On the Theory of an X-Ray Fabry-Perot Interferometer

Abstract

The theory of an X-ray Fabry-Perot interferometer (FPI) is developed as a particular case of the dynamical theory of X-ray Bragg diffraction in layered crystalline systems. Mathematical expressions are derived for the transmissivity and reflectivity of the X-ray FPI built as a system of two perfect crystal plates parallel to each other. The performance of the X-ray FPI is similar to that of the optical FPI. Both show fine interference structure in the transmission and reflection dependences. However, for the X-ray FPI this occurs only inside the region of the Bragg back diffraction peak. The influence of possible imperfections, such as the roughness of the crystal plate surfaces and the error in the parallelism of the atomic planes are discussed. It is shown that both factors may significantly deteriorate the performance of the X-ray FPI. Numerical estimations are given.

Anomalous Isotopic Effect on the Lattice Parameter of Silicon

“…The solid lines are fits using the dynamical theory of x-ray diffraction in layered crystal systems at normal incidence [17,18]. The experimentally observed interference fringes are damped because of some fluctuations in the thickness L e of the epitaxial layer.…”

Simulations of Bragg diffraction of a focused x-ray beam by a single crystal with an epitaxial layer

“…According to the treatment in Ref. 11, P MC ͑q͒ = R N ͑q͒, where N is the total number of layers in the multilayered system in which layers are numbered from the bottom ͑layer with the index 1, usually a substrate͒ to the top ͑layer with the index N͒. This result was obtained by the successive application of the recurrent formula…”

Sapphire hard X-ray Fabry–Perot resonators for synchrotron experiments

“…In order to design a FPR with a reasonable efficiency, numerical calculations of the transmittance of the resonator are performed using the dynamical diffraction theory for a Cartesian coordinate system (Stetsko & Chang, 1997) and the recursion relations for X-ray diffracted waves in a layered crystal system (Kohn et al, 2000).…”

“…The diffractive and transmitted amplitudes of each layer are calculated by the dynamical diffraction theory, denoted as r i ðd i Þ, t i ðd i Þ, r i ðd i Þ and t i ðd i Þ, respectively, where the subscripts are the layer indices. The effective diffractive and transmitted amplitudes of the layered system are derived from the recurrence formulae (Kohn et al, 2000), which are…”