X-Ray Dynamical Diffraction Analogue of Talbot Effect in Case of Incident Finite Front Wave

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.

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

Journal of Synchrotron Radiation ◽

10.1107/s1600577519009196 ◽

2019 ◽

Vol 26 (5) ◽

pp. 1650-1659 ◽

Cited By ~ 1

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.

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An X-Ray Dynamical Diffraction Analogue of Talbot Effect in the Transmitted Beam

Journal of Contemporary Physics (Armenian Academy of Sciences) ◽

10.3103/s1068337219030046 ◽

2019 ◽

Vol 54 (3) ◽

pp. 253-261 ◽

Cited By ~ 1

Author(s):

M. K. Balyan

Keyword(s):

Talbot Effect ◽

Transmitted Beam ◽

Dynamical Diffraction ◽

X Ray

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

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s2053273321001029 ◽

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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