Three-dimensional model of a split-crystal X-ray and neutron interferometer

Abstract

The observation of neutron interference using a crystal interferometer having a separate analyser opens the way to the construction and operation of interferometers with vast arm separation and length. Setting the design specifications requires a three-dimensional dynamical theory model of their operation. This paper develops the required three-dimensional mathematical framework, which also comprises coherent and incoherent illuminations; it is applied to study the visibility of the interference fringes.

Crystal bending in triple-Laue X-ray interferometry. Part I. Theory

“…It is seen in the p term in the argument of the reflection and transmission coefficients, which now depend on the X-ray incidence point. When scanning the X-ray incidence point, this misalignment mimics a continuous rotation of the crystal and it is equivalent to misalignments investigated by Mana & Vittone (1997a,b) and Sasso et al (2022). The implied phase changes are very small in all practical cases.…”

“…In this paper, we consider only the propagation of the coherent single-photon state (2). The averaging over their probabilistic superposition can be done by the density matrix formalism, as shown by Sasso et al (2022).…”

“…We limit this study to crystals that are symmetrically cut and plane parallel. This choice makes the X-ray propagation two dimensional and dependent only on the inward normal ẑ z to the crystal surfaces and an x coordinate that we choose opposite the reciprocal vector h 0 ¼ À2x x=d 0 , where d 0 is the spacing of the diffracting planes of the unstrained crystals (Mana & Palmisano, 2004;Sasso et al, 2022).…”

“…u ¼ # 0 z, then Á g and q t are equal to zero and g ¼ h 0 , Á u ¼ u ¼ # 0 t=2 and p ¼ 0 K z . Therefore, the scattering matrix ( 14) reduces to that given by Sasso et al (2022) to account for a tilted crystal.…”

Crystal bending in triple-Laue X-ray interferometry. Part II. Phase-contrast topography

“…In turn, these differences cause optical path differences and raise questions about source coherence. Investigations would require extending the two-dimensional interferometer model given by Sasso et al (2023) to three dimensions and partially coherent illumination (Sasso et al, 2022). Though we do not have a full understanding of the relevant physics, the phase-contrast images did not provide clues about problems related to them.…”