This paper describes, analyzes, and implements an approach to far-field determination from phaseless measurements over two planar surfaces. A proper formulation of the problem is considered as a quadratic inverse one whose data square amplitude near field. solution introduced global minimum appropriate functional. Next, perform such minimization procedure, finite dimensional representation field radiated by sources plane-wave spectrum becomes negligible outside fixed angular domain used....

The reliability of a recently introduced nonlinear estimation method for tomographic imaging is discussed in full detail. It shown how proper choice the functional spaces to which unknown quantities belong and exploitation expected properties object under test all available priori information positively affect robustness against false solutions inversion procedure. developed arguments allow authors understand causes possible solutions, suggesting countermeasures. In particular, it proposed...

A nonlinear estimation approach to solving the inverse scattering problem, and reconstructing space-varying complex permittivity of unknown objects is considered. The bilinear operator equations governing are approximated into finite dimensional spaces on basis degrees freedom data, simple concept that one cannot expect reconstruct an arbitrary function from a number independent equations. As consequence, discrete model, well suited numerical inversion, developed. particular nature...

A <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">through-wall</i> xmlns:xlink="http://www.w3.org/1999/xlink">imaging</i> problem for a 3-D geometry is considered. Scatterers are located beyond wall represented by dielectric slab whose features unknown or known with some degree of uncertainty. two-step imaging procedure presented. First, the thickness and permittivity estimated simple which takes into account that actual measurements concern total...

An innovative and effective technique to determine the far-field of a radiating system from near-field intensity data is introduced, analyzed, tested. The approach based on simultaneous measurement amplitude voltages received by two different probe antennas moving over single scanning surface in near zone performs phase retrieval assuming as unknown plane wave spectrum field. radiated field then straightforwardly evaluated. As compared existing phaseless techniques, use probes makes it...

The possibility of determining the far field radiating systems by measuring only near-field amplitude is investigated. main difficulties problem are examined in some detail and a new near-field/far-field transformation technique developed, based on measurement over two surfaces surrounding antenna under test. accuracy far-field reconstruction results related both to distance between such priori information concerning phase and/or system. system allows relaxation need for any provided that...

A shape reconstruction algorithm is formulated for the multimonostatic configuration and 2-D geometry. The imaging based on Kirchhoff approximation, works in frequency domain, exploits singular value decomposition tool to achieve a stable solution. effectiveness of shown by processing synthetic data time domain generated via finite-difference time-domain code. performance analysis solution addressed with varying host medium measurement configurations, also 3-D Finally, an experimental...

The inverse source problem for a 2-D geometry is considered in the circular geometry. mathematical relationship between radiated pattern and current investigated by appropriate singular value decomposition different planar curved shapes. spectral analysis allows discussing number of degrees freedom each reveals peculiar common passband behavior radiation operator. For some geometries, this can significantly affect reconstruction reducing class sources that be stably reconstructed, therefore,...

The problem of computing the singular system radiation operator pertaining to case strip currents is dealt with. associate eigenvalue involves a space-variant whose kernel not band-limited. As consequence, sampling approach, which has been recently introduced for eigenwavefronts some band-limited linear space-invariant imaging systems, cannot be used as such. To overcome this drawback, it shown that function can recast varying function. This allows exploiting pseudo-sampling series theory...

We investigate the problem of determining number degrees freedom radiated fields. In particular, this analysis concerns determination `information content' provided by knowledge field over bounded observation domains located both in Fresnel zone and near zone, when only a priori information about geometrical parameters planar source is known.

This paper deals with the problem of determining shape unknown perfectly conducting infinitely long cylinders, starting from knowledge scattered electric far field under incidence plane waves a fixed angle and varying frequency. The is formulated as nonlinear inverse one by searching for compact support distribution accounting objects contour. to data mapping then linearized means Kirchhoff approximation, which reduces it into Fourier transform relationship. Then, inversion incomplete dealt...

The reconstruction of the field radiated by a source from square amplitude-only data falls into realm phase retrieval. In this paper, we tackle retrieval with two different approaches. first one is based on convex optimization problem called PhaseLift. latter exploits lifting technique to recast as linear an increased number unknowns and then, because highly undetermined, it adds further constraints (based mathematical properties solution) estimate it. second approach formulates least...

