Abstract
The sampling of the near-field radiated by a planar source observed over a finite planar aperture is addressed. To this end, we employ the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">warping</i> method that amounts to properly change the observation variables and finding the sampling points as those that allow to approximate the singular values of the radiation operator up to the so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">number of degrees of freedom</i> . In particular, the warping transformations allow to approximate the kernel function of the relevant operator as a band-limited function and hence the sampling theorem is adopted to devise the discretization scheme. Here, we generalize the warping method to the full vector case and introduce a spatially varying oversampling strategy that allows to deal with measurement apertures which are larger than the source. It is shown that the sampling points need to be non-uniformly arranged across the measurement aperture but their number is generally much lower than classical half-wavelength sampling. A numerical analysis is included to support the theoretical arguments. Finally, numerical experiment-based results concerning the radiation pattern estimation of a planar array antenna are presented. To this end, experimental data collected under a uniform half-wavelength sampling scheme are first interpolated over the required non-uniform grid and then processed to obtain the radiation pattern.
Highlights
Near-field techniques [1], [2] have become a standard tool in antenna testing because of their high reliability. They basically consist in collecting near-field measurements and in order to evaluate the radiation pattern, processing them by some near-field to far-field transformations [2]–[6]
From a general perspective, devising the sampling scheme can be addressed by a sensor selection procedure [16]. This way, the problem is phrased as the search for a finite number of measurement positions, among candidates available over a dense grid, by optimizing some metrics related to the singular values of the radiation operator [17]–[21]
It is noted that for a given ν, since the intervals in ξx, as well as the sampling steps in the warped domains, are the same for both the uniform and the nonuniform oversampling strategies, the number of the required samples coincides: what changes is their deployment across the measurement aperture
Summary
Near-field techniques [1], [2] have become a standard tool in antenna testing because of their high reliability. This way, the problem is phrased as the search for a finite number of measurement positions, among candidates available over a dense grid, by optimizing some metrics related to the singular values of the radiation operator [17]–[21] Another approach takes into account the mathematical features of the Green function that suggests the field can be approximated by a band-limited function, once a suitable parametrization for the observation variables is employed and a proper demodulating exponential term is singled-out [22]. Thanks to suitable variable transformations, that warp the spatial observation variables, such a kernel function is approximated as a band-limited function and the Shannon sampling theorem is used for the discretization This method, unlike sensor selection procedures, does not require to run iterative optimization algorithms.
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