X-ray focusing optics. I. Applications of wave optics to doubly curved crystals with a point x-ray source

Abstract

A wave optics approach to the calculations of the intensity distribution of an x-ray point source image with a two-dimensional (2D) focusing geometry is presented. Analytical formulas are derived to calculate the intensity distribution at the focal plane. This approach has taken into account the effects of x-ray scattering within a 2D bent crystal, which includes the x-ray refraction and absorption inside the crystal, and the effects of elastically deformed crystals described by the anisotropic elasticity theory. Based upon the elastic bending model, the modified Bragg law and 2D lens equations are discussed. In addition, the x-ray extinction distance for curved crystals is found to be dependent on the size and the bending radius of bent crystals. For a monochromatic x-ray point source, calculation of the intensity distribution with a 2D bent silicon crystal is given for both perfect and misaligned sources. The spatial resolution and the size of the image are determined.