Electromagnetic degrees of freedom are instrumental in antenna design, wireless communications, imaging, and scattering. Larger number of degrees of freedom enhances control in antenna design, influencing radiation patterns and directivity, while in communication systems, it links to spatial channels for increased data rates and reliability, and resolution in imaging. The correlation between computed degrees of freedom and physical quantities is not fully understood, prompting a comparison between classical estimates, Weyl's law, modal expansions, and optimization techniques. In this paper, it is shown that the number of degrees of freedom for arbitrary shaped radiating structures approaches the shadow area measured in squared wavelengths asymptotically as the wavelength decreases.

翻译：电磁自由度在天线设计、无线通信、成像和散射分析中具有重要作用。更多的自由度可增强天线设计中对辐射方向图和指向性的控制能力；在通信系统中，自由度与空间信道相关联，有助于提高数据速率和可靠性；在成像领域则直接影响分辨率。目前对计算所得自由度与物理量之间的关联尚未完全明晰，这促使我们对经典估计方法、外尔定律、模态展开以及优化技术进行比较研究。本文证明，对于任意形状的辐射结构，当波长趋近于零时，其自由度数渐近趋近于以波长为单位的投影面积平方值。