Near-Field Sampling for Line Sources

Abstract

Near-fi eld sampling seeks to represent electromag- netic fi elds between transmitting and receiving regions using a minimal number of measurement points while preserving the dominant spatial modes. This paper develops a geometry- aware sampling framework based on spatial degrees of freedom (DoF). A view-length formulation is used to derive closed-form expressions for the propagating-mode DoF density for simple line-source geometries, providing both the total DoF and its local distribution. One-DoF sampling points are obtained from equal increments of the cumulative DoF density, yielding an adaptive nonuniform sampling strategy up to the knee of the singular-value spectrum. To improve the representation of the remaining modes beyond the knee, a reactive-mode density is introduced to guide the placement of additional edge samples. An operator-based sampling error functional is formulated and shown to be lower-bounded by the neglected singular values of the continuous channel operator. Numerical results demonstrate that the proposed sampling strategy closely approaches the optimal performance obtained from singular-value decomposition and signifi cantly outperforms sampling based solely on the propagating-mode DoF density.