Bragg diffraction from a material of circular cross section

The problem of dynamical Bragg diffraction from a set of Bragg planes in a material circular in the diffraction plane is solved by a combination of a Riemann-function technique and numerical integration of the Takagi-Taupin equations. In regions affected by non-Laue surfaces the solution is compared with an approximate Green-function method based on truncation of small arcs of the circle. The bright-field and dark-field intensity profiles are determined only by the radius of the circle compared to the extinction distance, and on the absorption parameters. The dependence of the profiles on these parameters is studied.