Near-field To Far-field Transformation Research Articles

Error Comparison of CNFFFT and Hankel Method in RCS Near-Field to Far-Field Transformation

At present, there are mainly two kinds of image-based near-field to far-field transformation (NFFFT) algorithms: Hankel method and circular near-field-to-far-field transformation (CNFFFT). Due to the approximation in the measurement distance, the accuracy of Hankel method is lower than that of CNFFFT. However, the implementation of CNFFFT is complex and time-consuming. It is necessary to determine the detailed relationship between the transformation error and the near-field test distance for both algorithms to provide a basis for the choice of which algorithm to use. In this paper, the effect of the near-field test distance approximation of the two algorithms is obtained by simulating 4, 5, and 9 scattering point models. Meanwhile, an accurate comparison method for two NFFFT algorithms under different test distances is proposed.

A method for optimizing the precision of weighted fourier integral transformation algorithm

RCS refers to the radar cross section, which is an important index to reflect the electromagnetic scattering characteristics of the object. RCS measurement is the only method to obtain the real RCS of objects. Since test range often cannot reach the far-field condition for large size object, the near-field-to-far-field transformation(NFFFT) technology is significant in the RCS measurement. The core of NFFFT are different algorithms. Among them, the weighted fourier integral transformation is a universal algorithm, but the data in the aspect angle is segmented in the process, which leads to the discontinuity of the transformation results at the splicing point. This paper introduces a method to optimize the precision of weighted fourier integral transformation algorithm, which can fully suppress the discontinuity of transform results and improve the precision of weighted fourier integral transformation algorithm under the paraxial constraint conditions. Finally, the result of simulation demonstrates the precision and efficiency of this method.

Measurement and transformation of continuously modulated fields using a short-time measurement approach

Abstract. Near-field measurements, which are performed in-situ, may suffer from the fact that the antenna under test (AUT) cannot be accessed to transmit or receive a specifically tailored test signal. In some scenarios, it might also be desired to test the AUT during its real operation state, especially when it comes to the verification of antenna systems. Therefore, the need to handle time- and space-modulated fields in combination with a time-harmonic near-field to far-field transformation (NFFFT) arises. For the case where unmanned aerial vehicles (UAVs) carry the field probe in in-situ measurement scenarios, long observation times, required for the resolution of the frequency spectra of modulated fields, are detrimental due to the UAV movement resulting in blurred measurement positions. The short-time measurement (STM) approach, presented in this article, offers a way to transform the measured field data using a time-harmonic NFFFT with short observation times for the collection of the individual field samples. Measurements are shown which demonstrate the applicability of the STM approach for the measurement and transformation of continuously time-modulated fields in different measurement scenarios.

Image-Based Radar Cross Section Synthesis for a Cluster of Multiple Static Targets

This study proposes a novel image-based method for radar cross-section (RCS) prediction of a cluster of multiple static targets by synthesizing replicas of an original radar image. In this approach, we first measured the near-field backscattering of a target and reconstructed a corresponding radar image. Subsequently, modified copies of this image with rotation, translation, and spatial filtering were generated according to the predefined desired arrangement, and they were coherently summed to create a single synthesized image in which all scattering contributions contained in the modified images were virtually included. Finally, the synthesized image was utilized to predict the far-field RCS of multiple targets based on the theory of image-based near-field-to-far-field transformation (NFFFT). By employing the proposed algorithm, we can avoid building multiple test targets, resulting in reduced production costs. Moreover, we can easily test several different experimental layouts for multiple targets without repeating real measurements. Numerical simulations and experiments are conducted to demonstrate the validity of the proposed image-based RCS synthesis. The measurement results show that the proposed approach is valid when the multiple scattering between targets can be ignored, and the shadowing, which refers to the effect that a target is masked by another target, is insignificant.

