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In this paper, we present a new simulator called pRediCS for the calculation of electromagnetic scattering and radar cross-section (RCS) from electrically large and complex targets. The simulator utilizes the geometric optics (GO) theory and launching of electromagnetic rays for tracing and calculating the electric field values as the electromagnetic waves bounce around the target. The physical optics (PO) theory is also exploited to calculate the final scattered electric field by calculating the far-field PO integration along the observation direction. The simulator is first tested with known objects of canonical shapes, whose analytical solutions are available in the literature. Next, our implemented GO-PO type algorithm is validated by simulating the benchmark targets that have been well studied and documented by various studies. Finally, the RCS computation from complex and electrically large objects is calculated. By utilizing the RCS values for different frequencies and aspects, a successful inverse synthetic aperture radar image of the target with fast simulation time is achieved.

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... An assessment of the utility of Pol-ISAR in improving recognition of complex targets, can also be made by means of simulation studies [27][28][29][30]. This could serve as a groundtruth validation of the relevant techniques, mainly the ones related to target decompositions. ...

... Toward this direction, this paper makes use of the simulated Pol-ISAR imagery to characterize the backscattering signatures of a SLICY (Sandia Laboratory Implementation of Cylinders) object and a stationary ground vehicle, i.e., a backhoe loader. Simulation studies have been carried out with our recently developed high-frequency RCS simulator tool, called PREDICS [27][28][29] that is based on shooting and bouncing ray (SBR) technique [33][34] and capable of gathering full linear polarization (LP) data. An analysis of the real experimental data of a T-72 tank resulted from turntablebased ISAR measurements has also been made to evaluate the validity of the electromagnetic code. ...

... All the electromagnetic scattering simulation experiments have been carried out by our recently developed highfrequency physical electromagnetic simulator tool called PREDICS [27][28][29]. PREDICS is based on SBR technique [33][34] that utilized ray launching with geometric optics (GO) theory and the application of the physical optics (PO) theory together with the physical theory of diffraction (PTD). The detailed theoretical derivation behind PREDICS and its accuracy validation studies in predicting the electromagnetic scattering and/or radar RCS from benchmark targets can be reached from [27], [28] and [29] and will not be repeated here. ...

An assessment of polarimetric inverse synthetic aperture radar (Pol-ISAR) imaging is accomplished for realistic target models with the use of our recently developed high-frequency radar cross-section simulator tool called PREDICS. X-band, narrow-angle and full-polarimetric ISAR data for the CAD models of the well-known test object SLICY and a ground vehicle, namely a backhoe loader are analyzed to infer their structural characteristics. Experimental data obtained from a tower-turntable ISAR measurements of a T-72 tank target have also been utilized to assess the validity of the simulator. First, the intensity images in linear and circular polarization bases are directly utilized to evaluate the data quality and to characterize target features for classification. Then, the Pauli image decomposition scheme is applied to separate the basic scattering mechanisms occurring at target pixels. The identifiable canonical target forms are successfully extracted as single, double and multi-bounce scattering mechanisms that are pinpointed at their true locations. The results indicate that PREDICS is able to generate high-fidelity synthetic Pol-ISAR signatures of complex targets whereby successful interpretation of innumerous target scattering mechanisms and features can be achieved through Pauli decomposition scheme for classification purposes.

... For electrically large problems, it is common to use asymptotic methods using the optical properties of the high frequency electromagnetic waves for approximating the electromagnetic propagation. The Physical Optics-Shooting and Bouncing ray [11,12] method is a popular approach which combines the method of Geometric Optics (GO) and Physical Optics (PO). In the GO solution the magnitude, direction and phase of the ray are added on the ray traces of reflection, refraction and divergence of the optical rays to mimic ray properties. ...

... The PO integration is carried out for a metallic surface at the wave front of the ray tube just before the ray escapes the target. These are described mathematically below [12]. ...

... As the m th ray hits P m n ðx n ; y n ; z n Þ points on the surface of the target, ðn ¼ 1; 2; ; ::; NÞ the electric-field value around the nth hit point P m n ðx n ; y n ; z n Þ can be found via [12]: ...

