<title>Development of a novel x-ray focusing technique using crystals with a two-dimensionally modulated surfaces</title>

Abstract

Theoretical investigations for obtaining x-ray point focusing by using crystals with two- dimensionally modulated surfaces are carried out. Based on the Bragg and Fresnel diffraction principles, formulae of modulated surfaces (structures) are derived for both flat and bent crystals for focusing x rays to micron or submicron size. It is found that elliptically shaped and linearly modulated structures are suitable for flat and cylindrically bent crystals, respectively. For the given Ti K(alpha) radiation and geometric parameters, Si (111) and InSb (111) reflections are used for the calculations of flat and bent crystals in terms of their focus characteristics, namely the focusing efficiency and the focus width. The influence of the distribution of the Bragg amplitude on flat and bent crystals is also discussed.