X-ray optics of diffractors curved to a logarithmic spiral

Abstract

Calculations are given for some properties of x-ray diffractors having the shape of a logarithmic spiral in one direction. The locus of points on a curved diffractor’s surface is calculated for a given deviation from the Bragg angle when the diffractor is used at Bragg angles ranging from 15° to 75°. Four cases are considered, including a cylindrical logarithmic spiral and logarithmic spirals of revolution about an axis lying in the plane of the Rowland circle with the source at the origin of the spiral and with the source displaced from the origin. The resulting collection solid angles are compared with the Johann, the Johansson, the spherical plate, the Wittry, and the point-to-point focusing geometries. It is concluded that the diffractors based on a logarithmic spiral are useful because they provide better performance than some of these other diffractors and may be easier to fabricate.