自由度采样

中文摘要 AI 辅助

提出了一种基于几何的框架，用于在表面上对电磁场进行采样。该方法将电磁自由度（DoF）的阴影面积公式从全局模式计数扩展到空间分辨的DoF密度，该密度决定了采样分布。观测表面被划分为包含大约一个自由度的单元，单元面积由DoF密度决定，单元形状由DoF密度矢量在观测表面上的投影决定。在远场中，源阴影区域定义了观测球面上的方向性DoF密度，而在近场中，相互阴影密度和DoF密度方向决定了局部采样几何。所提出的方法仅需要源-观测几何，不需要对传播算子进行显式奇异值分解。针对几种源和观测几何的数值结果表明，其重建性能接近基于算子的采样方法。波束形成解释进一步表明，采样单元对应于与几何相关的波束区域，建立了DoF、采样和波束形成之间的统一联系。

英文摘要

A geometry-based framework for sampling electromagnetic fields over surfaces is presented. The approach extends the shadow-area formulation of electromagnetic degrees of freedom (DoF) from a global mode count to a spatially resolved DoF density that determines the sampling distribution. The observation surface is partitioned into cells containing approximately one DoF, with the cell area determined by the DoF density and the cell shape determined by the projection of the DoF density vector onto the observation surface. In the far field, the source shadow area defines a directional DoF density over the observation sphere, while in the near field, the mutual-shadow density and a DoF density direction determine the local sampling geometry. The resulting method requires only the source-observation geometry and does not require an explicit singular-value decomposition of the propagation operator. Numerical results for several source and observation geometries demonstrate reconstruction performance close to that of operator-based sampling methods. A beamforming interpretation further shows that the sampling cells correspond to geometry-dependent beam regions, establishing a unified connection between DoF, sampling, and beamforming.

发表机构

• Lund University（隆德大学）

机构由 AI 辅助整理，请以论文原文为准。