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Antennas and Propagation, IEEE Transactions on

Issue 2 • Date March 1981

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Displaying Results 1 - 25 of 43
  • [Front cover and table of contents]

    Publication Year: 1981 , Page(s): 0
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  • Opening remarks

    Publication Year: 1981 , Page(s): 190 - 191
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  • Some mathematical considerations in dealing with the inverse problem

    Publication Year: 1981 , Page(s): 373 - 379
    Cited by:  Papers (47)
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    Many problems of mathematical physics can be formulated in terms of the operator equation Ax = y , where A is an integro-differential operator. Given A and x , the solution for y is usually straightforward. However, the inverse problem which consists of the solution for x when given A and y is much more difficult. The following questions relative to the inverse problem are explored. 1) Does specification of the operator A determine the set {y} for which a solution x is possible? 2) Does the inverse problem always have a unique solution? 3) Do small perturbations of the forcing function y always result in small perturbations of the solution? 4) What are some of the considerations that enter into the choice of a solution technique for a specific problem? The concept of an ill-posed problem versus that of a well-posed problem is discussed. Specifically, the manner by which an ill-posed problem may be regularized to a well-posed problem is presented. The concepts are illustrated by several examples. View full abstract»

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  • [Back cover]

    Publication Year: 1981 , Page(s): c4
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  • Use of Radon's projection theory in electromagnetic inverse scattering

    Publication Year: 1981 , Page(s): 336 - 341
    Cited by:  Papers (7)
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    In a wide variety of electromagnetic profile reconstruction or shape imaging techniques, a need often arises to deduce the three-, two-, or one-dimensional distribution of different physical quantities from their projections, e.g., in radio-astronomy, structural biology, roentgenology, geophysics, and also in electromagnetic imaging. Investigation of such problems in various specialized areas resulted in the establishment of the new interdisciplinary subject known as "reconstruction from projections." The underlying theory, which was first rigorously formulated by Radon, will become of increasing importance to radar target mapping, wave-imaging, and related electromagnetic inverse problems; therefore, a tutorial exposition is timely and well suited for this issue. Major emphasis will be placed on showing how Ludwig's theorems on support, determinacy, and self-consistency can be used favorably to analyze the data-limited reconstruction cases. The derived theorems will be applied to the specific case of physical optics far field inverse scattering, clearly proving that the Bojarski and the Kennaugh identities constitute a Fourier-Radon transform pair. View full abstract»

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  • Ramp response radar imagery spectral content

    Publication Year: 1981 , Page(s): 399 - 401
    Cited by:  Papers (4)
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    The physical optics (PO) approximation is examined in the time domain to illustrate certain relationships between an area function interpretation of the physical optics scattering estimate and the span of interrogating frequencies required to produce an image of the object. The consequences of extending the normal physical optics integration limit to encompass the entire object are demonstrated using conducting spheres, disks, cone spheres, and hemispherical objects. Low frequency interrogating signals are stressed for imaging purposes with an interpretation of when such signals must be supplemented by higher frequencies. View full abstract»

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  • Operator-theoretic and computational approaches to Ill-posed problems with applications to antenna theory

    Publication Year: 1981 , Page(s): 220 - 231
    Cited by:  Papers (29)
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    A general framework for regularization and approximation methods for ill-posed problems is developed. Three levels in the resolution processes are distinguished and emphasized: philosophy of resolution, regularization-approximation schema, and regularization algorithms. Dilemmas and methodologies of resolution of ill-posed problems and their numerical implementations are examined in this framework with particular reference to the problem of finding numerically minimum weighted-norm least-squares solutions of first kind integral equations (and more generally of linear operator equations with nonclosed range). A common problem in all these methods is delineated: each method reduces the problem of resolution to a "nonstandard" minimization problem involving an unknown critical "parameter" whose "optimal" value is crucial to the numerical realization and amenability of the method. The "nonstandardness" results from the fact that one does not have explicitly, or a priori, the function to be minimized; it has to built up using additional information, convergence rate estimates, and robustness conditions, etc. Several results are developed that complement recent advances in numerical analysis and regularization of inverse and ill-posed (identification and pattern synthesis) problems. An emphasis is placed on the role of constraints, function space methods, the role of generalized inverses, and reproducing kernels in the regularization and stable computational resolution of these problems. The results will be applied specifically to problems of antenna synthesis and identification. However the thrust of the paper is devoted to the interdisciplinary character of operator-theoretic and numerical methods for ill-posed problems. View full abstract»

