Comparison of two methods for simulation of hard X-ray nanofocusing by elliptical mirrors

Wave-optical calculations are essential for predicting the X-ray focusing performance of precisely figured elliptical mirrors. The complex wavefield in the vicinity of the focal plane of a mirror with RMS height error in the nanometer range compared to the best-fit ellipse has been calculated using two methods. A pupil function method that treats the surface topography of a mirror as an aberration to a perfect ellipse was used to obtain the reflected amplitude and phase around the focal point downstream. The results were compared with direct propagation of waves from a point source, and it was found that both methods were in good agreement. Each approach provides advantages that are useful in designing mirrors to achieve diffraction limited focusing.