Analytical Approximation ◽  
Object Image ◽  
Resolution Limit ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Numerical Reconstruction ◽  
Complex Transmission ◽  
Amplitude Transmission

A numerical method of reconstruction of an object image using an X-ray dynamical diffraction Fraunhofer hologram is presented. Analytical approximation methods and numerical methods of iteration are discussed. An example of a reconstruction of an image of a cylindrical beryllium wire is considered. The results of analytical approximation and zero-order iteration coincide with exact values of the amplitude complex transmission coefficient of the object as predicted by the resolution limit of the scheme, except near the edges of the object. Calculations of the first- and second-order iterations improve the result at the edges of the object. This method can be applied for determination of the complex amplitude transmission coefficient of amplitude as well as phase objects. It can be used in X-ray microscopy.

Computer simulations of X-ray spherical wave dynamical diffraction in one and two crystals in the Laue case

2018 ◽  
Vol 74 (6) ◽  
pp. 699-704 ◽  
Author(s):  
V. G. Kohn ◽  
I. A. Smirnova
Keyword(s):  
Single Crystals ◽  
Computer Simulations ◽  
Integral Intensity ◽  
Spherical Wave ◽  
Secondary Source ◽  
Weak Absorption ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Spherical Waves ◽  
Energy Spectrometer

This article reports computer simulations of X-ray spherical wave dynamical diffraction in one and two single crystals in the Laue case. An X-ray compound refractive lens (CRL) as a secondary radiation source of spherical waves was considered for the first time and in contrast to previous simulations with the assumption of the use of a slit. The main properties of the CRL as a secondary source are discussed and two focusing phenomena are analysed. The first one is the diffraction focusing effect for one single crystal in the reflected beam and in the case of a large source-to-detector distance. The second one is the same but for two single crystals and for the twice-reflected beam in the case of a short distance between the source and detector. The first effect is well pronounced in the case of strong absorption. However, it may also be used as an element of an energy spectrometer in the medium and even weak absorption case. The second effect will appear in the case of weak absorption. It is shown that it is not effective to use it in an energy spectrometer. In the case of weak absorption the transverse size of the diffraction focused beam will oscillate together with the reflected beam integral intensity. The oscillation period is close to the extinction length.

X-ray dynamical diffraction analogues of the integer and fractional Talbot effects

2019 ◽  
Vol 26 (5) ◽  
pp. 1650-1659 ◽  
Author(s):  
Minas K. Balyan
Keyword(s):  
Perfect Crystal ◽  
Talbot Effect ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Dispersion Branch ◽  
Talbot Distance ◽  
Rational Multiple ◽  
Talbot Effects ◽  
First Time ◽  
Initial Distributions

The X-ray integer and fractional Talbot effect is studied under two-wave dynamical diffraction conditions in a perfect crystal, for the symmetrical Laue case of diffraction. The fractional dynamical diffraction Talbot effect is studied for the first time. A theory of the dynamical diffraction integer and fractional Talbot effect is given, introducing the dynamical diffraction comb function. An expression for the dynamical diffraction polarization-sensitive Talbot distance is established. At the rational multiple depths of the Talbot depth the wavefield amplitude for each dispersion branch is a coherent sum of the initial distributions, shifted by rational multiples of the object period and having its own phases. The simulated dynamical diffraction Talbot carpet for the Ronchi grating is presented.

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.

X-ray dynamical diffraction Talbot effect behind a crystal in free space

2021 ◽  
Vol 77 (2) ◽  
pp. 149-159
Author(s):  
Minas Balyan ◽  
Levon Levonyan ◽  
Karapet Trouni
Keyword(s):  
Plane Wave ◽  
Free Space ◽  
Fourier Spectrum ◽  
Structural Defects ◽  
Bragg Angle ◽  
Talbot Effect ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Talbot Distance ◽  
Before And After

The dynamical diffraction Talbot effect takes place inside a crystal, when a periodic object is illuminated by a plane or spherical X-ray wave which then falls on the crystal at an angle close to the Bragg angle for some reflection. Both theoretical consideration and numerical calculations show that the dynamical diffraction Talbot effect also takes place behind the crystal. The effect is accompanied by the dynamical diffraction pendulum effect and wave focusing. Expressions are found for the dynamical diffraction Talbot distance for areas before and after focusing. The spatial Fourier spectrum of the periodic object is obtained on the focusing plane. Detailed analysis when the periodic object is illuminated by a plane wave has shown new features of this effect. The dynamical diffraction Talbot effect in free space can be used to determine the structure of a periodic object, to determine the structure of an arbitrary object placed before or after the periodic object, and to determine structural defects and deformations of the crystal.

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