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  • The unique reconstruction of a scalar or vectorial field from its values on an arbitrary surface to which it has propagated through an arbitrary medium

    Publication Year: 1981 , Page(s): 404 - 405
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    The problem of the determination of the values of a field on a surface to which it has propagated through an arbitrary medium is shown to have a unique solution if the field satisfies any linear elliptic partial differential equation. View full abstract»

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  • The K-pulse concept

    Publication Year: 1981 , Page(s): 327 - 331
    Cited by:  Papers (56)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (488 KB)  

    Two general classes of inversion techniques may be distinguished: those utilizing angular or spatial frequency analysis over as wide a range of target aspects as practicable, and those involving relatively few aspects but employing as wide a frequency spectrum as possible. The latter technique is discussed, and a special excitation waveform called the "kill-pulse" or K-pulse is proposed. By analogy with lumped and distributed networks, a unique aspect-invariant excitation waveform is postulated for an isolated scatterer. This waveform, of finite and minimal duration, then characterizes the pole spectrum of the scatterer as used in the singularity expansion method (SEM) or for target identification. The derivation of this excitation waveform and its relation to one or more surface waves is illustrated by several examples. Using surface waves initiated at certain points of an object, the complex attenuation of circumnavigating waves is estimated by the geometrical theory of diffraction. Three-parameter characteristic equations are derived which predict pole strings with excellent accuracy for conducting spheres and cylinders and lesser accuracy for prolate spheroids of several axial ratios. For spheres and cylinders, the same characteristic equation also yields good estimates of cavity resonance frequencies. View full abstract»

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  • Electromagnetic geophysical imaging incorporating refraction and reflection

    Publication Year: 1981 , Page(s): 288 - 292
    Cited by:  Papers (3)  |  Patents (1)
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    An accurate technique for remotely determining the internal structure of an object or underground environment would have a significant impact in mining, geoexploration, ultrasonics, and the life sciences. This process of resolving the intrinsic properties of an object or environment by the transmission of radiation or ultrasound through the unknown anomaly is known as reconstructive imaging or tomography. Several efforts have been made to apply imaging (reconstruction) methods to measurements taken between two boreholes on either side of an unknown geophysical structure. However, it became necessary, because of the nature of existing reconstruction methods, to assume a straight-line propagation path from source to receiver. This assumption is not valid in many important applications of geophysical imaging; thus it is desirable to develop a method to account for the radiation mechanisms of refraction and reflection in the unknown medium. An imaging scheme that explicitly incorporates refraction and first-order reflection in the reconstruction process is developed. Several examples of successful reconstruction of multicell underground environments are presented to demonstrate its accuracy. View full abstract»

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  • Iterative determination of permittivity and conductivity profiles of a dielectric slab in the time domain

    Publication Year: 1981 , Page(s): 239 - 245
    Cited by:  Papers (32)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (616 KB)  

    A numerical method is presented to compute one unknown constitutive parameter of an inhomogeoeous lossy dielectric slab from the reflected field in the time domain. The method is based upon a space-time discretization of the integral equation for the reflected field. In the inversion, especially those space-time points where the numerical computation of the electric-field strength in the slab is most accurate are taken into account. This is achieved by computing the unknown parameter iteratively. Alternately solving equations for an approximate direct-scattering problem and an approximate inverse-scattering problem yields successive approximations for the electric field in the slab and the unknown constitutive coefficient. Both problems lead to an infinite system of linear equations from which a finite subsystem is selected. General criteria for this selection are presented. Various profiles have been reconstructed numerically from the reflected field due to a sine-squared incident pulse. View full abstract»

