In this paper, a new sampling scheme of the near field radiated by a planar source is proposed and assessed. More in detail, the paper shows a uniform sampling criterion that allows representing the near field over a plane with a number of measurements lower than the classical half-wavelength sampling. At first, a discretization strategy of the near field based on the warping method is recalled from the literature. The latter requires to collect a non-redundant number of field measurements that are non-uniformly arranged over the observation domain. Despite this, the warping sampling scheme works well only if the measurement plane does not overcome the source. When the observation domain is larger, it does not predict the exact positions of the field samples at the edges of the measurement plane; accordingly, in these regions it is not possible to recover the near field behavior by the collected samples. To overcome this drawback, a spatially varying oversampling is exploited. The latter is chosen in such a way that the resulting sampling becomes uniform. Such choice also ensures a growth of the sampling rate only at the edges of the observation domain permitting the retrieval of the near field by its samples. Finally, numerical simulations based on experimental data corroborate the effectiveness of the approach in recovering both the near and the far field.

In this paper, we address the problem of computing the dimension of data space in phase retrieval problem. Starting from the quadratic formulation of the phase retrieval, the analysis is performed in two steps. First, we exploit the lifting technique to obtain a linear representation of the data. Later, we evaluate the dimension of data space by computing analytically the number of relevant singular values of the linear operator that represents the data. The study is done with reference to a 2D scalar geometry consisting of an electric current strip whose square amplitude of the electric radiated field is observed on a two-dimensional extended domain in Fresnel zone.

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.