以平顶高斯光束通过多个硬边光阑ABCD复杂光学系统的传输为例,分别用矩阵表示法和复高斯函数展开法推导出其对应的解析公式,并通过大量数值计算对两种方法进行比较.研究表明,矩阵表示法其解析公式形式简洁、规范,它在菲涅尔和夫琅禾费衍射区都很精确,但仅适用于圆对称光束和光学系统.复高斯函数展开法其解析公式形式较为复杂,它在非常靠近光阑的菲涅尔衍射区的误差较大,但是它可适用于圆对称和非圆对称光束和光学系统.两种方法与直接对Collins公式积分比较都能节约大量机时.

By using the methods of matrix representation and complex Gaussian function expansion, the recurrence propagation formulae of a flattened Gaussian beam through multi-apertured optical ABCD systems are derived. Numerical examples are given to compare the two numerical simulation methods. It is shown that the form of matrix formulae is simple, and the matrix formulation is the applicable to the Fraunhofer and Fresnel regions. However, this method is suited only to circularly symmetric optical beams and systems. On the other hand, the form of formulae derived by the method of complex Gaussian function expansion is complex, and its calculation errors become noticeable in the near Fresnel region closer to the aperture. But this method is suited to both circularly symmetric and circularly un-symmetric optical beams and systems. In addition, both methods reduce the computational time greatly in comparison with the direct integration of the Collins formula.