夫琅禾费衍射的线性变换计算

Calculate of Fraunhofer diffraction by linear transformation

夫琅禾费衍射在二维小孔的线性变换下具有简单的变换特性,利用线性变换的方法简便求得了位于坐标系中任何位置的任意三角形小孔和任意平行四边形小孔夫琅禾费衍射复振幅的一般解析表达式,从而提供了一种普遍的方法,无需通过积分计算而仅由代数运算来求得任意多边形小孔夫琅禾费衍射光强分布的解析表达式.作为应用例子讨论了正六边形小孔夫琅禾费衍射的光强分布,并依据所得解析结果进行了计算机模拟.

Fraunhofer diffraction transforms in a simple way under a linear deformation of the shape of the two-dimensional aperture. Based on simple linear transformation, we derive general analytic expressions for the diffraction amplitude in the case of triangular and rhomboidal apertures of arbitrary shape at any given position in a coordinate system. Without performing integration, we solve the Fraunhofer diffraction by any polygon aperture of any shape, through purely algebraic operations. As an example, we apply the present method to find the diffraction intensity distribution for a regular hexagon aperture, and simulate it on a computer based on our analytical results.