This article presents a general technique for the far-field transformation of near fields measured over arbitrary surfaces and multimode probe correction in an efficient and accurate way. The use of not only one but several spherical wave expansions to model the antenna under test fields allows to incorporate full probe correction for arbitrary orientations with low computation cost. Combining this approach with a hierarchical subdomain decomposition strategy, the transformation problem is solved with a low computational complexity. In this method, the fields produced by neighbor subdomains are gradually aggregated and interpolated following a multilevel scheme, leading to a good scalability with frequency compared with other matrix-based transformation methods. The numerical and experimental results are provided to show the efficiency and capabilities of the proposed algorithm.

中文翻译：

---

通过多级球面波扩展在任意表面上进行近场到远场变换

本文介绍了一种以高效准确的方式对任意表面上测量的近场进行远场变换和多模探头校正的通用技术。不仅使用一种而是使用几种球面波扩展来模拟测试场下的天线，允许以低计算成本结合针对任意方向的完整探头校正。将此方法与分层子域分解策略相结合，以较低的计算复杂度解决了转换问题。在这种方法中，相邻子域产生的场按照多级方案逐渐聚合和插值，与其他基于矩阵的变换方法相比，具有良好的频率可扩展性。