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  • The applicability of an inverse method for reconstruction of electron-density profiles

    Publication Year: 1981 , Page(s): 245 - 252
    Cited by:  Papers (6)
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    Inverse scattering theory is used to reconstruct profiles of electron density from the analytic representation of the reflection coefficient. The complex reflection coefficient r(k) is represented as a rational function of the wavenumber k . Using a three-pole approximation for r(k) , the one-dimensional inverse scattering theory is applied to obtain a closed-form expression for the electron-density profile function q(x) . The integral equation of the inverse scattering theory (Gelfand-Levitan equation) is solved by a differential-operator technique, and several numerical examples are given. Three-pole reflection coefficients are found to be applicable to the reconstruction of relatively thin electron layers which might be generated in the laboratory. Rational reflection coefficients with an increased number of poles are found to be necessary to simulate other electron layers of physical interest. This is demonstrated by comparison of multipole reflection coefficients in the Butterworth approximation with reflection coefficients calculated from Epstein's direct scattering theory for electron layers. A parameter in the Epstein theory, which characterizes the total electron content of the layer, is related to the number of poles needed to reconstruct that layer. Estimates are thus obtained of the number of poles needed to reconstruct ionospheric layers and other plasmas of physical interest. View full abstract»

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  • Physical optics imaging with limited aperture data

    Publication Year: 1981 , Page(s): 332 - 335
    Cited by:  Papers (1)
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    Some results are reported of an applied research effort concerning the imaging and/or identification of conducting cones based on measured transient response data. An important restriction on the effort was that data were available at only a few look angles, all within \pm30\deg of nose-on incidence. The accuracy between measured data set and physical optics inverse scattering results is first examined, and then the problem of inverse scattering from limited look angle data is discussed. View full abstract»

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  • Estimation of the volume and the size of a scatterer from band-limited time domain signature

    Publication Year: 1981 , Page(s): 398 - 399
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    An inverse scattering model, based on the time domain concepts of electromagnetic theory, is developed using the first five (zeroth to fourth) moment condition integrals to recover the Rayleigh coefficient and the next higher order nonzero coefficient of the power series expansion in k (wavenumber) of the target backscattering response. The Rayleigh coefficient and the other coefficient thus recovered are used to determine the dimensions and orientation of the object (with the ellipsoidal assumption for the object shape). The input data required for this coefficient recovery technique (CRT) are the object backscatter response to a band-limited pulse over a finite number of interrogating direction. View full abstract»

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  • The phase retrieval problem

    Publication Year: 1981 , Page(s): 386 - 391
    Cited by:  Papers (32)  |  Patents (1)
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    The phase retrieval problem arises in applications of electromagnetic theory in which wave phase is apparently lost or impractical to measure and only intensity data are available. The mathematics of the problem provides unusual insights into the nature of electromagnetic fields. The theory is reviewed and illustrated. The basic issue of the phase retrieval problem, stated for a one-dimensional field, is that although a unique Fourier transform relation exists between the field F(x) in the Fraunhofer plane and the field u(x') in the object plane, the infinite fold phase ambiguity which appears as the result of the possibilities of conjugating the zeros of F(z), z = x + jy implies that additional information or processing of the object wave must be available to obtain the phase. Among the possible solutions which are described are reference beam addition, apodization and the use of multiple intensity distributions, permitting the use of iterative computational procedures in some applications. View full abstract»

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  • Self-consistent evaluation of complex constitutive parameters