The design of the flying wing and its variants shapes continues to have a profound influence in the design of the current and future use of military aircraft. There is very little in the open literature available to the understanding and by way of comparison of the radar cross section of the different wing planforms, for obvious reasons of security and sensitivity. This paper aims to provide an insight about the radar cross section of the various flying wing planforms that would aid the need and amount of radar cross section suppression to escape detection from surveillance radars. Towards this, the shooting and bouncing ray method is used for analysis. In this, the geometric optics theory is first used for launching and tracing the electromagnetic rays to calculate the electromagnetic field values as the waves bounce around the target. The physical optics theory is next used to calculate the final scattered electric field using the far field integration along the observation direction. For the purpose of comparison, all the planform shapes are assumed to be having the same area, and only the aspect ratio and taper ratio are varied to feature representative airplanes.

... Since its introduction to the RCS community [2], the method has been successfully employed in radio wave propagation as well as RCS computations of cavities, inlets with protrusions, jet aircrafts [3][4][5][6][7]. With ever increasing maturity in the field of subsonic aircraft design, there exists the desire to tailor the performance of an aircraft to suit specific flight conditions. ...

... Combined with Computer Aided Design and Graphical Modeling tools the method has been studied to evaluate RCS of complex structure of aircrafts. This work follows closely the methods of [6] and is used for validations with canonical objects first and then actual target models considered. ...

As the design for subsonic aircraft is gaining maturity, there exists a desire to tailor the performance of the aircraft to suit specific conditions. The fifth generation aircraft is concerned with the low observability design and prediction of the Radar Cross Section of the aircraft by enemy radars. The aim of the paper is to predict the Radar Cross Section of a possible future generation combat aircraft using the shooting and bouncing ray techniques and show its superiority in shape design over previous generation of aircraft. Since RCS is sensitive to aspect changes in flight, the monostatic RCS value is predicted in pitch, roll and yaw planes. The simulator is first tested and validated on benchmark targets which are publicly available in open literature before applying to aircraft scenarios. The XB-70 Valkyrie bomber, the F-16 and a possible futuristic Delta flying swept wing aircrafts is chosen for RCS comparison.

... PREDICS is a fast and effective simulation tool for the fast and accurate calculation of RCS from electrically large and complex-shaped platforms at high frequencies. The detailed information about PREDICS tool; including the theory behind the code and other technical features can be reached at (Özdemir et al, 2014a;Özdemir et al, 2014b;Kırık et al, 2019). The main graphical user interface (GUI) screen of PREDICS for the simulation of Mil-UAV is viewed in To evaluate and the RCS characteristics of Mil-UAV, two sperate RCS simulations have been carried out. ...

In this study, a quantitative radar cross section (RCS) analysis of different
unmanned aerial vehicle (UAV) models were accomplished by means of a series of
RCS simulations. The simulations were carried out by high-frequency RCS
simulation and analysis tool called PREDICS. To quantify the RCS features of
the UAV model, both the angle-variation and frequency-variation simulations for
all polarization excitations were performed. The results of the simulations
suggested that RCS values were dramatically varying with respect to look angle
with some special angles providing the large values of RCS. Generally, the RCS
values of the UAV model was increasing with frequency as expected. A
quantitative radar detection range analyses were also accomplished to assess the
visibility of both the military-type and civil-type UAV models. The outcome of
these studies has suggested that large-size UAV model can be easily detected by
a high-sensitive radar on the ranges of tens of kilometers while these numbers
reduce to a few kilometers for a civilian UAV model that is much smaller than
the its military counterpart.

With the use of polarization in inverse synthetic aperture radar (ISAR) images will offer the opportunity of using the phase information of each single‐polarization ISAR image for further signal and image processing tools to improve the automatic target classification and automatic target recognition applications. This chapter explores all these features of polarimetric usage of ISAR imaging. The chapter briefly reviews the types and sensitivities of polarization since the main focus is just the usage of polarization in radar imaging. The scattering matrix can be measured in any basis of orthogonal polarizations without losing any polarization information. One of the most basic and practical techniques that has been used in extracting features from Pol‐ISAR images is the CLEAN algorithm. This technique relies on standard procedure of scattering center extraction together with its spread response from the image based on polarimetric assessment of the scattering characteristics of this particular scattering center.

