Radial field retrieval in spherical scanning for currentreconstruction and NF-FF transformation

A near-field to far-field (NF-FF) transformation is addressed for the case of spherical scanning using equivalent magnetic currents (EMCs) and matrix methods. It is based on the decoupling of the field components and the iterative retrieval of the radial component of the electric field. The technique is applied for far-field calculation as well as for the estimation of the current distribution of the antenna under test (AUT) using spherical near-field facilities. Results from measured near-field data of several antennas are presented and compared to those of the analytical solution via a spherical wave mode expansion method     

球面近远场和远近场变换算法

天线的远场对于研究天线辐射特性具有重大意义，近场测量技术因其能够避免直接测量远场而得到广泛应用，该技术采用近远场变换获得远场，然而，检验该远场的准确性也是很重要的.为了解决此类问题，文中以球面近场测量为例，提供了一种解决方案.该方案主要探讨了球面波模式展开理论，该理论是实现球面近远场变换算法的关键，其将待测天线在空间建立的场展开成球面波函数之和，天线的加权系数既包含了远场信息也包含了近场信息.因此，不仅能够利用近场测量信息获得远场辐射特性，同样能够利用远场辐射特性反推得到近场处电场，这样就能检验由近远场变换算法得到的远场是否准确.文中首先推算得到了近远场变换公式，随后进一步推算得到远近场变换的公式，最后将本文算法计算结果与FEKO测量结果进行比较，二者吻合良好，从而证实了本文两种算法的有效性.     

Fully Probe-Corrected Near-Field Far-Field Transformation Employing Plane Wave Expansion and Diagonal Translation Operators

Near-field antenna measurements combined with a near-field far-field transformation are an established antenna characterization technique. The approach avoids far-field measurements and offers a wide area of post-processing possibilities including radiation pattern determination and diagnostic methods. In this paper, a near-field far-field transformation algorithm employing plane wave expansion is presented and applied to the case of spherical near-field measurements. Compared to existing algorithms, this approach exploits the benefits of diagonalized translation operators, known from fast multipole methods. Due to the plane wave based field representation, a probe correction, using directly the probe's far-field pattern can easily be integrated into the transformation. Hence, it is possible to perform a full probe correction for arbitrary field probes with almost no additional effort. In contrast to other plane wave techniques, like holographic projections, which are suitable for highly directive antennas, the presented approach is applicable for arbitrary radiating structures. Major advantages are low computational effort with respect to the coupling matrix elements owing to the use of diagonalized translation operators and the efficient correction of arbitrary field probes. Also, irregular measurement grids can be handled with little additional effort.     

Electromagnetic radiation from a prolate spheroidal antenna enclosed in a confocal spheroidal radome

The solution of electromagnetic radiation from a prolate spheroidal antenna, excited by a delta voltage across an infinitesimally narrow gap and enclosed in a confocal radome, is obtained. The method used is that of separating the scalar wave equation in prolate spheroidal coordinates and representing the solution in terms of prolate spheroidal wave functions. A simplified solution of the electric and magnetic fields, taking into account the symmetry of the antenna in the /spl phi/ direction, is obtained. Boundary conditions are then applied on the tangential fields to obtain a linear system of equations. The system of equations is cast into matrix form and solved using an iterative technique for the unknown expansion coefficients of the fields. Radiation patterns of the antenna are obtained and presented here for the first time.     

Scattering of electromagnetic waves by a system of two dielectricspheroids of arbitrary orientation

By means of modal series expansion of the incident, scattered, and transmitted electric and magnetic fields in terms of appropriate vector spheroidal eigenfunctions an exact solution is obtained to the problem of electromagnetic scattering by two dielectric spheroids of arbitrary orientation is obtained. The incident wave is considered to be a monochromatic uniform plane electromagnetic wave of arbitrary polarization and angle of incidence. To impose the boundary conditions at the surface of one spheroid, the electromagnetic field scattered by the other spheroids is expressed as an incoming field to the first one, in terms of the spheroidal coordinates attached to it, using rotational-translational addition theorems for vector spheroidal wave functions. The solution of the associated set of algebraic equations gives the unknown expansion coefficients. Numerical results are presented in the form of plots for the bistatic and backscattering cross sections of two lossless prolate spheroids having various axial ratios, center-to-center separations, and orientations     

Electromagnetic wave scattering by a system of two spheroids ofarbitrary orientation

An exact solution to the problem of the scattering of a plane electromagnetic wave by two perfectly conducting arbitrarily oriented prolate spheroids is obtained by expanding the incident and scattered electric fields in terms of an appropriate set of vector spheroidal eigenfunctions. The incident wave is considered to be a monochromatic, uniform plane electromagnetic wave of arbitrary polarization and angle of incidence. To impose the boundary conditions, the field scattered by one spheroid is expressed in terms of its spheroidal coordinates, using rotational-translational addition theorems for vector spheroidal wave functions. The column matrix of the scattered field expansion coefficients is equal to the product of a square matrix which is independent of the direction and polarization of the incident wave, and the column matrix of the known incident-field expansion coefficients. The unknown scattered-field expansion coefficients are obtained by solving the associated set of simultaneous linear equations. Numerical results for the bistatic and backscattering cross sections for prolate spheroids with various axial ratios and orientations are presented     

