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.
Highlights
Near-field source characterization consists of reconstructing the radiating features of a transmitter by measuring its radiated field in the near-zone using field sensors [1,2,3,4]
We show that Singular Value Optimization (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
The “virtual” sensors defined by the Singular Value Decomposition (SVD) are “optimal” since they are the minimum number of sensors capable to extract all the information of the field radiated by the transmitter belonging to a specified class of transmitters on the measurement area and for the considered geometry of the link
Summary
Near-field source characterization consists of reconstructing the radiating features of a transmitter by measuring its radiated field in the near-zone using field sensors [1,2,3,4]. The “virtual” sensors defined by the SVD are “optimal” since they are the minimum number of sensors capable to extract all the information of the field radiated by the transmitter belonging to a specified class of transmitters on the measurement area and for the considered geometry of the link. They are “virtual” because, as will be remarked below, the most convenient representation is by arrays or segmented sensors. Modelling of the Sensor We describe the sensing process as a scattering process, see Figure 2—left, and generalize the concept of effective length
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