X-ray focusing by bent crystals in Bragg backscattering

Focusing of a spherical X-ray wave in Bragg backscattering from weakly and strongly bent crystals is considered theoretically. The analytical formula describing the dimensions of the diffraction backscattering region is obtained. It is shown that, along with the well-known Johann scheme, the use of the backscattering scheme allows one to increase the aperture ratio of the crystal optics by two to three orders of magnitude. The spectral characteristics of bent crystals providing diffraction backscattering (θ = π/2) are discussed. It is shown that the spectral resolution can attain a value of the order of 10−11.