This paper deals with the classical question of estimating achievable resolution in terms configuration parameters inverse source problems. In particular, study is developed for two-dimensional prototype geometry, where a strip (magnetic or electric) to be reconstructed from its radiated field observed over bounded rectilinear domain parallel source. Resolution formulas are well known when collected far Fresnel zone Here, plan expand those results by removing geometrical limitations due...

In this analysis some limitations of the linear Born approximation in diffraction tomography problem from far-zone data are pointed out. The is performed by means singular-value decomposition scattering operator scalar two-dimensional case a circular dielectric cylinder illuminated TM-polarized plane wave. It shown that validity entails important condition object not present too-fast spatial variations permittivity profile. For rotationally symmetric cylinder, evidence presented imaginary...

The problem of determining the achievable resolution limits in reconstruction a current distribution is considered. analysis refers to one-dimensional, scalar case rectilinear, bounded electric when data are collected by measurement radiated field over finite rectilinear observation domain located Fresnel zone, orthogonal and centered with respect source. investigation carried out means analytical singular-value decomposition radiation operator connecting unknown, which made possible...

Signal reconstruction from phaseless data occurs in electromagnetics both the diagnostics of large reflector antennas and near‐field testing microwave millimeter wave antennas. The main difficulty solving such problems arises its inherent nonlinearity. Because latter, fact, solution procedure can converge to a function which has nothing deal with actual solution. In this paper we review summarize properties recently proposed approach phase retrieval allows understand possibly avoid false...

The problem of determining radiated electromagnetic fields from phaseless distributions on one or more surfaces surrounding the source is considered. We first examine theoretical aspects and basic points an appropriate formulation show advantage tackling as inversion quadratic operator, which, by acting real imaginary parts field, provides square amplitude distributions. Next, useful properties representations both are introduced, thus making it possible to come a convenient...

The reliability of two different implementations a quadratic phase retrieval approach to the problem determining far field radiating system from only square amplitude information on near zone is studied. first implementation exploits data over scanning surfaces. second one voltages received by probes moving single surface. It pointed out how diversity between surface or gives rise "cancellation effects" which help in avoiding local minima problem. Numerical examples are shown discuss global...

We consider the problem of reconstructing shape perfectly conducting cylinders under physical optics approximation. For direct scattering, provides small model errors when scatterers are convex, smooth, have large radii curvature as compared to impinging wavelength, and noninteracting. In this paper, we investigate whether these hypotheses can be relaxed for inverse problem. particular, three classes (circular cylinder with radius smaller than multiple cylinders, a concave cylinder) show...

In this paper, a 1-D inverse-scattering problem laying within the framework of through-wall imaging is addressed. particular, localizing interfaces slab hidden behind an obstacle, another whose electromagnetic features and thickness are known, considered. To end, approximate linear mathematical relationship between scattered field unknown slab-interface positions stated. Such arises from neglecting multiple-reflections two slab's obstacle. The locations represented as support Dirac-delta...

In this paper, a simple strategy to detect changes in through-the-wall imaging scenarios is presented. particular, tomographic reconstructions taken at different instants of time are exploited. This allows increase the detectability scatterers whose positions varied two data collections. The feasibility technique demonstrated with both synthetic and experimental data.

A through-wall-imaging problem where the scatterers are located beyond a 1-D nonhomogeneous unknown wall is considered. As well known, as part of propagation takes place within wall, knowledge its electromagnetic properties mandatory in order to obtain properly focused images. Accordingly, this paper's focus on estimation problem. To end, simple procedure estimate transmission coefficient introduced and validated by synthetic data. The proposed works for symmetric lossless does not rely...

The singular value decomposition of the far-zone scattering operator for weak strip-like objects is studied under multiple view and/or frequency illuminations. aim to highlight how such diversities impact number degrees freedom (NDF) problem. When angles incidence frequencies vary within discrete finite sets, values are analytically determined. It shown that they exhibit a multistep behavior. For continuous case, upper and lower bounds found, which allows us obtain estimations NDF...