Scattering is the physical phenomenon that occurs when an electromagnetic (EM) wave hits a discontinuity/nonuniformity or an object. This chapter derives the far‐field EM scattering from a perfectly conducting object. When the EM wave experiences multiple bounces around the object, it is called multiple scattering or multi‐bounce scattering. Radar cross section can be regarded as the measure of the EM energy intercepted and reradiated by an object. The main goal of a typical radar is to detect the scattered EM echoes from a target and to extract the information within those EM signatures. The farthest distance of the target can be easily calculated starting from the radar range equation. The most commonly used radar waveforms are continuous wave, frequency‐modulated continuous wave, stepped‐frequency continuous wave, short pulse, and chirp (linear frequency modulated) pulse. Pulsed radar systems are commonly used especially in synthetic aperture radar and inverse synthetic aperture radar systems.

In radar imaging, the scattering center concept provides various advantages, especially when dealing with radar cross‐sections of objects and synthetic aperture radar/inverse synthetic aperture radar (SAR/ISAR) imaging. Scattering/radiation center model is motivated by the observation that an ISAR image exhibits strong point‐scatterer‐like behavior as can easily be seen from the presented ISAR images. Once the model is defined, these scattering centers can now be extracted from the image together with their corresponding point spread functions. Although it is more convenient and practical to extract these point radiators or scattering/radiation centers directly in the image domain, it is also possible to convey the extraction process in the Fourier (or frequency‐aspect) domain. Because the ISAR image itself is the display of these point radiators, it is easier to implement the extraction procedure in the image domain.

Inverse synthetic aperture radar (ISAR) is a powerful signal processing technique for imaging moving targets in range‐Doppler domains. Although ISAR processing is similar to synthetic aperture radar (SAR) processing, ISAR imaging procedure has some conceptual differences when compared to the SAR imagery. ISAR image can be regarded as the display of range/cross‐range profiles of the target on the two‐dimensional range cross‐range plane. The chapter presents a simplified ISAR imaging theory for the monostatic case. The algorithm for 2D ISAR imaging is provided for the monostatic case. ISAR imaging is based on single‐bounce assumption of the scattered waves. ISAR systems generally use narrow angular integration widths that may typically extend to only a few degrees while collecting the reflectivity data from the target. The chapter also presents three‐dimensional ISAR imaging for small frequency bandwidth and narrow‐angle approximation while collecting the backscattered field data.

In the highly squinted spotlight synthetic aperture radar (SAR) image simulation of complex electrically large targets, the principal difficulties consist of the generation and the processing of SAR echo. Concerning the above two issues, this paper proposed a complete procedure for highly squinted SAR image simulation. Firstly, in order to generate the SAR echo efficiently and accurately, the geometrical optics and physical optics (GO-PO) hybrid method is employed to get the spatial distributed scattering fields, which is an essential step for the generation of SAR echo. Secondly, regarding to the processing of highly squinted SAR echo, the amendatory frequency scaling algorithm (AFSA) is adopted. Compared with the benchmark frequency scaling algorithm (FSA), AFSA eliminates the trouble caused by the range-dependent secondary range compression (SRC) error in high squint mode through the nonlinear frequency scaling (NFS) operation. Finally, according to the complete simulation procedure, SAR images of a complex ship target under different radar parameters are simulated and analysed. The simulation results indicate the performance of AFSA in the processing of highly squinted SAR echo. Meanwhile, the effectiveness and the reasonability of the complete simulation procedure are revealed as well.

