A Fourier optics approach to the dynamical theory of X-ray diffraction - continuously deformed crystals

X-ray diffraction in continuously deformed crystals is considered by application of Fourier optics and from the viewpoint of the analogy between X-ray dynamics and the motion of two-level systems in quantum mechanics. Different forms of Takagiʹs equations are traced back to a common framework and it is shown that they are different ways to represent the same propagation equation. A novel way to solve Takagiʹs equations in the presence of a constant strain gradient is presented and approximation methods derived from quantum mechanics are considered. Crystal deformation in X-ray interferometry and two-crystal spectrometry are discussed and it is demonstrated that Si lattice-parameter measurements depend on the diffracting plane spacing on the crystal surface.