218 research outputs found

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

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    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 twodimensional extended domain in Fresnel zone

    On the Sampling of the Fresnel Field Intensity over a Full Angular Sector

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    In this article, the question of how to sample the square amplitude of the radiated field in the framework of phaseless antenna diagnostics is addressed. In particular, the goal of the article is to find a discretization scheme that exploits a non-redundant number of samples and returns a discrete model whose mathematical properties are similar to those of the continuous one. To this end, at first, the lifting technique is used to obtain a linear representation of the square amplitude of the radiated field. Later, a discretization scheme based on the Shannon sampling theorem is exploited to discretize the continuous model. More in detail, the kernel of the related eigenvalue problem is first recast as the Fourier transform of a window function, and after, it is evaluated. Finally, the sampling theory approach is applied to obtain a discrete model whose singular values approximate all the relevant singular values of the continuous linear model. The study refers to a strip source whose square magnitude of the radiated field is observed in the Fresnel zone over a 2D observation domain

    A novel phase retrieval technique based on propagation diversity via a dielectric slab.

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    This paper deals with a novel technique to determine the far field of an aperture starting from the knowledge of two near-field intensity data sets collected over the same measurement plane. The diversity between the two intensity data sets is achieved by ensuring different conditions of the near field propagation between the aperture and the measurement plane. In particular, one measurement is performed under free-space propagation condition while the second one is performed by exploiting a dielectric slab, with known properties, filling partly the space between the aperture and the measurement plane. A phase retrieval technique, that faces a non linear inverse problem, is solved by assuming as unknown the plane wave spectrum of the aperture field. The feasibility of the novel approach is presented also in comparison with the usual near field phase retrieval technique exploiting measurements of the near field intensity over two scanning planes. © 2007 Optical Society of America

    Numerical Investigation about Frequency Behaviour of Conformal FSS

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    Frequency selective surfaces (FSSs) are spatial filters widely employed in high-performance applications like hybrid radomes for radars and antennas. While planar geometries are widely studied, less attention has been devoted to conformal ones, where we must consider the influence of both the lattice geometry and the shape and size of the individual elements. In the planar case, periodicity first impacts on the general reflecting properties of the surface, while the shape and the size of the individual element affect its detailed both spatial and frequency filtering behaviour. In particular, the frequency response is dictated mainly by the scattering by the individual element and attains its maximum at resonance conditions. We mean to numerically investigate whether the same also occurs for non-planar surfaces and curved elements, for both cylindrical and conical surfaces. We compare the results of the general frequency behaviour of FSS both made of strips in free space and slots cut in a perfectly conducting material. The effect of the lattice geometrical parameters is also appreciated. The main conclusions are that also for curved elements a frequency selective behaviour can be appreciated and the interaction with the single elements plays an important role, when mutual coupling is not strong

    The Dimension of Phaseless Near-Field Data by Asymptotic Investigation of the Lifting Operator

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    In this paper, the question of evaluating the dimension of data space in an inverse source problem from near-field phaseless data is addressed. The study is developed for a 2D scalar geometry made up by a magnetic current strip whose square magnitude of the radiated field is observed in near non-reactive zone on multiple lines parallel to the source. With the aim of estimating the dimension of data space, at first, the lifting technique is exploited to recast the quadratic model as a linear one. After, the singular values decomposition of such linear operator is introduced. Finally, the dimension of data space is evaluated by quantifying the number of “relevant” singular values. In the last part of the article, some numerical simulations that corroborate the analytical estimation of data space dimension are shown

