Sagittal focusing of high-energy synchrotron X-rays with asymmetric Laue crystals. I. Theoretical considerations

The ability of asymmetric Laue crystals to focus X-rays sagittally is demonstrated. The extent of such focusing is similar to that of sagittal focusing by a Bragg crystal, except for a factor related to the asymmetry angle. The anticlastic bending facilitates the use of inverse-Cauchois geometry in the meridional plane to provide better energy resolution and to increase the photon flux by an order of magnitude compared with traditional sagittal focusing with Bragg crystals. Furthermore, for sagittal focusing at X-ray energies above 30 keV, a Laue crystal is preferred to a Bragg crystal because the length of the beam's footprint on a Laue crystal, unlike on a Bragg crystal, is small and insensitive to energy. The conditions imposed on the asymmetry angle of the Laue crystal to achieve simultaneous sagittal focusing and inverse-Cauchois geometry in the meridional plane are derived for both single-crystal and double-crystal fixed-exit sagittally focusing monochromators.