A computationally efficient method to solve the Takagi-Taupin equations   for a large deformed crystal
  We present a treatise on solving the Takagi-Taupin equations in the case of a strain field with an additional, spatially slowly varying component (owing to \emph{e.g.}~heat expansion or angular compression). We show that the presence of such a component in a typical case merely shifts the reflectivity curve as a function of wavelength or incidence angle, while having a negligible effect on its shape. On the basis of the derived result, we develop a computationally efficient method to calculate the reflectivity curve of a large deformed crystal. The validity of the method is demonstrated by comparing computed reflectivity curves with experimental ones for bent silicon wafers. A good agreement is observed. 
Ari-Pekka Honkanen, Giulio Monaco, Simo Huotari
physics.optics physics.ins-det