The X-ray optics of singly and doubly curved crystals are studied using a vector procedure and rotation matrices and general relations for the angular deviation from the Bragg angle over the crystal surface with a source aligned or misaligned on the Rowland circle. Hence, the effective scattering area, collection solid angle and diffracted X-ray intensity profile on the crystal surface are derived. The effective areas and the diffracted X-ray intensity profiles on the crystal surface for both aligned and misaligned source cases are plotted and compared. It is argued that the introduced point-focusing crystal configuration confirms the radii that have been obtained previously by a trial and error method by optimizing the crystal collection solid angle.
Study of the collection solid angle of doubly curved crystals