Direct Method for Reconstructing the Radiating Part of a Planar Source from Its Far-Fields

Abstract

A planar current is generally divided into a radiating part that mainly generates propagation fields and a non-radiating part that mainly generates evanescent fields. This paper proposes a direct method to reconstruct the radiating part of a planar source from its far-fields based on their explicit relationships. A standard reconstruction process is provided in which the far-fields are sampled at the peaks of their propagation modes. An analysis shows that the achievable reconstruction resolution of the source distribution is about half a wavelength. The paper also demonstrates that it is possible to reconstruct the source by sampling the far-fields on a plane or along a linear path. The performance of the reconstruction algorithm is illustrated with numerical examples.

Synthesis of Non-Mirror-Symmetrical Far-Field Patterns Using Two Parallel Current Sheets

“…We consider the 2-D array factor of the x-polarization alone, as the y-polarization can be independently handled in exactly the same away. The x-polarized radiation pattern of the two current sheets can be expressed as [28],…”

“…For a single-current sheet, it has been proposed in [28] that the mn-th mode is a propagation mode if k zmn is real; otherwise, it is an evanescent mode. The main lobes of the propagation modes fall in the visible region of the antenna, while only part of the side lobes of the evanescent modes fall in the visible region.…”

“…The main lobes of the propagation modes fall in the visible region of the antenna, while only part of the side lobes of the evanescent modes fall in the visible region. The far fields are mainly determined by those modes in the propagation constellation P, where P is defined as the following [28]:…”

“…For a linear current or a single layer of the rectangular current sheet, its far field can be directly calculated using the Fourier transformation. Generally, the current can be expanded with harmonic components with the Fourier series, and the field generated by each harmonic component of the current is referred to as mode field [28]. A mode can be regarded as a propagation one if at the direction of the peak of its main radiation lobe, it can propagate away from the source and contribute to the far field.…”

“…Consequently, the harmonic components of the current corresponding to these propagation modes can be directly obtained from the far-field values at these sampling directions. If the current sources are spatially band-limited and consist of only propagation harmonic components, i.e., the harmonic components of currents corresponding to the propagation modes, then the relationship between the radiation pattern and the current distribution is rigorous [28]. Unfortunately, a practical current is usually not spatially band-limited.…”