    Performance of the Linear Model Scattering of 2D Full Object with Limited Data

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    Inverse scattering problems stand at the center of many important imaging applications, such as geophysical explorations, radar imaging, and synthetic-aperture radar (SAR). Several methods have been proposed to solve them when the full data are available, usually providing satisfactory reconstructions. However, it is impossible to acquire the full data in many practical circumstances, such as target detection and ground penetrating radar (GPR); consequently, only limited data are available. Thus, this paper focuses on the mathematical analysis and some numerical simulations to estimate the achievable resolution in reconstructing an object from the knowledge of the scattered far-field when only limited data are available, with multi-view excitations at a single frequency. We focus on 2D full rectangular geometry as the investigation domain (ID). We also examine the number of degrees of freedom (NDF) and evaluate the point spread function (PSF). In particular, the NDF of the considered geometry can be estimated analytically. An approximated closed-form evaluation of the PSF is recalled, discussed, and compared with the exact one. Moreover, receiving, transmission, and angle sensing modes are considered to apply the analysis to more realistic scenarios to highlight the difference between the corresponding NDF and the resulting resolution performances. Finally, interesting numerical applications of the resolution analysis for the localization of a collection of point-like scatterers are presented to illustrate how it matches the expectations

    A sampling strategy of the radiation operator in near-zone based on an asymptotic kernel

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    In this paper, we address the problem of discretizing the singular system of the radiation operator concerning the case of a magnetic strip current whose radiated field is observed in near-zone on a bounded line parallel to the source. This question has been already addressed in previous articles with the limitation that the extension of the observation domain does not overcome the source size. In this article, we remove such limitation, hence, we provide a discrete model that well approximates the singular values of the radiation operator in the case where the observation domain is larger than the source

    NDF and PSF Analysis in Inverse Source and Scattering Problems for Circumference Geometries

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    This paper aims at discussing the resolution achievable in the reconstruction of both circumference sources from their radiated far-field and circumference scatterers from their scattered far-field observed for the 2D scalar case. The investigation is based on an inverse problem approach, requiring the analysis of the spectral decomposition of the pertinent linear operator by the Singular Value Decomposition (SVD). The attention is focused upon the evaluation of the Number of Degrees of Freedom (NDF), connected to singular values behavior, and of the Point Spread Function (PSF), which accounts for the reconstruction of a point-like unknown and depends on both the NDF and on the singular functions. A closed-form evaluation of the PSF relevant to the inverse source problem is first provided. In addition, an approximated closed-form evaluation is introduced and compared with the exact one. This is important for the subsequent evaluation of the PSF relevant to the inverse scattering problem, which is based on a similar approximation. In this case, the approximation accuracy of the PSF is verified at least in its main lobe region by numerical simulation since it is the most critical one as far as the resolution discussion is concerned. The main result of the analysis is the space invariance of the PSF when the observation is the full angle in the far-zone region, showing that resolution remains unchanged over the entire source/investigation domain in the considered geometries. The paper also poses the problem of identifying the minimum number and the optimal directions of the impinging plane waves in the inverse scattering problem to achieve the full NDF; some numerical results about it are presented. Finally, a numerical application of the PSF concept is performed in inverse scattering, and its relevance in the presence of noisy data is outlined

    On the Singular Spectrum of the Radiation Operator for Multiple and Extended Observation Domains

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    The problem of studying how spatial diversity impacts on the spectrum (singular values) of the radiation operator is addressed. This topic is of great importance because of its connection with the so-called number of degrees of freedom concept which in turn is a key parameter in inverse source problems as well as to the problem of transmitting information by waves from a source domain to an observation domain. The case of a bounded rectilinear source with the radiated field observed over multiple bounded rectilinear domains parallel to the source is considered. Then, the analysis is generalized to two-dimensional extended observation domains. Analytical arguments are developed to estimate the pertinent singular value behavior. This allows highlighting the way observation domain features affect spectrum behavior. Numerical examples are shown to support the analytical results

    Radio-Frequency Breast Cancer Imaging Results for a Simplified Cylindrical Phantom

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    Microwave imaging is a pervasive research field andis useful in numerous applicative diagnostic noninvasive contexts. This paper focuses on two aspects. First, we perform a numerical investigation to assess the role played by fundamental parameters (i.e. number of sensors, operating frequency bandwidth) on cancer detection. To this end, a simplified cylindrical phantom probed by ideal two-dimensional dipoles (i.e. infinitely long along the axis of invariance) is considered. Second, in order to focus on the role of the antennas, we analyze, still by numerical simulations and for a simplified breast model, how performances vary when a realistic antenna is adopted
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