Fu Malong, Zhao Yang
Opt Express. 2021 Feb 15;29(4):6257-6270. doi: 10.1364/OE.418065.
The Huygens' principle is thoroughly investigated under scalar theory. The rigorous expressions of Huygens' principle must be independent of ∂u/∂n, and their boundaries can only be taken as either spherical or flat; thus, three cases can be concluded. An extended version of Huygens' principle is proposed to cover these cases, whose rigorous expressions are shown in this paper. Specifically, when the radius of the spherical boundary approaches infinity, the corresponding expressions become the form corresponding to the flat boundary. Expressions with spherical boundary can change the area and average intensity of small angle diffraction pattern proportionally, thus providing a promising mathematical tool for the design of curved imaging systems.
在标量理论下对惠更斯原理进行了深入研究。惠更斯原理的严格表达式必须独立于∂u/∂n，其边界只能取为球形或平面；因此，可以得出三种情况。本文提出了惠更斯原理的一个扩展版本来涵盖这些情况，并给出了其严格表达式。具体而言，当球形边界的半径趋近于无穷大时，相应的表达式就变成了对应于平面边界的形式。具有球形边界的表达式可以按比例改变小角度衍射图样的面积和平均强度，从而为曲面成像系统的设计提供了一种很有前景的数学工具。
