Focusing and reflection by a bent crystal for high-energy synchrotron radiation

The focusing properties and resolution of a doubly bent crystal in the Bragg case have been analytically studied from a geometrical viewpoint. Simulation using the Takagi-Taupin equations was also performed for singly bent crystal reflections to study the reflectivity. The critical radius of curvature for changing from dynamical to kinematical diffraction is calculated to be of the order of a few tens of metres for an Si 400 reflection of 110 keV X-rays.