X-ray two-wave dynamical diffraction analogue of Talbot effect

Abstract

Imaging of periodic objects in free space brings us to the Talbot effect in optics, for x-rays and for matter waves. X-ray dynamical diffraction imaging of periodic objects inside a crystal has scientific and applied interest. Thus, we arrive at the concept of the dynamical diffraction Talbot effect in a crystal. This work is the first attempt to investigate the Talbot effect inside a medium. Using the Green function formalism, an exact formula for the diffracted wave amplitude is found. By means of 'paraxial' approximation, which is an analogue of the paraxial approximation in optics, it is shown that the dynamical diffraction Talbot effect takes place. Expressions for polarization sensitive Talbot and corrected Talbot distances are obtained. We analyse the influences of absorption, Bragg filtration of harmonics and polarization on the dynamical diffraction Talbot effect. For the first time, simulated Talbot carpets inside the crystal are obtained, which show that the predictions, obtained by 'paraxial' approximation, are true. We present the dynamical diffraction Talbot carpets observation method by means of a wedgeshaped crystal. The dynamical diffraction Talbot effect can be used for investigation of objects and crystal defects and deformations. Dynamical diffraction Talbot effect investigations in optics, for electrons and neutrons, are possible.

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

“…Therefore, 0i ( j 0r j and j hi j ( j hr j. It is easy to see that, with the accuracy of the terms hi /| hr | inclusive (Balyan, 2019), the following approximation is valid,…”

“…In the case of -polarization, in the final formulas, h and " h h must be replaced by h cos 2 and " h h cos 2, respectively. According to Balyan (2019), the solution (3) can be presented as…”

“…The condition p 2 nr < 1 of the paraxial approximation, according to definition (15), is equivalent to the condition n 2 < ðD=2Ã r tan Þ 2 . A more accurate analysis, based on the evaluation of the neglected terms (Balyan, 2019), shows that it is sufficient to require the condition…”

“…The integral dynamical diffraction Talbot effect has already been studied by Balyan (2019). We will analyze this effect here based on formulas (28)-(31).…”

“…In the work of Balyan (2019), for the first time the investigation of the X-ray Talbot effect was performed in a perfect crystal under the conditions of two-wave dynamical diffraction. The symmetrical Laue case was considered.…”