Prediction of the far field radiated by a flat antenna under test from a reduced set of near‐field bi‐polar measurements

In this article, a bi-polar near-field-to-far-field (NFTFF) transformation with probe compensation, which is very convenient from the data reduction standpoint when characterising a flat antenna under test (AUT), is developed. It takes advantage from the non-redundant sampling representations of the electromagnetic fields to devise a sampling representation on the scanning plane, which requires the knowledge of the bi-polar NF samples at a reduced number of sampling points. To account for the AUT geometry, it properly adopts as modelling surface a disc having diameter equal to the largest size of such an AUT. This surface allows a more effective AUT modelling from the NF data reduction standpoint than the formerly proposed modelling surfaces for quasi-planar antennas (the oblate ellipsoid or the two-bowls), because, unlike these last, it has the capability to best fit the AUT geometry, thus reducing very significantly the involved volumetric redundancy. An ad hoc developed two-dimensional optimal sampling, interpolation formula is then employed to reconstruct the plane-rectangular NF data which would be necessary to execute the classical NFTFF transformation developed by Leach and Paris. Some results of numerical simulations and experimental proofs are reported to demonstrate the efficiency of the so developed technique.

Three-Dimensional Near-Field to Far-Field Transformation for Radar Cross Section Estimation of Elongated Targets via Subdimensional Hybrid Conversion

Image-based (IB) near-field to far-field transformation (NFFFT) is a useful method for the valid prediction of radar cross sections (RCSs) from short-range monostatic measurements. Many previous studies on the IB NFFFT algorithm have been limited to two-dimensional (2D) measurement cases. In this work, a subdimensional hybrid conversion approach is proposed as a relevant three-dimensional (3D) NFFFT method consisting of the following procedures. First, the spherical-wave information collected through 3D scanning is converted to a cylindrical waveform by applying the 2D circular NFFFT (CNFFFT) method to every vertical subplane (<i>r-θ</i> plane). Then, a horizontal far-field radar image on the <i>x-y</i> plane and an RCS pattern are extracted through direct integration of a 2D focusing operator modified to compensate for a magnitude error through distance approximation during the CNFFFT procedure. The results of a comparative study with direct integration of a 3D focusing operator are presented to show the validity and performance of the proposed method.

Designing outcoupling of light from nanostructured emitter in stratified medium with parasitic absorption

We demonstrate dipole-based modeling for designing nanostructured emitters in a stratified surrounding medium in the presence of parasitic absorption, while giving equivalent information about far-field emission as Lorentz reciprocity. We consider the challenging modeling case of a single nanowire with a parasitically absorbing planar top contact layer. The main advantage of our approach is the use of a near-field-to-far-field transformation (NFFT) adapted for stratified surrounding, which speeds up the simulations compared to approaches without such a NFFT. We show how the thickness of the contact layer, nanowire geometry, emitter position within the nanowire, refractive index of encapsulation layer, and orientation of the dipole moment of the emitter strongly affect the extraction of internally emitted photons.

Near-Field to Far-Field RCS Prediction on Arbitrary Scanning Surfaces Based on Spherical Wave Expansion.

Near-field to far-field transformation (NFFFT) is a frequently-used method in antenna and radar cross section (RCS) measurements for various applications. For weapon systems, most measurements are captured in the near-field area in an anechoic chamber, considering the security requirements for the design process and high spatial costs of far-field measurements. As the theoretical RCS value is the power ratio of the scattered wave to the incident wave in the far-field region, a scattered wave measured in the near-field region needs to be converted into field values in the far-field region. Therefore, this paper proposes a near-field to far-field transformation algorithm based on spherical wave expansion for application in near-field RCS measurement systems. If the distance and angular coordinates of each measurement point are known, the spherical wave functions in an orthogonal relationship can be calculated. If each weight is assumed to be unknown, a system of linear equations as numerous as the number of samples measured in the near electric field can be generated. In this system of linear equations, each weight value can be calculated using the iterative least squares QR-factorization method. Based on this theory, the validity of the proposed NFFFT is verified for several scatterer types, frequencies and measurement distances.

Radar Cross Section Near-Field to Far-Field Prediction for Isotropic-Point Scattering Target Based on Regression Estimation.