基于未知源域重构的无相位近场测量技术

天线的远场对于研究天线辐射特性具有重大意义,由于远场的直接测量有着诸多限制,近场测量技术计算远场因其简洁准确的特点得到广泛应用. 然而,传统的近场测量技术要求获取近场区的幅度和相位分布才能发挥作用,随着天线频率的升高,人们想要在近场区获取准确的相位信息变得十分困难. 为了解决该技术难题,文中提出一种无相位近场测量技术. 利用一个封闭面上的幅度信息重建或猜测出包围待测天线的球面切向电场分布,并采用遗传算法进行全局优化,其最初为四组随机数据,经过数次优化后将逐渐接近准确结果. 仿真结果表明,本文方法能够在忽略相位信号的前提下,计算出准确的远场辐射特性.     

零阶角长球面波函数与长球面波函数的研究

本文深入研究了零阶角长球面波函数与长球面波函数,给出描述零阶角长球面波函数的微分方程与描述长球面波函数的积分方程不是相对应的关系。给出亥姆霍兹方程在球坐标系中与长旋转椭球坐标系中微分方程解之间的关系,可对零阶角长球面波函数了解得更清楚。对由信号最优波形设计法导出的长球面波函数积分方程,给出一种理论综合分析法,可以解决信号最优波形设计的具体实现。对长球面波函数命名尝试给出一种解释。      

Transformation formulas for spherical and spheroidal multipole fields

A transformation linking spherical multipole fields with generalized spheroidal multipole fields is derived. Applications including the inverse diffraction problem for spherically scanned near-field data for sources that due to conformal considerations are efficiently described using spheroidal (either oblate or prolate) volume support regions are discussed with the aid of numerical illustrations.     

旋转椭球函数的数值计算

本文给出了计算旋转长椭球和扁椭球函数的程序流图和相应的有用数学公式，并讨论算法，所编ＦＯＲＴＲＡＮ程序具有适应参变量范围较宽和可获较高精度的数值结果。     

A direct optimization approach for source reconstruction and NF-FFtransformation using amplitude-only data

In this paper, we present a direct optimization procedure that utilizes phaseless electric field data over arbitrary shaped surfaces for the reconstruction of an equivalent magnetic current density that represents the radiating structure of an antenna under test. Once the equivalent magnetic current density is determined, the electric field at any point can be calculated. Numerical results (both simulated and experimental) are presented to illustrate the applicability of this approach for nonplanar near-field to far-field (NF-FF) transformation as well as to antenna diagnostics. The results are presented using both theoretical and experimental phaseless data over one and two planes     

Irradiation of Prolate Spheroidal Models of Humans in the Near Field of a Short Electric Dipole

Analysis of the near-field irradiation of prolate spheroidal models of humans and animals by a short electrical dipole is described. The method of solution involves an integral equation formulation of the problem in terms of the transverse dyadic Green's function and expanding the fields irradiated by a short dipole in terms of the vector spherical harmonics. The extended boundary condition method (EBCM) is employed to solve the integral equations. The power distribution and the average specific absorption rate (SAR) are calculated and plotted as a function of the separation distance. It is shown that for a dipole placed along the major axis of the spheroidal (k-polarization), and for a very short separation distance, d= 0.15 lambda, the relative power values at both ends of the spheroid are about 40 compared with the ratio of 15 in the planewave exposure case. Furthermore, the calculated average SAR values as a function of the separation distance were found to oscillate around the constant value obtained from the planewave irradiation case. Differences between the near-and far-field exposure cases occurred only at separation distances shorter than 0.5 lambda where the magnitudes of the electric and magnetic energy densities are higher than the time-average radiation power density.     

Statistical modal analysis applied to near-field measurements of random emissions

The problem of near-field to far-field transformation of narrow-band incoherent electromagnetic fields is analyzed. The coherence matrix of signals sampled in the time domain on a surface enclosing incoherent sources is derived. Two equivalent formulations based on the processing of the coherence matrix are introduced: The signal subspace analysis and the bimodal transformation. In the signal-subspace approach, the coherence matrix is processed using a method based on singular value decomposition, giving rise to a set of functions on the surface enclosing the incoherent sources. Each of these functions is individually transformed to the far field via a modal decomposition and the sum of the transformed functions gives the total far field. In the second formulation, the bimodal transformation is used to transform the near field coherence matrix into the far field coherence matrix from which the far-field pattern is derived. The applications of the proposed transformations in the presence of noise are illustrated. A numerical example using incoherent radiating dipoles inside a leaking wire-grid enclosure validates the two formulations of near-field to far-field transformation. The proposed methodology gives the mathematical foundation for designing a compact time domain measurement facility well suited to incoherent electromagnetic radiation.     

