2022
DOI: 10.1109/tap.2022.3168652
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Reflector Antennas Characterization and Diagnostics Using a Single Set of Far-Field Phaseless Data and Crosswords-Like Processing

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Cited by 14 publications
(6 citation statements)
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“…At least four-fold oversampling is a typical choice. Furthermore, the computational complexity of phase retrieval algorithms is a concern, since they often scale with the square of the number of unknowns or observations [29], [30] or even worse [31], [32]. This renders well thought out algorithms useless in practice.…”
Section: Introductionmentioning
confidence: 99%
“…At least four-fold oversampling is a typical choice. Furthermore, the computational complexity of phase retrieval algorithms is a concern, since they often scale with the square of the number of unknowns or observations [29], [30] or even worse [31], [32]. This renders well thought out algorithms useless in practice.…”
Section: Introductionmentioning
confidence: 99%
“…(2018) and Palmeri et al. (2022), Equation can be rewritten in an operator form, that is, Fl=Alfl ${F}_{\mathscr{l}}={A}_{\mathscr{l}}{f}_{\mathscr{l}}$ and, then, the Singular Value Decomposition (SVD) of Al ${A}_{\mathscr{l}}$ can be performed. Hence, denoting with uscriptl,n ${u}_{\mathscr{l},n}$ the resulting n $n$‐th right‐hand singular function associated with the ℓ‐th order, each OAM spectrum mode can be expanded as follows (Palmeri et al., 2022): Fl(k)=n=1Nlbl,nuscriptl,n(k) ${F}_{\mathscr{l}}(k)=\sum\limits _{n=1}^{{N}_{\mathscr{l}}}{b}_{\mathscr{l},n}{u}_{\mathscr{l},n}(k)$ with Nl=2aλ|scriptl|π ${N}_{\mathscr{l}}=\frac{2a}{\lambda }-\frac{\vert \mathscr{l}\vert }{\pi }$ }{bl,n $\left\{{b}_{\mathscr{l},n}\right\}$ being suitable coefficients.…”
Section: Background On Oam Beam Propertiesmentioning
confidence: 99%
“…By denoting with (k $k$, ϕ $\phi $) and (ρ,ϕ) ${\rho }^{\prime },{\phi }^{\prime })$ the radial and azimuth coordinates respectively spanning the spectral and aperture planes, the far‐field pattern and the corresponding continuous aperture distribution can be respectively expanded in terms of the ℓ‐order OAM modes fl()ρ ${f}_{\mathscr{l}}\left({\rho }^{\prime }\right)$ and Fl(k) ${F}_{\mathscr{l}}(k)$ as follows: F(k,ϕ)=l=+Fl(k)ejscriptlϕ $F(k,\phi )=\sum\limits _{\mathscr{l}=-\infty }^{+\infty }{F}_{\mathscr{l}}(k){e}^{j\mathscr{l}\phi }$ f()ρ,ϕ=l=+fl()ρejscriptlϕ $f\left({\rho }^{\prime },{\phi }^{\prime }\right)=\sum\limits _{\mathscr{l}=-\infty }^{+\infty }{f}_{\mathscr{l}}\left({\rho }^{\prime }\right){e}^{j\mathscr{l}{\phi }^{\prime }}$ where proper truncations can be performed by following the rules in Palmeri et al. (2022), while the following relationship between fl()ρ ${f}_{\mathscr{l}}\left({\rho }^{\prime }\right)$ and Fl(k) ${F}_{\mathscr{l}}(k)$…”
Section: Background On Oam Beam Propertiesmentioning
confidence: 99%
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