Abstract
Field sampling should be devised to preserve the information required for the knowledge of the radiation of an antenna. In this paper, we introduce a sampling scheme based on an inverse source problem approach to the far field radiated by a conformal current source. The regularized solution of the problem requires the computation of the Singular Value Decomposition (SVD) of the relevant linear operator, leading to introduce the Point Spread Function in the observation domain, which can be related to the capability of the source to radiate a focusing beam. Then, the application of the Kramer generalized sampling theorem allows introducing a non-uniform discretization of the angular observation domain, tailored to each source geometry. The nearly optimal property of the scheme is compared with the best approximation achievable under a regularized inversion of the pertinent SVD. Numerical results for different two-dimensional curve sources show the effectiveness of the approach with respect to standard sampling approaches with uniform spacing, since it allows to reduce the number of sampling points of the far field.
Highlights
The question of the selection of the optimal sensor location in imaging problems has a mathematical relevance and practical interest because it may reduce the cost of any sensing equipment and the time to achieve field data
The goal of this paper is to investigate the possibility to devise an optimal discretization scheme of the far field radiated by a scalar 2D source current, supported on a convex curve of the plane, when the observation domain lies on the same side of the convexity of the curve
This geometry is chosen for the sake of the illustration of the approach, which is founded on the solution of the corresponding inverse source problem
Summary
The question of the selection of the optimal sensor location in imaging problems has a mathematical relevance and practical interest because it may reduce the cost of any sensing equipment and the time to achieve field data. The goal of this paper is to investigate the possibility to devise an optimal discretization scheme of the far field radiated by a scalar 2D source current, supported on a convex curve of the plane, when the observation domain lies on the same side of the convexity of the curve. This geometry is chosen for the sake of the illustration of the approach, which is founded on the solution of the corresponding inverse source problem.
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