Far-field pattern determination from the near-field amplitude ontwo surfaces

The possibility of determining the far field of radiating systems by measuring only the near-field amplitude is investigated. The main difficulties of the problem are examined in some detail and a new near-field/far-field transformation technique is developed, based on the measurement of the near-field amplitude over two surfaces surrounding the antenna under test. The accuracy of the far-field reconstruction results are related both to the distance between such surfaces and to some a priori information concerning the near-field phase and/or the radiating system. The information on the radiating system allows relaxation of the need for any information on the near-field phase provided that the distance between the measurement surfaces is high enough. Conversely, the knowledge of a more or less corrupted near-field phase allows reduction of such distances without affecting the accuracy of the far-field reconstruction. Numerical examples validating the effectiveness of the developed algorithm are provided for the planar scanning case     

Near-Field Absorption Characteristics of Biological Models in the Resonance Frequency Range (Short Paper)

In this paper, we utilized the new iterative extended boundary condition method (IEBCM) to calculate the near-field absorption characteristics of a spheroidal model of man in the resonance frequency range. These calculations complement our previous near-field results in the preresonance frequency range. Calculations were made for simple sources such as an electric dipole and a small current loop antenna. The near fields of these sources are known exactly and hence helped in explaining the absorption results in terms of the field components of the incident radiation. Numerical results for the normalized average SAR values are presented as a function of frequency for different near-field separation distances from the sources. It is generally observed that while the far-field results converge to the plane wave values, different near-field absorption characteristics occur for the two different sources. It was possible in both cases to explain the differences in the near-field average SAR values in terms of the incident near fields from the sources.     

A genetic algorithm based method for source identification andfar-field radiated emissions prediction from near-field measurements forPCB characterization

A new method for predicting the far-field radiated emissions and for finding the radiation sources of a device from near-field measurements is presented. It is based on the substitution of the original device by an equivalent set of elemental dipoles, placed over the main radiating sources, which radiate the same near-field (and therefore, far-field). This equivalent set of elemental dipoles is generated using a genetic algorithm. From the position and type of the equivalent elemental dipoles, the position of the actual radiating sources is determined. Since the field produced by an elemental dipole is known, the far-field radiation of the actual radiating source can be calculated. The new method has been tested using synthetic data and real measurements from the radiation generated by a modem PCB demonstrating its viability and usefulness     

Electromagnetic plane wave scattering by a system of two parallel conducting prolate spheroids

By means of modal series expansions of electromagnetic fields in terms of prolate spheroidal vector wave functions, as exact solution is obtained for the scattering by two perfectly conducting prolate spheroids in parallel configuration, the excitation being a monochromatic plane electromagnetic wave of arbitrary polarization and angle of incidence. Using the spheroidal translational addition theorems recently presented by the authors which are necessary for the two-body (or multibody) scattering solution, an efficient computational algorithm of the translational coefficients is given in terms of spherical translational coefficients. The field solution gives the column vector of the series coefficients of the scattered field in terms of the column vector of the series coefficients of the incident field by means of a matrix transformation in which the system matrix depends only on the scatterer ensemble. This eliminates the need for repeatedly solving a new set of simultaneous equations in order to obtain the scattered field for a new direction of incidence. Numerical results in the form of curves for the bistatic and monostatic radar cross sections are given for a variety of prolate spheroid pairs having resonant or near resonant lengths.     

Reconstruction of Equivalent Currents Distribution Over Arbitrary Three-Dimensional Surfaces Based on Integral Equation Algorithms

A technique for the determination of the equivalent currents distribution from a known radiated field is described. This Inverse Radiation Problem is solved through an Integral Equation algorithm that allows the characterization of antennas of complex geometry both for near field to far field (NF-FF) transformation purposes as well as for diagnostic tasks. The algorithm is based on the representation of the radiating structure by means of a set of equivalent currents over a three-dimensional (3D) surface that can be fitted to the arbitrary geometry of the antenna. The innovative formulation uses an integral equation involving the electric field due to the currents tangential components to the represented antenna 3D surface. For that purpose, both the magnetic and electric equivalent currents are considered in the integral equations. Regularization techniques are also introduced to improve the convergence of the proposed iterative solution. The paper concludes with several results related to the practical verification of the Equivalence Principle and the characterization of a horn antenna.     

The field of a horizontal electric dipole in the presence of a conducting protrusion

A solution to the problem on the field of a horizontal dipole located over a conducting protrusion is constructed and investigated. The protrusion is a semisphere or a semispheroid having small electric dimensions. The function of the effect of the protrusion on the field is studied in the case when the protrusion’s shape changes from a prolate spheroid through a sphere to an oblate spheroid. It is shown that the field scattered by a strongly prolate spheroidal protrusion can be substantially increased in comparison with the field scattered by a spherical protrusion with the same properties.     

ELF Electric Field Coupling to Dielectric Spheroidal Models of Biological Objects

The extremely low frequency (ELF) electric field coupling to dielectric spheroidal models of biological objects is studied. Simple expressions are obtained to determine the internal electric field strength induced inside two nonspherical spheroids; a prolate dielectric spheroid and an oblate dielectric spheroid. Certain numerical results are graphically presented for various geometric shapes of the spheroid. The results show that, unlike the symmetric dielectric sphere, the relative position of the spheroid with respect to the orientation of the impressed electric field is an extremely important parameter which considerably affects the electric field coupling.