On the Optimal Field Sensing in Near-Field Characterization

Abstract

We deal with the problem of characterizing a source or scatterer from electromagnetic radiated or scattered field measurements. The problem refers to the amplitude and phase measurements which has applications also to interferometric approaches at optical frequencies. From low frequencies (microwaves) to high frequencies or optics, application examples are near-field/far-field transformations, object restoration from measurements within a pupil, near-field THz imaging, optical coherence tomography and ptychography. When analyzing the transmitting-sensing system, we can define “optimal virtual" sensors by using the Singular Value Decomposition (SVD) approach which has been, since long time, recognized as the “optimal” tool to manage linear algebraic problems. The problem however emerges of discretizing the relevant singular functions, thus defining the field sampling. To this end, we have recently developed an approach based on the Singular Value Optimization (SVO) technique. To make the “virtual” sensors physically realizable, in this paper, two approaches are considered: casting the “virtual” field sensors into arrays reaching the same performance of the “virtual” ones; operating a segmentation of the receiver. Concerning the array case, two ways are followed: synthesize the array by a generalized Gaussian quadrature discretizing the linear reception functionals and use elementary sensors according to SVO. We show that SVO is “optimal” in the sense that it leads to the use of elementary, non-uniformly located field sensors having the same performance of the “virtual” sensors and that generalized Gaussian quadrature has essentially the same performance.

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

“…In Fig. 10, the exact field radiated by the electric and magnetic current in ( 35) is compared with the interpolated field provided by (29). Despite the number of field samples is only 41, the interpolated field matches well with the exact one; indeed, 𝑒𝑟𝑟 = 0.0061 in the case of electric current and 𝑒𝑟𝑟 = 0.0244 in the case of magnetic current.…”

“…In this section a numerical analysis is performed 1. to corroborate the analytical expression of the NDF provided by ( 25), 2. to validate the interpolation formula of the near field (29). Such validation is performed by comparing the exact field computed by the radiation model (2) with the interpolation series (29). To establish the mismatch between the exact field and its approximation provided by (29), the relative error…”

“…Such validation is performed by comparing the exact field computed by the radiation model (2) with the interpolation series (29). To establish the mismatch between the exact field and its approximation provided by (29), the relative error…”

“…is considered. In particular, the exact field corresponding to 𝐽 𝑒 (𝑥 ′ ) and 𝐽 𝑚 (𝑥 ′ ) is compared with the approximation provided by (29) in Fig. 6.…”

“…Note that, apart for the exponential terms appearing in (29), the main difference between the sampling expansion of the near-field and the correspondent expansion of the near-field intensity is the bandwidth of the sampling functions that doubles. Accordingly, the sampling step for the field intensity halves and number of sampling points doubles.…”