Harness Anthony
Opt Express. 2020 Nov 9;28(23):34290-34308. doi: 10.1364/OE.405485.
Fourier optics is a powerful and efficient tool for solving many diffraction problems, but relies on the assumption of scalar diffraction theory and ignores the three-dimensional structure and material properties of the diffracting element. Recent experiments of sub-scale starshade external occulters revealed that the inclusion of these physical properties is necessary to explain the observed diffraction at 10 of the incident light intensity. Here, we present a methodology for implementing non-scalar diffraction while maintaining the efficiency and ease of standard Fourier optics techniques. Our methodology is based on that of Braunbek, in which the Kirchhoff boundary values are replaced with the exact field in a narrow seam surrounding the edge of the diffracting element. In this paper, we derive the diffraction equations used to implement non-scalar diffraction and outline the computational implementation used to solve those equations. We also provide experimental results that demonstrate our model can replicate the observational signatures of non-scalar diffraction in sub-scale starshades, in effect validating our model to better than 10 in relative intensity. We believe this method to be an efficient tool for including additional physics to the models of coronagraphs and other optical systems in which a full electromagnetic solution is intractable.
傅里叶光学是解决许多衍射问题的强大而有效的工具，但它依赖于标量衍射理论的假设，忽略了衍射元件的三维结构和材料特性。亚尺度遮阳板外部遮光器的最新实验表明，考虑这些物理特性对于解释在10%的入射光强度下观察到的衍射是必要的。在这里，我们提出了一种在保持标准傅里叶光学技术的效率和简便性的同时实现非标量衍射的方法。我们的方法基于布劳恩贝克的方法，其中基尔霍夫边界值被衍射元件边缘周围窄缝中的精确场取代。在本文中，我们推导了用于实现非标量衍射的衍射方程，并概述了用于求解这些方程的计算实现。我们还提供了实验结果，证明我们的模型可以复制亚尺度遮阳板中非标量衍射的观测特征，实际上在相对强度方面将我们的模型验证到优于10%。我们相信这种方法是一种有效的工具，可用于在日冕仪和其他光学系统的模型中纳入额外的物理因素，而在这些系统中完整的电磁解决方案是难以处理的。
