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

In this paper, the problem of computing the number of degrees of freedom (NDF) of the field radiated by a strip current along all the possible lines orthogonal to the source is addressed.

As well known, the NDF is equal to the number of singular values of the radiation operator that are before a critical index at which they abrupt decay. Unfortunately, in the considered case, the solution of the associate eigenvalue problem is not known in closed-form, and this prevents us from directly evaluating the singular values of the radiation operator. To overcome this drawback, a weighted adjoint operator is exploited. The latter allows obtaining an eigenvalue problem whose solution is known in closed-form but, at the same time, it modifies the singular values behavior. However, since the change affects only the dynamics of the singular values but not the critical index at which they abrupt decay, the NDF of the radiated field can be analytically estimated by resorting to the weighted adjoint operator.