硬边光阑光学计算方法的比较研究

Comparative study of simulation algorithm for hard-edge optics

对通过硬边光阑光学系统光束传输问题的直接数值积分法、复高斯函数展开法、矩阵法和光束模式展开法作了比较研究。研究表明 ,直接数值积分应用范围广泛 ,但随着光阑数的增加 ,它变得既烦琐又耗时。复高斯函数展开法为快速模拟硬边衍射光束在菲涅耳区和夫琅和费区的传输提供了一个有用方法 ,只是在很近的场存在着显著的计算误差。矩阵法能用于菲涅耳区和夫琅和费区 ,但只适用于旋转对称的光学系统与光束。光束模式展开法可用于近似计算远场的弱截断光束。

The direct numerical integration,the complex-Gauss ia n-function expansion,the matrix approach and the beam mode expansion used to s imulate beam propagation through optical systems containing hard-edged aperture s are compared. It is shown that the direct numerical integration is a widely ap plicable method,but is very cumbersome and time-consuming as the number of ape rtures increases. The complex-Gaussian-function expansion provides a useful me thod for fast simulating the hard-edged diffracted beam propagation in the Fres nel and Fraunhofer regions,and obvious calculation errors exist only in the ext reme near field. The matrix representation is applicable to the hard-edged diff racted beam propagation in both Fresnel and Fraunhofer regions,but holds only f or rotationally symmetrical optical systems and beams. The beam expansion method is suited to approximate the weakly truncated beams in the far field.