To investigate highly squinted spotlight synthetic aperture radar (SAR) images of an electrically large ship target over a rough sea surface, this work focuses on the simulation analysis of SAR images from such a composite scene. For this problem, there are two key issues need to be considered, namely the simulation and the processing of SAR echoes. Considering the first issue, an efficient facet scattering model based on capillary wave modification facet scattering model and geometrical optics and physical optics hybrid method is applied to calculate the electromagnetic (EM) scattering characteristics from a real ship-ocean scene, based on which SAR echoes can be obtained. For the second issue, a non-linear frequency scaling algorithm (NFSA) is employed to efficiently process the highly squinted SAR echoes. Compared with the traditional frequency scaling algorithm, the NFSA extends the frequency scaling operation to the cubic order and makes a more accurate secondary range compression. With the solutions to the two issues, SAR images of a complicated ship-ocean scene under different incident and squint angles are presented and analysed. The reasonable results demonstrate the validity of the simulation approach and the practicability of the model for highly squinted spotlight SAR images.

Taking into account the influences of scatterer geometrical shapes on induced currents, an algorithm, termed the sparse-matrix method (SMM), is proposed to calculate radar cross section (RCS) of aircraft configuration. Based on the geometrical characteristics and the method of moment (MOM), the SMM points out that the strong current coupling zone could be predefined according to the shape of scatterers. Two geometrical parameters, the surface curvature and the electrical space between the field position and source position, are deducted to distinguish the dominant current coupling. Then the strong current coupling is computed to construct an impedance matrix having sparse nature, which is solved to compute RCS. The efficiency and feasibility of the SMM are demonstrated by computing elec-tromagnetic scattering of some kinds of shapes such as a cone-sphere with a gap, a bi-arc column and a stealth aircraft configuration. The numerical results show that: (1) the accuracy of SMM is satisfied, as compared with MOM, and the computational time it spends is only about 8% of the MOM; (2) with the electrical space considered, making another allowance for the surface curvature can reduce the computation time by 9.5%.

This paper presents a new and original approach for computing the
high-frequency radar cross section (RCS) of complex radar targets in
real time with a 3-D graphics workstation. The aircraft is modeled with
I-DEAS solid modeling software using a parametric surface approach.
High-frequency RCS is obtained through physical optics (PO), method of
equivalent currents (MEC), physical theory of diffraction (PTD), and
impedance boundary condition (IBC). This method is based on a new and
original implementation of high-frequency techniques which the authors
have called graphical electromagnetic computing (GRECO). A graphical
processing approach of an image of the target at the workstation screen
is used to identify the surfaces of the target visible from the radar
viewpoint and obtain the unit normal at each point. High-frequency
approximations to RCS prediction are then easily computed from the
knowledge of the unit normal at the illuminated surfaces of the target.
The image of the target at the workstation screen (to be processed by
GRECO) can be potentially obtained in real time from the I-DEAS
geometric model using the 3-D graphics hardware accelerator of the
workstation. Therefore, CPU time for RCS prediction is spent only on the
electromagnetic part of the computation, while the more time-consuming
geometric model manipulations are left to the graphics hardware. This
hybrid graphic-electromagnetic computing (GRECO) results in real-time
RCS prediction for complex radar targets

This paper describes an electromagnetic computer prediction code for
generating radar cross section (RCS), time domain signatures, and
synthetic aperture radar (SAR) images of realistic 3-D vehicles. The
vehicle, typically an airplane or a ground vehicle, is represented by a
computer-aided design (CAD) file with triangular facets, curved
surfaces, or solid geometries. The computer code, XPATCH, based on the
shooting and bouncing ray technique, is used to calculate the
polarimetric radar return from the vehicles represented by these
different CAD files. XPATCH computes the first-bounce physical optics
plus the physical theory of diffraction contributions and the
multi-bounce ray contributions for complex vehicles with materials. It
has been found that the multi-bounce contributions are crucial for many
aspect angles of all classes of vehicles. Without the multi-bounce
calculations, the radar return is typically 10 to 15 dB too low.
Examples of predicted range profiles, SAR imagery, and radar cross
sections (RCS) for several different geometries are compared with
measured data to demonstrate the quality of the predictions. The
comparisons are from the UHF through the Ka frequency ranges. Recent
enhancements to XPATCH for MMW applications and target Doppler
predictions are also presented.

