Performance of Phase Retrieval via Phaselift and Quadratic Inversion in Circular Scanning Case

Moretta, Raffaele; Pierri, Rocco

doi:10.1109/tap.2019.2930127

Cited by 33 publications

(21 citation statements)

References 45 publications

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“…One is the expansion of the theory in order to find more general warping transformations that allow to rigorously deal with the cases addressed herein. Also, it is of sure interest to consider the cases when the radiation system is not planar [28] or amplitude only measurements are available [29].…”

Section: Acknowledgmentmentioning

confidence: 99%

Efficient Planar Near-Field Measurements for Radiation Pattern Evaluation by a Warping Strategy

et al. 2021

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The sampling of the near-field radiated by a planar source observed over a finite planar aperture is addressed. To this end, we employ the warping method that amounts to properly change the observation variables and finding the sampling points as those that allow to approximate the singular values of the radiation operator up to the so-called number of degrees of freedom. In particular, the warping transformations allow to approximate the kernel function of the relevant operator as a band-limited function and hence the sampling theorem is adopted to devise the discretization scheme. Here, we generalize the warping method to the full vector case and introduce a spatially varying oversampling strategy that allows to deal with measurement apertures which are larger than the source. It is shown that the sampling points need to be non-uniformly arranged across the measurement aperture but their number is generally much lower than classical half-wavelength sampling. A numerical analysis is included to support the theoretical arguments. Finally, numerical experiment-based results concerning the radiation pattern estimation of a planar array antenna are presented. To this end, experimental data collected under a uniform half-wavelength sampling scheme are first interpolated over the required non-uniform grid and then processed to obtain the radiation pattern INDEX TERMS Antenna measurements, Near-field far-field (NFFF) transformation, Sampling methods, Antenna radiation patterns, Non-uniform sampling

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Section: Acknowledgmentmentioning

confidence: 99%

Efficient Planar Near-Field Measurements for Radiation Pattern Evaluation by a Warping Strategy

et al. 2021

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“…However, when the singular values are not known in closed form, as for the case at hand, different approaches can be followed to get an estimation of it. For example, in optics, it is common to estimate the NDF as the number of distinguishable spots that can be realized within a given observation aperture [33]. By following the same reasoning, here, the NDF is estimated by counting how many nonoverlapping point spread function main beams are required to fill the observation domain.…”

Section: Number Of Degree Of Freedom Estimationmentioning

confidence: 99%

On-Axis Resolution of a Circular Aperture

Maisto

2021

Electronics

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In this paper, the problem to estimate the on-axis resolution in creating a desired field profile by radiation of an aperture A is addressed. The latter applies in both diffractive optics and antenna synthesis. This is because the ‘aperture theory’, A can schematize a source, for example, an antenna or a lens illuminated by an incident field radiating a significant field only on the same aperture. The analysis refers to a customary axicon geometry consisting of a circle aperture transverse to the observation domain. The aim was to find a resolution formula allowing to highlight the impact of aperture geometrical parameters for configurations that are below the Fresnel approximation. The results show that the aperture cannot approximate the target field with the same level of accuracy along with the observation domain. In particular, near the aperture, smaller details can be retrieved and as the distance increases this ability degrades.

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“…To overcome this drawback, the lifting technique can be used [3]. The latter, starting from the quadratic formulation in (1), exploits a redefinition of unknown space to recast the phase retrieval problem as a linear one.…”

Section: Introductionmentioning

confidence: 99%

“…From this discussion, it is evident that the dimension of data space plays a key role in phase retrieval via quadratic approach; hence, it is worth investigating how to evaluate it from an analytical point of view. As shown in [3], the dimension of data space can be evaluated by counting the number of significant singular values of the lifting operator. However, to the best of our knowledge, analytical results concerning the singular values behavior of lifting operator are not available in literature.…”

Section: Introductionmentioning

confidence: 99%

An evaluation of the data space dimension in phase retrieval: results in Fresnel zone

Pierri¹,

Moretta²

2021

Preprint

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<div>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.</div>

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Performance of Phase Retrieval via Phaselift and Quadratic Inversion in Circular Scanning Case

Cited by 33 publications

References 45 publications

Efficient Planar Near-Field Measurements for Radiation Pattern Evaluation by a Warping Strategy

Efficient Planar Near-Field Measurements for Radiation Pattern Evaluation by a Warping Strategy

On-Axis Resolution of a Circular Aperture

An evaluation of the data space dimension in phase retrieval: results in Fresnel zone

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