Radar cross section near-field to far-field transformation (NFFFT) is a well-established methodology. Due to the testing range constraints, the measured data are mostly near-field. Existing methods employ electromagnetic theory to transform near-field data into the far-field radar cross section, which is time-consuming in data processing. This paper proposes a flexible framework, named Neural Networks Near-Field to Far-Filed Transformation (NN-NFFFT). Unlike the conventional fixed-parameter model, the near-field RCS to far-field RCS transformation process is viewed as a nonlinear regression problem that can be solved by our fast and flexible neural network. The framework includes three stages: Near-Field and Far-field dataset generation, regression estimator training, and far-field data prediction. In our framework, the Radar cross section prior information is incorporated in the Near-Field and Far-field dataset generated by a group of point-scattering targets. A lightweight neural network is then used as a regression estimator to predict the far-field RCS from the near-field RCS observation. For the target with a small RCS, the proposed method also has less data acquisition time. Numerical examples and extensive experiments demonstrate that the proposed method can take less processing time to achieve comparable accuracy. Besides, the proposed framework can employ prior information about the real scenario to improve performance further.

A Nonredundant Sampling Representation Managing an Offset Mounting of an Elongated Antenna in a Spherical Near-Field Facility

An efficient spherical near-field-to-far-field transformation (NFTFFT), which takes into account the offset mounting of an elongated antenna and employs the same nonredundant (NR) amount of near-field (NF) data as in the onset mounting case, is presented. The interest for this NFTFFT is due to the fact that, for practical reasons, a mounting where the antenna and the scan sphere centers coincide is not always possible. In this case, the amount of NF measurements required by the traditional spherical NFTFFT can significantly increase. In the developed NFTFFT, this drawback has been overcome by accurately recovering these NF data from the gathered NR probe voltage samples through a sampling expansion, attained by suitably using the NR sampling representations and assuming the antenna as enclosed in a prolate spheroid. Numerical and experimental results are reported in order to assess the efficacy of the developed technique.

On the Minimum Number of Samples for Sparse Recovery in Spherical Antenna Near-Field Measurements

A thorough picture is presented on the capability of compressed sensing to reduce the number of measurement samples that are required for a near-field to far-field transformation (NFFFT), based on the spherical vector wave expansion of the radiated field of an antenna under test. To this end, the minimum number of samples for a sparse recovery is determined such that a predefined far-field accuracy can be achieved. As no suitable sampling theorem exists, this is done by performing extensive numerical simulations, considering possible deviations from exact sparsity, the influence of measurement noise, the sampling scheme, and the probe correction. Particularly, the influences are determined not only qualitatively but also quantitatively. The resulting modified phase transition diagrams (PTDs) show that a reconstruction by the quadratically constraint basis pursuit strategy is sufficiently stable and robust for practical purposes. The simulation and measurement results of NFFFTs show that the predictions for the required number of samples hold true. Consequently, the presented approach using modified PTDs allows to reduce the number of measurement samples with predictable accuracy, when the sparsity level is known.

Non-redundant Spherical Near-Field to Far-Field Transformation for a Volumetric Antenna in Offset Configuration

Background: The development of fast Near-Field (NF) measurement techniques allowing the precise determination of the Far-Field (FF) radiation features of an antenna is becoming more and more challenging nowadays. Objective: The goal of the article is the development of an NF To FF Transformation (NFTFFT) with spherical scan for offset mounted volumetric Antennas Under Tests (AUTs) requiring, unlike the classical technique, a reduced set of NF data, that is of the same amount as for the onset mounting case, thus making data gathering faster. In fact, the number of NF data needed by the standard approach may considerably increase in this case, since the size of the smallest sphere surrounding the AUT and centered at the center of the measurement sphere rises. Methods: This goal has been achieved by profitably exploiting the non-redundant sampling representation of electromagnetic field and assuming a volumetric AUT as contained in a sphere. An optimal sampling interpolation algorithm is then employed to precisely reconstruct the input NF data for the traditional spherical NFTFFT from the reduced set of the collected ones. Conclusion: The numerical simulations and experimental tests demonstrate the effectiveness of the developed approach accounting for an offset mounting of the AUT.