The purpose of this work is to analyze the physical optics method as applied to electromagnetic scattering theory and to point out its physical and mathematical drawbacks. The main conclusions are (1) that the boundary values assumed by physical optics lead to electromagnetic fields that do not satisfy the finiteness of energy condition and, as a consequence, that integral representations of these fields cannot be obtained via the divergence theorem; (2) that the commonly accepted representations are not solutions of the physical optics problem because they fail to reproduce the assumed discontinuities of the fields on the scatterer. Despite the above conclusions, the present work should not be construed as an attempt to discredit the method but rather as an effort toward a better understanding of it. As it is well known, there have been a number of occasions in which physical optics has yielded quite satisfactory results.

We present an iterative inner-outer scheme for the efficient solution of large-scale electromagnetics problems involving perfectly-conducting objects formulated with surface integral equations. Problems are solved by employing the multilevel fast multipole algorithm (MLFMA) on parallel computer systems. In order to construct a robust preconditioner, we develop an approximate MLFMA (AMLFMA) by systematically increasing the efficiency of the ordinary MLFMA. Using a flexible outer solver, iterative MLFMA solutions are accelerated via an inner iterative solver, employing AMLFMA and serving as a preconditioner to the outer solver. The resulting implementation is tested on various electromagnetics problems involving both open and closed conductors. We show that the processing time decreases significantly using the proposed method, compared to the solutions obtained with conventional preconditioners in the literature.

Using OpenMP to further accelerate the pure MPI parallel MLFMA, an efficient and flexible parallel multilevel fast multipole al-gorithm (MPI-OpenMP-MLFMA) is proposed. Compared with previous MPI parallel schemes, the MPI-OpenMP-MLFMA improves the load-bal-ance and scalability greatly. The computational capability of the proposed MPI-OpenMP-MLFMA is demonstrated by computing scattering from two extremely large targets: a sphere with a diameter of 1200 wavelengths, modeled by 1,063,706,700 unknowns, and an airplane model with the largest dimension of 1600 wavelengths, involving 288,151,344 unknowns.

This paper presents radar cross section (RCS) measurements of different targets suitable for electromagnetic software comparison and validation. The targets have been designed, fabricated and measured at INTA to study different scattering mechanisms such as reflection and diffraction on curved surfaces and edges (truncated cone), reflection and diffraction on planar surfaces and straight wedges (triangular prism) or tip diffraction and travelling waves (conesphere). These measurements can be used as a valuable tool to validate and adjust the input parameters of electromagnetic prediction codes according to the requirements of the engineer.

A large variety of simulation tools for calculating scattered fields have been published in literature. Basically, there are two main approaches, the so-called numerically exact or full-wave solutions, e.g. using Method of Moments (MoM), and the high-frequency or asymptotic solutions, e.g. using rays for modeling propagation paths. However, most of these simulation tools are limited to perfectly conducting surfaces or homogeneous dielectric bodies. The present paper studies the enhancement of a ray tracing code based on the well-known Shooting-and-Bouncing-Rays (SBR) technique for calculating scattered fields of arbitrary objects, whose surfaces are coated with a dielectric multi-layer structure.

In this paper, A SAR image simulation code of 3D complex targets named CASpatch is introduced. This code is based on the high frequency technique of shooting and bouncing rays (SBR). The original purpose to design the code is for SAR automatic target recognition (ATR) applications, but it can also be used for RCS prediction and high resolution range profile (HRRP) generation. A GB-SAR indoor experiment is used to validate the CASpatch system. The simulation results of complex targets show that high resolution, full polarimetry and wide bandwidth SAR images can be obtained via CASpatch, which means our code can support multiple SAR ATR applications. What's more, an improved PolSAR ATR algorithm is also proposed in this paper. The full PolSAR ATR experiment based on simulated data is firstly reported in this paper, and higher recognition rate is achieved comparing with the single PolSAR result.

