Goswami Neha, Popescu Gabriel
Opt Express. 2021 Nov 22;29(24):39107-39114. doi: 10.1364/OE.443996.
Light diffraction at an aperture is a basic problem that has generated a tremendous amount of interest in optics. Some of the most significant diffraction results are the Fresnel-Kirchhoff and Rayleigh-Sommerfeld formulas. These theories are based on solving the wave equation using Green's theorem and result in slightly different expressions depending on the particular boundary conditions employed. In this paper, we show that the diffraction by a thin screen, which includes apertures, gratings, transparencies etc, can be treated more generally as a particular case of scattering. Furthermore, applying the first order Born approximation to 2D objects, we obtain a general diffraction formula, without angular approximations. Finally, our result, which contains no obliquity factor, is consistent with the 3D theory of scattering. We discuss several common approximations and place our results in the context of existing theories.
光在孔径处的衍射是一个在光学领域引发了大量关注的基本问题。一些最重要的衍射结果是菲涅耳 - 基尔霍夫公式和瑞利 - 索末菲公式。这些理论基于利用格林定理求解波动方程，并且根据所采用的特定边界条件会得出略有不同的表达式。在本文中，我们表明，包括孔径、光栅、透明片等在内的薄屏衍射可以更普遍地作为散射的一种特殊情况来处理。此外，将一阶玻恩近似应用于二维物体，我们得到了一个无角度近似的通用衍射公式。最后，我们不含倾斜因子的结果与三维散射理论一致。我们讨论了几种常见的近似，并将我们的结果置于现有理论的背景下。
