X-RAY OPTICS OF DIFFRACTORS CURVED TO A LOGARITHMIC SPIRAL

Calculations are given for some properties of x-ray diffractors having the shape of a logarithmic spiral in one direction. The locus of poin ts on a curved diffractor's surface is calculated for a given deviatio n from the Bragg angle when the diffractor is used at Bragg angles ran ging from 15-degrees to 75-degrees. Four cases are considered, includi ng a cylindrical logarithmic spiral and logarithmic spirals of revolut ion about an axis lying in the plane of the Rowland circle with the so urce at the origin of the spiral and with the source displaced from th e 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 bas ed on a logarithmic spiral are useful because they provide better perf ormance than some of these other diffractors and may be easier to fabr icate.