Based on the importance of spherical harmonics and their applicability in many physical problems, this research aimed to study the diffraction pattern of light by a circular aperture starting from the first Rayleigh–Sommerfeld diffraction equation and to expand the polar radius of a point on the surface of the circular aperture based on spherical harmonics. We depended on this theoretical framework in our paper. We calculated the optical intensity compounds for . We studied the intensity distributions in three special cases (along the optical axis, at the geometrical focal plane, and along the boundary of the geometrical shadow). We presented numerical comparative examples to illustrate the variation of the intensity versus a ratio ( is the ratio of the distance between the circular aperture and the observation plane to a radius of the circular aperture), and we used Maple program to represent these results. We noticed that the expansion we made using spherical harmonic analysis led to an increase in the number of fringes bright enough to be visible to the naked eye. We then concluded with a brief discussion of the results.

中文翻译：

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利用球谐函数分析圆孔光的衍射。

基于球谐函数的重要性及其在许多物理问题中的适用性，本研究旨在研究从第一个Rayleigh-Sommerfeld衍射方程开始的圆形孔径的光的衍射图，并扩大表面上一个点的极半径基于球谐函数的圆形孔径的变化。我们在本文中依赖此理论框架。我们计算了光强度化合物 对于 。我们研究了三种特殊情况下的强度分布（沿光轴，在几何焦平面上以及沿着几何阴影的边界）。我们提供了数值比较示例，以说明强度与比率的变化（是圆形孔径和观察平面之间的距离与圆形孔径的半径之比），我们使用Maple程序来表示这些结果。我们注意到，使用球谐分析进行的扩展导致了足以使肉眼可见的条纹数量增加。然后，我们对结果进行了简短的讨论。