硬边衍射多色部分相干光束谱强度的快速计算

A fast algorithm for the spectrum of partially coherent beams diffracted at an hard-edge aperture

为了在微机上快速地计算各类被硬边光澜衍射后的谱强度,采用复高斯函数展开模拟硬边衍射效应,推导出了多色高斯-谢尔模型光束被硬边光阑衍射后谱强度的近似解析表达式,并将所得结果与传统方法(直接对交叉谱密度函数传输公式数值积分)进行了比较。结果表明,所得公式在保证计算精度的前提下,具有大大地节省计算机时的优点,以平顶高斯光束为例,证明所采用方法可同样推广用于其它光束被硬边光阑衍射后谱强度的计算。该方法具有普遍意义。

In order to calculate the intensity of beams diffracted at an hard-edge aperture, by expanding a hard-edge aperture function into a finite sum of complex Gaussian functions, an approximate expression for the spectrum of polychromatic Gaussian-Schell model beams diffracted at the aperture was derived. Simulation results were compared with those obtained by means of the conventional method, i. e. , the direct integral of the cross-spectral density function. It is shown that the computing time is strongly reduced under the condition of satisfying calculation accuracy. Taking flattened Gaussian beams as an example, this method is applicable for calculation of the spectrum of other kinds of beams propagating through a hard-edge aperture.