Different to visible light, X-rays can only be reflected with high losses at metal surfaces. Only for small grazing angles the total reflection of X-rays can be used for a significant reflection of the radiation. Wilhelm Conrad Röntgen, himself, was convinced that X-rays cannot be deflected at all.
However, shortly after their detection, Laue and Bragg found out that X-rays exhibit diffraction at the atoms of a crystal lattice. The superposition of all diffracted waves can be considered as reflection of the incoming wave at the lattice planes of the crystal. For a long time this method has been regarded as the only possibility to reflect X-rays. Since it was not possible to find a suitable lattice for every application, high efforts have been made to fabricate artificial, one-dimensional periodic structures. These so-called multilayers with single layer thicknesses in the nanometer range caused a renaissance in the field of X-ray optics.
In order to calculate the optical properties of multilayers and complete optical systems, different simulation techniques can be applied. For the calculation of reflection and transmission at the interfaces, Fresnel`s formulas are used. For the determination of the imaging properties of complete optical systems we use ray-tracing algorithms. This combination allows an effective optimization of the desired beam and imaging characteristics in the design phase of optics manufacturing.