The paper addresses the question of efficiently sampling the near field and its intensity over an arbitrary curved line. It aims at finding the minimum number of measurements and their position for discretizing the near field and its square amplitude without loss of information and follows a common approach for both the radiation operator and the correspondent lifting operator. A scalar geometry is examined for both electric and magnetic current sources. At first, the singular values of the radiation / lifting operator are evaluated by an asymptotic approach and a change of variables which lead to an operator with a widely investigated spectrum. As the number of relevant singular values is available in closed form, the dimensions of the near field and its intensity over the curve are found. Next, starting from a sampling expansion of the pertinent left singular functions, a non-redundant sampling representation of the near field and its square amplitude is provided. Some numerical results confirm the analysis. The results may be of great interest especially in antenna testing by near field data (both standard and phaseless) with an unconventional field scanning system as, for instance, an UAV mounted probe.

中文翻译：

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近场的尺寸和采样及其曲线强度

本文解决了在任意曲线上有效采样近场及其强度的问题。它旨在找到最小数量的测量及其位置，以在不丢失信息的情况下离散近场及其平方幅度，并遵循辐射算子和相应的提升算子的通用方法。检查电流源和磁电流源的标量几何。首先，辐射/提升算子的奇异值通过渐近方法和变量的变化来评估，这导致算子具有广泛研究的光谱。由于相关奇异值的数量以封闭形式可用，因此可以找到近场的尺寸及其在曲线上的强度。下一个，从相关左奇异函数的采样扩展开始，提供了近场及其平方幅度的非冗余采样表示。一些数值结果证实了这一分析。结果可能非常有趣，特别是在使用非常规场扫描系统（例如，安装在无人机上的探头）通过近场数据（标准和无相）进行天线测试时。