The Truncation Region to Predict the Far-Field RCS From the Bistatic Near Field

Because of the distortion of scatter pattern when measuring multiple-scattering targets in the condition of not satisfying the far-field condition, existing measurements are not favorable. We present a novel algorithm to research near-field to far-field transformation (NFFFT) for multiple-scattering targets. This paper introduces the method of NFFFT using “multiple emission multiple reception” and then chooses a dihedral angle, which has multiple-scattering structure to simulate. The results show a good agreement with the far-field radar cross section (RCS) pattern. Taking into account the feasibility of design, the cost of system, and other limitations in practical application, the bistatic measurement system with a full 360° is obviously hard to achieve. In the bandwidth-limited scattering field, we give the rule of angular truncation based on the transfer function for reducing receiving region. To make the conclusion more reliable, simulations should be set in different parameters, concluding testing frequencies, target size and measuring distance, to observe their effects on the receiving region. We get the mean error of different receiving region by comparing the results of NFFFT and far-field RCS. As a result, a principle for choosing a proper receiving region, say angular truncation, is summarized for multiple-scattering targets, with mean errors 0.5 dB below the full 360° results near the center of far-field pattern.

A SEMI-ANALYTICAL METHOD TO CALCULATE THE ENTRIES OF THE METHOD OF MOMENTS MATRIX FOR THE MIXED POTENTIAL INTEGRAL EQUATION OF A SOURCE RECONSTRUCTION PROBLEM

In this article, the mixed potential integral equation is discretized using the Rao-Wilton- Glisson basis functions in order to obtain a method of moments matrix equation for a source reconstruction problem. The weighting functions used in the setup of the moments equation are Dirac delta functions. The entries of the moments matrix are computed using a semi-analytical method which is applicable to any method of moments problem with point matching. The analytical calculation is made possible by employing a differentiation property of the scalar Green function and the properties of the mesh elements of the source plane. The semi-analytical method makes it easier to increase the accuracy of the moments matrix elements. The accuracy of the method is shown by comparing the results obtained using the semi-analytical method to those obtained by a fully numerical procedure. The source reconstruction for a specific electromagnetic field distribution is the procedure of either setting up equivalent electromagnetic problems in order to determine equivalent sources or determining the actual sources by solving the related integral equations. The source reconstruction method is used in several areas which can be mentioned as near-field to far-field (NF-FF) transformation, microwave imaging, antenna design, antenna characterization, antenna diagnostics, electromagnetic interference estimation in electronic circuits, corrections in antenna measurements, radome defect localization. The most important aspect of the source reconstruction method is that it takes the electromagnetic problem into consideration just as it is, with all of the real world factors included through the electromagnetic field measurement results. The literature on the source reconstruction method can be divided into two parts with respect to the type of the integral equation formulation for the problem. In the first group, a single integral equation formulation is done whereas in the second group, a dual-integral equation formulation is preferred. In the single equation formulation, the equivalent sources obtained using the equivalence principle are related to the field measurement results using the radiation integrals. In the dual equation formulation, an extra equation is set up using the Love's equivalence principle at the measurement surface. Some of the articles in the single equation formulation group are to be cited now. In (7-30), several NF-FF transformation formulations using the source reconstruction method and the related applications are studied. In (7), equivalent magnetic currents are constructed on a plane including the aperture of an antenna using the near electric field data on a plane. These currents are then used to calculate the far-field. In (8), equivalent magnetic currents are built on a plane including the aperture of an antenna again. However, the near electric field data is not necessarily to be obtained on a plane and can be gotten from a surface with an arbitrary geometry. In (9), an equivalent electric current is set up on a

An Improved Image-Based Circular Near-Field-to-Far-Field Transformation

An improved version of the near-field-to-far-field transformation (NFFFT) for determining the radar cross section (RCS) of electrically large targets from the scattered field measured with a monostatic radar over a circle in the near field of the targets is presented. The characteristic feature of the proposed NFFFT is an improved imaging operator which is derived by requiring that the integral transformations involved in the NFFFT scheme be self-consistent for every electrically small scatterer. The presented NFFFT version is expected to lead to more accurate RCS values for strongly asymmetric targets measured at smaller facilities.

