Analysis of tilted multilayer Laue lens with stochastic layer thickness error

The propagation of X-rays in tilted multilayer Laue lenses (MLLs) with stochastic layer thickness error is analyzed by using the beam propagation method (BPM). The accuracy of BPM is studied by comparing wave fields calculated by BPM and the Takagi-Taupin description (TTD) of X-ray dynamical diffraction theory. Influences of the stochastic layer thickness error on the focusing performance are evaluated. This study shows that, because of the stochastic layer thickness error, the zone plate law could be broken locally, which would lead to undesired foci around the principal focus. Simulation results suggest that for a typical tilted MLL, the root mean square (RMS) value of the stochastic layer thickness error should be smaller than about 1.5% in order to keep the MLL׳s performance. It is demonstrated that BPM can serve as an efficient tool for the analysis of tilted MLLs with imperfections.