    Publication Year: 1981 , Page(s): 408 - 412
    Cited by:  Papers (2)
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    An inverse process in remote sensing inverts the constitutive parameters of matter from measurable quantities at sensors. Analytical models relating the measurable and desired parameters are usually formulated with simplifying assumptions. However real matter and sensors often do not behave as assumed. Undue errors arising from discrepancies between assumed conditions and in situ measurements can be reduced through calibration and self-cansistency checks. Multipole expansion techniques are used here as a basis to check whether the sensors and the matter being interrogated are behaving as assumed. The self and transfer impedances of coaxial coils in an earth formation are formulated as an example to invert constitutive parameters from measurable impedances. The formulation assumes that the earth is linear, isotropic, and homogeneous and that the coils support only dipole and quadrupole interactions. For the analytical models to be self-consistent under the assumed conditions, several sets of inverted parameters from measurable impedances would have to agree to within acceptable uncertainties. Self-consistent evaluations of constitutive parameters can reduce costly undue errors that may arise, e.g., in locating gas/oil-bearing strata underground. View full abstract»

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  • The inverse electromagnetic scattering problem for a perfectly conducting cylinder

    Publication Year: 1981 , Page(s): 364 - 368
    Cited by:  Papers (9)
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    The problem of determining the shape of the cross section of a simply connected perfectly conducting infinite cylinder from a knowledge of the far-field pattern for all angles of observation and small values of the wavenumber is considered. The method proposed relies heavily on conformal mapping techniques. In particular it is shown that if the transfinite diameter is known each Fourier coefficient of the far-field pattern of the electric field determines a Laurent coefficient of the conformal mapping taking the exterior of the unit disk onto the exterior of the unknown cross section. The transfinite diameter is determined by changing the polarization of the incoming wave and measuring the far-field pattern of the resulting magnetic field. Of particular interest is the case when only a finite number of the Fourier coefficients of the far-field pattern are known. In this situation error estimates are obtained by using results on coefficient estimates for univalent functions. View full abstract»

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  • Improved resolution in microwave holographic images

    Publication Year: 1981 , Page(s): 320 - 326
    Cited by:  Patents (1)
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    Microwave holography is a useful experimental technique for imaging remote or inaccessible objects and for diagnostics of antennas, radomes, and scatterers; however, diffraction restricts image resolution. A method is described for improving resolution in microwave holography. The holograms are spherical or circular. Porter's scalar theory of curved holograms is extended to vector fields by using rectangular components to treat the effects of wave polarization. The mathematical formulation is a Helmholtz diffraction integral. We show that this integral can be written as a convolution for currents on line segments. The convolution is applied to the spatial frequency spectra of images. Theoretical examples, an infinitesimal dipole and a half-wave dipole, are reconstructed exactly, by a theory of analytic continuation. An experimental example is described; it is diffraction of a half-wavelength wide slit in a conducting screen. The analytic continuation of the holographically reconstructed near-field produced images with resolution approximately one quarter wavelength. Before continuation, resolution was 0.6 wavelength. In addition, the boundary condition of the vanishing tangential field over the metal screen is better satisfied by the image produced by continuation. View full abstract»

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  • On computation of electromagnetic fields on planar surfaces from fields specified on nearby surfaces

    Publication Year: 1981 , Page(s): 402 - 404
    Cited by:  Papers (15)
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    A technique is presented for solution of the inverse problem of calculating the electric field on a planar surface from the electric field specified on a nearby surface. An integral equation is derived that relates two orthogonal components of the electric field on the nearby surface to the respective components of the plane wave spectrum of the planar electric field. The integral equation is solved by an iterative technique, and the planar near field is calculated by an inverse Fourier transform of the plane wave spectrum. View full abstract»

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  • Time domain approach to inverse scattering

    Publication Year: 1981 , Page(s): 359 - 363
    Cited by:  Papers (4)
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    A plane wave is considered incident upon a medium, the inhomogeneities of which can vary arbitrarily in three-dimensional space, except that changes in wave polarization must be negligible. Observation of the scattered field is assumed over a plane. An algorithm for reconstructing the inhomogeneous frequency-independent refractive index is outlined. The analysis, which is conducted wholly in the time domain, is introduced by a discussion (supported by numerical examples) of several scattering problems involving a single-space dimension. View full abstract»

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  • Improved performance of a subsurface radar target identification system through antenna design

