Achromatic focusing systems for hard X-rays are examined which consist of a refractive lens paired with a diffractive lens. Compared with previous analyses, we take into account the behaviour of thick refractive lenses, such as compound refractive lenses and waveguide gradient index refractive lenses, in which both the focal length and the position of the principal planes vary with wavelength. Achromatic systems formed by the combination of such a thick refractive lens with a multilayer Laue lens are found that can operate at a focusing resolution of about 3 nm, over a relative bandwidth of about 1%. With the appropriate distance between the refractive and diffractive lenses, apochromatic systems can also be found, which operate over relative bandwidth greater than 10%. These systems can be used to focus short pulses without distorting them in time by more than several attoseconds. Such systems are suitable for high-flux scanning microscopy and for creating high intensities from attosecond X-ray pulses.

用于硬 X 射线的消色差聚焦系统由一个折射透镜和一个衍射透镜组成。与以前的分析相比，我们考虑了厚折射透镜的行为，例如复合折射透镜和波导梯度折射率折射透镜，其中焦距和主平面的位置都随波长而变化。发现由这种厚折射透镜与多层劳厄透镜组合形成的消色差系统可以在约3nm的聚焦分辨率下在约1％的相对带宽上工作。通过折射透镜和衍射透镜之间的适当距离，还可以找到复消色差系统，其工作在大于 10% 的相对带宽上。这些系统可用于聚焦短脉冲，而不会及时将其扭曲超过几阿秒。此类系统适用于高通量扫描显微镜，并适用于从阿秒 X 射线脉冲中产生高强度。