NDF of the near-zone field on a line perpendicular to the source

Abstract

<div><div>In the manuscript, we address the problem of evaluating the</div><div>number of degrees of freedom (NDF) of the field radiated by a strip source along all the directions orthogonal to it. </div><div>The NDF represents at the same time the number of independent functions required to represent the data with a given degree of accuracy, and the dimension of the unknowns subspace that can be stably reconstructed. For such reason, the knowledge of the NDF gives insight on the forward and on the inverse problems and it represents one of the metrics to evaluate the achievable performance in the inversion.</div></div><div>The main difficulty arises since in near-zone the eigenvalue</div><div>problem that must be solved for the computation of the NDF,</div><div>involves a non-convolution and non-bandlimited kernel. In the paper, we show how to overcome this drawback and how to obtain a closed-form expression of the NDF which highlights the role played by the configuration parameters.</div>

Dimension and Sampling of the Near-Field and Its Intensity Over Curves

“…However, as shown in Appendix A, no stationary points appears when all the possible straight lines linking two different point of the observation curve do not intersect the source. Instead, an interesting setup where the phase function admits a stationary point is analyzed in [54].…”