A new approach to the solution of the Takagi± Taupin equations for X-ray optics: application to a thermally deformed crystal monochromator

A new computational approach to the Takagi±Taupin equations for the analysis of X-ray optics is presented and applied to heat-loaded synchrotron monochromators. The new numerical approach is based on the assumption that the incoming wave is completely incoherent (incoherent point source). The simulation avoids any kind of simpli®cation: it takes into account the thermal deformation of the crystals calculated by the ®nite-element method, the transverse beam direction and the beam spatial distribution. As an application example, the theoretical rocking curves for low-energy low-order and highenergy high-order re ̄ections are compared with results of measurements carried out at the Advanced Photon Source (APS) on a cryogenically cooled double-crystal monochromator. The good agreement shows that the adopted approach succeeds in simulating very closely the actual experimental setup while exhibiting satisfactorily short execution times.