The shooting and bouncing ray (SBR) method is highly effective in the radar cross section (RCS) prediction. For electrically large and complex targets, computing scattered fields is still time-consuming in many applications like range profile and ISAR simulation. In this paper, we propose a GPU-based SBR that is fully implemented on the graphics processing unit (GPU). Based on the stackless kd-tree traversal algorithm, the ray tube tracing can rapidly evaluate the exit position in a single pass on the GPU. We also present a technique for fast electromagnetic computing that allows the geometric optics (GO) and Physical optics (PO) integral to be carried out on the GPU efficiently during the ray tube tracing. Numerical experiments demonstrate that the GPU-based SBR can significantly improve the computational efficiency of the RCS prediction, about 30 times faster, while providing the same accuracy as the CPU-based SBR.

For analysis of large-scale electromagnetic scattering problems, high-frequency asymptotic methods are fast but approximate, whereas low-frequency numerical methods are accurate but slow. Neither can produce an efficient and accurate solution to scattering by large bodies containing small structures. A promising approach is to combine the best features of both types of methods to produce a hybrid technique that is sufficiently fast, reasonably accurate, and applicable to a class of unsolvable problems such as the scatterers mentioned above. There are two extremes for this type of hybridization. One is simply to superimpose solutions from asymptotic and numerical methods. While this approach is most widely used in practical applications, it neglects the interactions between the two solutions, which can be significant in many problems. The other extreme is to combine an asymptotic and a numerical method in an exact manner. In this approach, the effect of a large body is included by incorporating its diffraction into the Green's function in the integral equation for the small structures, which accounts for all interactions. While this approach is accurate, it is difficult to be implemented in a general-purpose computer code because of its complex nature. A more practical approach is to develop a technique that can include all significant interactions and neglect all trivial interactions. The resulting hybrid technique can produce sufficient accuracy and can be implemented in a general-purpose computer code. In this paper, we develop a technique that combines the shooting and- bouncing-ray (SBR) method and the method of moments (MoM) to solve for the scattering by large conducting bodies with small structures mounted on their surfaces.

A ray-shooting approach is presented for calculating the interior radar cross section (RCS) from a partially open cavity. In the problem considered, a dense grid of rays is launched into the cavity through the opening. The rays bounce from the cavity walls based on the laws of geometrical optics and eventually exit the cavity via the aperture. The ray-bouncing method is based on tracking a large number of rays launched into the cavity through the opening and determining the geometrical optics field associated with each ray by taking into consideration (1) the geometrical divergence factor, (2) polarization, and (3) material loading of the cavity walls. A physical optics scheme is then applied to compute the backscattered field from the exit rays. This method is so simple in concept that there is virtually no restriction on the shape or material loading of the cavity. Numerical results obtained by this method are compared with those for the modal analysis for a circular cylinder terminated by a PEC plate. RCS results for an S-bend circular cylinder generated on the Cray X-MP supercomputer show significant RCS reduction. Some of the limitations and possible extensions of this technique are discussed.

The radar cross-section (RCS) analysis of open-ended cavities with rectangular and circular cross sections is carried out using the waveguide modal approach and the shooting-and-bouncing ray (SBR) approach. For a cavity opening on the order of ten wavelengths or larger, the comparison between the two approaches is excellent. It is also observed that at lower frequencies the SBR results deviate from the more accurate modal results. On the other hand, the SBR approach allows for greater flexibility in geometrical modeling, and can be applied to problems where waveguide modes cannot be easily found. SBR results for an offset rectangular cavity and a circular cavity with rounded endplate are presented.

The transmission of a spherical or plane wave through an arbitrarily curved dielectric interface is solved by the geometrical optics theory. The transmitted field is proportional to the product of the conventional Fresnel's transmission coefficient and a divergence factor (DF), which describes the cross-sectional variation (convergence or divergence) of a ray pencil as the latter propagates in the transmitted region. The factor DF depends on the incident wavefront, the curvatures of the interface, and the relative indices of the two media. Explicit matrix formulas for calculating DF are given, and its physical significance is illustrated via examples.

