抛物面型X 射线组合折射透镜是一种适用于硬X 射线波段的新型光学元件。由于采用抛物面型，可以消除球差，因而能够产生亚微米尺度焦斑并具有更好的成像性能。本文给出了旋转轴对称抛物面型X 射线组合透镜的理论研究成果。首先，利用矩阵光学方法，推导了其精确的焦距公式，得到了薄透镜判定准则；其次，根据衍射理论，推导出焦点处的光强分布，得到其极限焦斑大小。最后，本文还给出了透过率和有效孔径的理论公式。针对用Al、Be、PMMA 三种材料制作的抛物面型X 射线组合折射透镜，本文给出了各个光学性能指标的数值计算结果。

The Compound Parabolic Refractive X-ray Lenses (CPRXLs) are a kind of novel optical components, especially suitable for hard X-rays. Due to their parabolic profiles, they are free of spherical aberration and are genuine devices for sub-micrometer focusing and imaging. The properties of a rotationally symmetric parabolic X-ray lens are studied theoretically and numerically in this paper. Firstly, the exact focal length formula is derived by using matrix optics method and a criterion of the thin lens approximation is obtained. Secondly, according to the diffraction theory, intensity distribution near focus is analyzed, which can give the limited focal spot size. Finally, the theoretical formulas of effective aperture and the transmittance are deduced. In addition, the numerical results of the designed CPRXLs made of various materials are also shown.