Abstract
We present a fast and accurate method for wave propagation through a set of inclined reflecting planes. It is based on the coordinate transformation in reciprocal space leading to a diffraction integral, which can be calculated only by using two 2D Fast Fourier Transforms and one 2D interpolation. The method is numerically tested, and comparisons with standard methods show its superiority in both computational speed and accuracy. The direct application of this method is found in the X-ray phase contrast imaging using the Bragg magnifier-an optics consisting of crystals asymmetrically diffracting in Bragg geometry.
Highlights
Many applications of electromagnetic radiation rely on the accurate description of the wave propagation through the air or an arbitrary medium
We present a fast and accurate method for wave propagation through a set of inclined reflecting planes
The direct application of this method is found in the X-ray phase contrast imaging using the Bragg magnifier—an optics consisting of crystals asymmetrically diffracting in Bragg geometry
Summary
Many applications of electromagnetic radiation rely on the accurate description of the wave propagation through the air or an arbitrary medium. Another approach based on Rayleigh–Sommerfeld integral was proposed in [6, 7] It uses similar theoretical treatment as presented in this paper with comparable results, and can be viewed as an alternative method for the wave propagation on an inclined plane. Our approach further generalizes the formalism in two ways It provides relationships allowing wave-field propagation through an inclined reflecting plane (see Fig. 1) with the same computational demands as for a propagation on an inclined plane.
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