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X-ray wavefront modeling of Bragg diffraction from crystals

DOI: 10.1117/12.892697 DOI Help

Authors: John Sutter (Diamond Light Source)
Co-authored by industrial partner: No

Type: Conference Paper
Conference: Advances in Computational Methods for X-Ray Optics II
Peer Reviewed: No

State: Published (Approved)
Published: September 2011

Abstract: The diffraction of an X-ray wavefront from a slightly distorted crystal can be modeled by the Takagi-Taupin theory, an extension of the well-known dynamical diffraction theory for perfect crystals. Maxwell's equations applied to a perturbed periodic medium yield two coupled differential equations in the incident and diffracted amplitude. These equations are discretized for numerical calculation into the determination of the two amplitudes on the points of an integration mesh, beginning with the incident amplitudes at the crystal's top surface. The result is a set of diffracted amplitudes on the top surface (in the Bragg geometry) or the bottom surface (in the Laue geometry), forming a wavefront that in turn can be propagated through free space using the Fresnel- Huygens equations. The performance of the Diamond Light Source I20 dispersive spectrometer has here been simulated using this method. Methods are shown for transforming displacements calculated by finite element analysis into local lattice distortions, and for efficiently performing 3-D linear interpolations from these onto the Takagi-Taupin integration mesh, allowing this method to be extended to crystals under thermal load or novel mechanical bender designs.

Journal Keywords: X-Ray; Wavefront; Propagation; Crystal; Takagi-Taupin; Numerical

Subject Areas: Technique Development

Technical Areas: Optics