10 - Diffractive X-ray and Neutron Optics

Abstract

Derived in this chapter are the Helmholtz–Kirchhoff integral theorem and the Kirchhoff–Fresnel diffraction equation with the obliquity factor. The paraxial approximation is then applied to the Kirchhoff–Fresnel diffraction equation. Also covered is the Fraunhofer diffraction of X-rays or neutrons from single, paired, and multiple slits and rectangular and circular apertures. The Abbe theory of imaging applied to X-rays or neutrons is then detailed. Using the Huygens–Fresnel approach, the Kirchhoff equation is derived for a compound refractive lens (CRL), which is used with X-rays or neutrons. Next, the compound refractive Fresnel lens (CFL) for X-rays and neutrons, followed by the Fresnel diffraction of X-rays or neutrons from a knife edge and circular and rectangular apertures, is discussed. Also presented are the Fresnel zone plates (FZPs) for X-rays or neutrons and an achromat fabricated from an FZP and a CRL. Finally, the Helmholtz paraxial differential equation and its solution are derived for a Gaussian, spherical, X-ray laser beam.