部分相干光通过受光阑限制近轴ABCD光学系统传输是实际工作中一个十分有意义却是很困难的问题。虽然使用“Mathematia”编制的程序可对Collins公式作数值积分,但随着光阑数目的增加,计算变得非常繁琐和耗时。用有限个复高斯函数之和来逼近硬边光阑窗函数的方法,推导出了部分相干光通过多个硬边光阑ABCD光学系统传输的递推公式,提供了一种模拟部分相干光通过硬边光学系统传输的快速算法。计算示例表明,当离光阑不太近时,使用解析公式和直接对Collins公式作数值积分的结果符合甚好,并具有快速计算的主要优点,因此大为节约了机时。此外,由于将单光阑推广到多光阑的ABCD光学系统,并考虑了光束的部分空间相干性,因此所得结果更具一般性,且对多模部分相干激光是适用的。

The propagation of partially coherent beams through an apertured paraxial ABCD optical system is an interesting but difficult problem encountered in practice. Although the integration based on the Collins formula can be evaluated numerically using such programs as “Mathematia”, it becomes very cumbersome and time consuming with increasing number of apertures. In this paper, by using the method of expanding the hard-edge aperture function into a finite sum of complex Gaussian functions, the recurrence propagation expression for the propagation of partially coherent beams through a multiple apertured ABCD optical system is derived, which provides a fast algorithm for simulating the propagation of partially coherent beams through hard-aperture optics. Numerical calculation examples are given, which show that the calculation results by using our analytical formula are consistent with those by straightforward integral of the Collins formula in the region not close to the aperture. THe main advantage of this method is the fast computation, so that the computing time can be greatly reduced. In addition, the extension to multi-apertured ABCD system is made, where the partial coherence of beams is taken into account, so that the expression is applicable to the more general case and is suitable to partially coherent multimode lasers.