    Publication Year: 1981 , Page(s): 307 - 311
    Cited by:  Papers (19)
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    Improved identification performance of a video pulse subsurface radar system is reported. The video pulse system, which utilizes complex natural resonances of the target and a prediction correlation processing, is improved in comparison to the system reported previously by better fitting the system bandwidth to the bandwidth which contains the complex natural resonances of the desired target. The antenna and associated hardware modifications to achieve this are described. Identification performance of the modified system is given using actual buried land mine-like targets. Significant improvement of the quality of the received waveforms and hence the signal-to-clutter ratio is obtained. Potential further improvement is discussed. This may be achieved by removing the natural resonance associated with the antenna from the data prior to the application of the predictor correlator. View full abstract»

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  • Target classification with multiple frequency illumination

    Publication Year: 1981 , Page(s): 352 - 358
    Cited by:  Papers (7)
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    Target classification may be viewed as a crude form of inverse scattering that determines which of M prespecified body shapes is most consistent with the scattered field data. A method is described for discriminating between different target shapes by appropriately processing the backscattered waveforms or target signature observed in radar receivers. Although this general subject has received considerable attention in the recent literature, the present paper is among the first to theoretically examine the automatic target classification problem for a specific application with currently operational radars. The method for shape classification uses scattered returns from two or more collocated sources operating at different frequencies and polarizations. The basic technique consists of appropriately comparing the received data with the contents of a stored signature library that has been obtained a priori by either calculations or measurements. The technique is demonstrated for the case of radar space object identification which often involves very noisy observations of the target signature. The target classification algorithm is synthesized from decision theoretic principles, which, coupled with a rigorous technique for target response calculation, provides for reliable classification of simple space objects during their first pass in view of the sensor. The classification technique requires no a priori information concerning target motion and estimates the aspect angle automatically. It operates sequentially on incoming data, gives an improved estimate of target class after each additional data point, and provides a confidence measure associated with the current decision. Finally, the classifier determines if the target is not in the signature library by means of its target rejection capability. View full abstract»

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  • Encoding of information in inverse scattering problems

    Publication Year: 1981 , Page(s): 406 - 408
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    The use of functions of class E for encoding information in inverse scattering-and in general inverse optical-problems is outlined. The way in which zeros describe all the information about band-limited functions is presented. Subsequently, the advantages of utilizing this description are considered. View full abstract»

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  • Synthetic imaging from coherent backscattering

    Publication Year: 1981 , Page(s): 380 - 385
    Cited by:  Papers (1)
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    Scattered fields from radar targets can be processed to construct target images. An analytical simulation of coherent backscattering and synthetic imaging is reviewed. Conducting objects with an axial symmetry are used as examples to demonstrate the results of analytical backscattering and synthesis procedure. An interrogating radar waveform is simulated using the Hamming weighting function. The pulse repetition frequency is selected so as to avoid slant-range image ambiguity. Backscatterings from axially symmetric targets are formulated by using the diffraction coefficients in the plane containing symmetry axis. Target-backscattered pulses are coherently processed along the aspect angles of interrogation. Coherent data are then synthesized using the Woodward method to construct target images. Four examples of synthesized images demonstrate that adequate shape and size estimates can be made even with partial backscatterings. The totally analytical simulations on scattering and imaging constitute an economical tool to visualize scattering mechanisms of complex targets and to more effectively utilize synthetic-imaging capability. View full abstract»

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  • Time domain inverse scattering

    Publication Year: 1981 , Page(s): 213 - 219
    Cited by:  Papers (15)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (640 KB)  

    The inverse scattering problem is addressed directly in the time domain using an exact space-time integral equation as the basis for solution. A time domain approach to the solution is presented and demonstrated for the case of conducting rotationally symmetric targets with both axial incidence and broadside incidence. Both an iterative and a direct solution technique are illustrated and compared. View full abstract»

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IEEE Transactions on Antennas and Propagation includes theoretical and experimental advances in antennas.

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Editor-in-Chief                                                 Kwok W. Leung