Multilevel physical optics (MLPO) algorithm provides a speed-up for computing the physical-optics integral over complex bodies for a range of aspect angles and frequencies. On the other hand, when computation of the RCS pattern as a function of θ, φ, and frequency is desired, the O N<sup>3</sup> memory complexity of the algorithm may prevent the solution of electrically large problems. In this paper, we propose an improved version of the MLPO algorithm, for which the memory complexity is reduced to O N<sup>2</sup> log N. The algorithm is based on the aggregation of only some portion of the scattering patterns at each aggregation step. This way, memory growth in each step is prevented, and a significant amount of saving is achieved.

The finite-element method is applied to compute the skin current and radar cross-sections of perfectly conducting square surfaces. The predictions are compared with those given other methods. The efficiency, economy, accuracy and applications

The paper presents the RANURS code (radar cross section-NURBS
surfaces) for the analysis of the monostatic radar cross section (RCS)
of electrically large complex targets. The geometric representation of
the targets is given in terms of parametric surfaces, which allow an
excellent fit between the model and the real surface. The parametric
surfaces used are NURBS (non-uniform rational B-spline) surfaces. This
technique of modeling is used in many industries to represent complex
bodies. Most of the CAGD (computer aided geometric design) tools use the
NURBS format for modeling, because it can represent complicated objects
using limited information. Therefore, an important feature of the code
is its compatibility with most of the available CAGD codes, in order to
ensure that the entire design process, involving different engineering
aspects (structural, mechanical, aerodynamical, electrical, etc.) can be
developed with compatible models. The scattered fields are calculated by
using the physical optics and the equivalent currents methods (PO+ECM).
The following contributions to the RCS are taken into account: reflected
field, diffracted field, double-reflected field, and
diffracted-reflected field. In addition, a method for determining the
hidden parts of the targets is used. The PO+ECM approach is directly
applied on the parametric surfaces, and the final expressions of the
fields are given as functions of the coefficients of the numerical
description of the NURBS patches

Low- and high-frequency measurements are presented of five
differently shaped targets: the NASA almond, ogive, double ogive,
cone-sphere, and cone-sphere with gap. These were measured from 700 MHz
to 16 GHz. The metallic targets are made of aluminum, and were cut by a
numerically controlled mill to maintain the surface precision. Except
for the almond target, all the targets were made in two parts and joined
by sleeves and screws. The measurements are computational
electromagnetics (CEM) validation measurements for the Electromagnetic
Code Consortium (EMCC)

The finite-difference time-domain (FD-TD) method is proposed as a means of accurately computing electromagnetic scattering by arbitrary-shaped extremely complex metal or dielectric objects excited by an external plane wave. In the proposed method, one first uses the FD-TD method to compute the near total fields within a rectangular volume which fully encloses the object. Then, an electromagnetic-field equivalence principle is invoked at a virtual surface of this rectangular volume to transform the tangential near scattered fields to the far field. To verify the feasibility of this method, the surface currents, near scattered fields, far scattered fields, and radar cross section of two canonical two-dimensional objects are presented. For these cases, it is shown that the FD-TD method provides magnitude of current and field predictions which are within Â± 2.5 percent and further phase values within Â± 30 of values predicted by the method of moments ( MOM) at virtually every point including in shadow regions.

The present paper deals with a new efficient approach in order to assess the simulation of scattered fields from arbitrary metallic objects. The basic idea is to combine a ray tracing algorithm with the principles of physical optics (PO) and the physical theory of diffraction (PTD). The ray tracing algorithm stochastically launches discrete rays and uses a ray density normalization. In order to perform simulations at finite objects the PO/PTD formulation is required. Thus, fast intersection routines can be implemented, while the ray density formulation reduces the PO and PTD integrals to a pure sum of ray contributions. Simulation results obtained with this model are verified by comparison with both exact simulations using a method of moments (MoM) code and measurement results, proving an excellent accuracy and fast computation even at complex objects. With this asymptotic approach, scattering properties of large objects that are too complex for exact methods can be analyzed with rather moderate computation efforts. Typical applications include the simulation of low observability (LO) designs as well as the generation of databases for identifying unknown aircraft by their radar signature.

