Sommargren G E, Weaver H J
Appl Opt. 1990 Nov 1;29(31):4646-57. doi: 10.1364/AO.29.004646.
In this paper we discuss the diffraction pattern resulting from the propagation of light past an opaque obstacle with a circular cross section. A mathematical description of the diffraction pattern is obtained in the Fresnel region using scalar diffraction theory and is presented in terms of the Lommel functions. This description is shown experimentally to be quite accurate, not only for near axis points within the shadow region but also well past the shadow's edge into the directly illuminated region. The mathematical description is derived for spherical wave illumination and an isomorphic relation is developed relating it to plane wave illumination. The size of the central bright spot (as well as the subsequent diffraction rings), the axial intensity, and the intensity along the geometric shadow are characterized in terms of point source location and the distance of propagation past the circular obstacle.
在本文中，我们讨论了光经过具有圆形横截面的不透明障碍物传播时产生的衍射图样。利用标量衍射理论在菲涅耳区域获得了衍射图样的数学描述，并以隆梅尔函数的形式给出。实验表明，这种描述不仅对于阴影区域内的近轴点非常准确，而且在阴影边缘之外进入直接照明区域时也非常准确。该数学描述是针对球面波照明推导出来的，并建立了一个同构关系将其与平面波照明联系起来。根据点源位置和经过圆形障碍物传播的距离，对中心亮点（以及随后的衍射环）的大小、轴向强度和沿几何阴影的强度进行了表征。
