为了研究平顶高斯光束通过扩束系统的传输特性，从柯林斯衍射积分公式出发，推导出场强分布的解析式。以伽利略式和开普勒式这两种常见的扩束系统为例，对平顶高斯光束扩束后在接收面的光强分布进行数值计算及分析。结果表明，平顶高斯光束通过同等倍数但不同形式的扩束系统的传输特性不同，且对于不同焦距的扩束系统，其传输特性也有比较明显的差别；平顶高斯光束通过开普勒式扩束系统，不仅在成像面距离获得平顶光束，还可在一定轴向范围之内保持平顶分布，并且轴向范围和所选扩束系统的放大倍数有关，随着放大倍数的增大，轴向范围也增大。

Starting from the Collins diffraction integral formula, the propagation formula of flattened Gaussian beam passing through a beam expander was derived. Taking both Galileo and Kepler beam expander systems as examples, the intensity distribution was simulated. The numerical calculation shows that the propagation properties are different between the Galileo and Kepler beam expander systems with the same amplification as well as different focus length of the lens. What is more, the flat-topped beam is also obtained during certain axial displacement as well as the image plane of the Kepler beam expander, and the axial displacement is increased with the increase of the expander amplification.