In this paper, we address the problem of how to efficiently sample the radiated field in the framework of near-field measurement techniques. In particular, the aim of the article is to find a sampling strategy for which the discretized model exhibits the same singular values of the continuous problem. The study is done with reference to a strip current whose radiated electric field is observed in the near zone over a bounded line parallel to the source. Differently from far zone configurations, the kernel of the related eigenvalue problem is not of convolution type, and not band-limited. Hence, the sampling-theory approach cannot be directly applied to establish how to efficiently collect the data. In order to surmount this drawback, we first use an asymptotic approach to explicit the kernel of the eigenvalue problem. After, by exploiting a warping technique, we recast the original eigenvalue problem in a new one. The latter, if the observation domain is not too large, involves a convolution operator with a band-limited kernel. Hence, in this case the sampling-theory approach can be applied, and the optimal locations of the sampling points can be found. Differently, if the observation domain is very extended, the kernel of the new eigenvalue problem is still not convolution. In this last case, in order to establish how to discretize the continuous model, we perform a numerical analysis.

中文翻译：

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近区带状电流辐射算子的渐近研究

在本文中，我们解决了如何在近场测量技术框架内有效地采样辐射场的问题。特别地，本文的目的是找到一种采样策略，对于该采样策略，离散模型表现出相同的连续问题奇异值。这项研究是参照一个带状电流进行的，该带状电流在平行于电源的边界线上的近区中观察到了辐射电场。与远区配置不同，相关特征值问题的内核不是卷积类型，也不是带宽受限的。因此，采样理论方法不能直接应用于建立如何有效收集数据的方法。为了克服这个缺点，我们首先使用渐近方法来明确特征值问题的核。后，通过利用翘曲技术，我们将原来的特征值问题重铸为新的问题。如果观察域不是太大，则后者涉及具有带限内核的卷积算子。因此，在这种情况下，可以应用采样理论方法，并且可以找到采样点的最佳位置。不同的是，如果观察域非常扩展，则新特征值问题的内核仍不会卷积。在后一种情况下，为了确定如何离散化连续模型，我们进行了数值分析。并找到采样点的最佳位置。不同的是，如果观察域非常扩展，则新特征值问题的内核仍不会卷积。在后一种情况下，为了确定如何离散化连续模型，我们进行了数值分析。并找到采样点的最佳位置。不同的是，如果观察域非常扩展，则新特征值问题的内核仍不会卷积。在后一种情况下，为了确定如何离散化连续模型，我们进行了数值分析。