Tip optimization for improvement of detection in scanning near-field optical microscopy

The scattering of evanescent waves by several kinds of tips commonly used in the frame of near-field optical microscopy was explored. Finite-difference time-domain (FDTD) calculations coupled to a near-field to far-field transformation (NFTFF) were used to model the interaction between a tip and a plane sample according to the shape of the tip, the tip material and the polarization of the excited evanescent waves. The purpose of the study was optimization of the scattering efficiency which is particularly important when the available signal is very low. Simulation results indicated that an appropriate choice of tip shape and material can enhance by several orders of magnitude the detected signal according to the polarization of the evanescent wave. Two distinct optical devices used to collect the scattered signal were simulated in the calculations. Investigations of tip and micro-sphere association were also carried out in order to appraise the importance of the resonance phenomenon. Calculations showed that a silicon carbide sphere set at the extremity of a tungsten tip significantly increases the measured signal in the mid-infrared range.

Application of Near-Field to Far-Field Transformation to Doppler Features From Wind Turbine Scattering

The near-field to far-field transformation (NFFFT) algorithm from Mensa and Vaccaro is applied to obtain the far-field Doppler signatures of wind turbines based on near-field measurement data. A set of angular window and sampling criteria are derived to aid in the data collection and processing. Simulations are performed to demonstrate the effectiveness of the NFFFT and sampling criteria. Near-field measurements are made of a three-arm wire turbine model and a small commercial turbine. The NFFFT is applied to recover the far-field backscattering. The NFFFT is shown to effectively correct the Doppler features from the wind turbine scattering. The measurement results are corroborated with near-field and far-field simulations.

Finite-difference time-domain and near-field-to-far-field transformation in the spectral domain: application to scattering objects with complex shapes in the vicinity of a semi-infinite dielectric medium

We present the study of a spectral-domain near-field-to-far-field (NFTFF) transformation, taking into account an interface in the vicinity of a particle. This technique is associated with a three-dimensional finite-difference time-domain (FDTD) model, which solves the Maxwell equations in the time domain. Moreover, material properties are considered with the use of dispersion models. First, particular attention is paid to the description of the modeling, especially concerning the NFTFF transformation using the dyadic Green tensors. Second, several simulation cases are considered to evaluate the ability of the developed technique to model the scattering by different kinds of "particles/interface" configurations and for various illuminating waves. Then validation test cases are used in order to assess the model accuracy through comparisons with T-matrix simulations. Finally, perspectives to this work and its application to near-field detection devices are discussed.

Rigorous interference and diffraction analysis of diffractive optic elements using the finite-difference time-domain method

The Finite-Difference Time-Domain (FDTD) method has proven to be a useful tool to analyze electromagnetic scattering phenomena. In this work, the FDTD method is applied at optical wavelengths. More precisely, we present the results obtained using the FDTD algorithm to simulate the performance of optical devices such as volume diffraction gratings. The Perfectly Matched Layers (PML), Total-Field Scattered-Field formulation (TF/SF) and Near-Field to Far-Field transformation (NF/FF) are some add-ons included in order to correctly calculate the far field distribution obtained from the numerical near-field values computed in the simulation region. These values in the near-field region are computed by illuminating the grating with of a plane wave at the Bragg angle of incidence. In addition, we compare the results obtained by the FDTD method to those obtained using the Rigorous Coupled Wave Theory (RCWT) applied to diffraction gratings. As will be seen in this paper there is good agreement between the two approaches, thus validating our FDTD implementation.

On the Comparison Between the Spherical Wave Expansion and the Sources Reconstruction Method

A comparison between two well-known near field to far field (NF-FF) transformation methods is presented: the spherical wave expansion (SWE) and the sources reconstruction method (SRM). The goal of this paper is to show the methods performance for NF-FF transformation pointing out the advantages and limitations of each one. First, the computational cost is studied, showing its dependence with the antenna under test (AUT) electric size. Second, the NF-FF transformation accuracy of each method is compared for a fixed AUT electric size, analyzing also the influence of the main parameters that affect the SRM and SWE accuracy. Third, the SRM capabilities are presented, with focus on the NF-NF transformation inside the minimum sphere. Practical applications of the SWE and SRM are illustrated by means of an example of NF-FF transformation and antenna diagnostics problem using measured NF data.