Theoretical foundations of spiral scannings

Abstract

In the previous chapter, the non-redundant (NR) sampling representations of the radiated electromagnetic (EM) fields have been described in detail and it has been stressed that they can be conveniently exploited to get an effective sampling representation of the voltage, acquired by the probe on the scanning surface, using a NR number of its samples. This allows the development of NR near-field to far-field (NF-FF) transformation techniques (see the next chapters), requiring a number of NF data remarkably lower than that needed by the corresponding classical NF-FF transformations, so that a considerable acquisition time saving is gained.In this chapter, efficient sampling representations of the probe voltage over a rotational scanning surface, from a NR number of its samples collected along a proper spiral wrapping such a surface, are presented. These representations allow, as will be shown in the following chapters, the development of effective NR NF-FF transformations which adopt innovative spiral scannings. As a matter of fact, the massive NF data needed by the corresponding traditional NF-FF transformation are accurately determined, using an optimal sampling interpolation (OSI) expansion, from the NR samples acquired along the spiral. A further considerable measurement time saving can be so achieved, since the acquisition of these samples is sped up by gathering them on fly and adopting continuous and synchronized motions of the antenna under test (AUT) and probe. The NR representations and related OSI expansions are obtained by adopting a suitable model of the AUT, by considering a spiral such that its step coincides with the sample spacing needed for the interpolation along the related meridian curve, and by determining the NR sampling representation along the spiral.