为研究平顶高斯光束通过高斯光阑透镜系统的传输特性, 基于光学矩阵的方法和Collins公式导出了平顶高斯光束通过该复杂光学系统后的场分布的解析表达式和近轴光强分布值, 进而分析了平顶高斯光束通过高斯光阑透镜系统后的传输特性。研究结果表明, 平顶高斯光束通过高斯光阑透镜系统后, 实际焦点位置和几何焦点位置并不重合, 即发生焦移现象。焦移量的大小与高斯光阑宽度及光阑与透镜间的距离等因素有关, 即在一定条件下, 光阑宽度增大, 相对焦移量变小, 光阑与透镜之间的距离与焦距的比越小, 相对焦移量就越小。

In this paper, we study propagation properties of flattened Gaussian beam passing through a Gaussian aperture-lens system. Based on the optical matrix method and Collins formula, the analytical expression of field distribution and axial intensity distribution of flattened Gaussian beam passing through the complicated system are obtained. Propagation properties of the flattened Gaussian beam passing through Gaussian aperture-lens system are analyzed. Results show that, as the beam passing through the optical system, the actual focus position is not at the position of the geometric focus, that is, the focal shift occurs. The focal shift is not only determined by the width of the Gaussian aperture, but also affected by the distance between the aperture and lens distance. Under certain conditions, if the aperture width increases, the relative focal shift diminishes. The ratio of the distance between the aperture and lens and focal length is smaller and the relative focal shift is smaller.