Numerical solutions of electromagnetic scattering and radiation problems including arbitrarily shaped objects are obtained by solving integral equations with the method of moments (MoM). Fast and efficient solution of the integral equation with low computation and memory complexity is provided by the multilevel fast multipole method (MLFMM). The presence of electrically large conducting objects leads to hybrid MoM techniques with high-frequency methods. For ray-based high-frequency methods no discretization of the electrically large objects is needed, resulting into a more efficient numerical treatment of the problem. However, in order to retain low computation and memory complexity, the high-frequency fields must be taken into account in the matrix-vector product computations in the various levels of the MLFMM. In this contribution, a ray-based hybridization of the MLFMM with the uniform geometrical theory of diffraction (UTD) is proposed within a hybrid finite element-boundary integral (FEBI) technique, using the combined field integral equation (CFIE), resulting into a hybrid FEBI-MLFMM-UTD method. The hybridization is performed at the translation procedure on the various levels of the MLFMM, using a far-field approximation of the appropriate translation operator to obtain the high-frequency incident fields at the critical points of the UTD. The formulation of this new hybrid technique is presented and numerical results are shown.

Physical optics (PO) and the physical theory of diffraction (PTD) are used to determine the backscatter cross sections of dihedral corner reflectors in the azimuthal plane for the vertical and horizontal polarizations. The analysis incorporates single, double, and triple reflections; single diffractions; and reflection-diffractions. Two techniques for analyzing these backscatter mechanisms are contrasted. In the first method, geometrical optics (GO) is used in place of physical optics at initial reflections to maintain the planar nature of the reflected wave and subsequently reduce the complexity of the analysis. The objective is to avoid any surface integrations which cannot be performed in closed form. This technique is popular because it is inherently simple and is readily amenable to computer solutions. In the second method, physical optics is used at nearly every reflection to maximize the accuracy of the PTD solution at the expense of a rapid increase in complexity. In this technique, many of the integrations cannot be easily performed, and numerical techniques must be utilized. However, this technique can yield significant improvements in accuracy. In this paper, the induced surface current densities and the resulting cross section patterns are illustrated for these two methods. Experimental measurements confirm the accuracy of the analytical calculations for dihedral corner reflectors with right, acute, and obtuse interior angles.

A hybrid technique combining the shooting-and-bouncing-ray (SBR)
method and the method-of-moments (MoM) is presented for analyzing
scattering by large conducting bodies having small protrusions. In this
technique, the MoM with an approximate Green's function is used to
characterize the small protrusions, yielding an admittance matrix,
which, when multiplied with the incident field on the protrusions,
yields the currents induced on the protrusions. The incident field in
the presence of the large bodies is calculated using the SBR method. The
field radiated by the currents on the protrusions is also calculated
using the SBR method with the aid of reciprocity. Furthermore, an
iterative approach is developed, which can reduce the error introduced
by the use of the approximate Green's function, Numerical results are
given to demonstrate the accuracy and capability of the hybrid technique

In this paper, we propose a deterministic approach to model the
radio wave propagation channels in complex indoor environments. This
technique applies the modified shooting-and-bouncing-ray (SBR) method to
find the equivalent sources (images) for each launched ray tube. In
addition, the first-order wedge diffraction from furniture is included
and the diffracted rays also can be attributed to the corresponding
images. By summing the contributions of all these images coherently, we
can obtain the total received field at a receiver. Besides, the
vector-effective height (VEH) of an antenna is introduced to consider
the polarization coupling effect resulting from multiple reflection
inside the rooms. We verify this approach by comparing the numerical
results in three canonical examples where closed-form solutions exist.
The good agreement indicates that our method can provide a good
approximation of high-frequency radio propagation inside rooms where
multiple reflection is dominant. Work reported in this paper has shown
that the propagation loss in indoor environments varies considerably
according to furniture and polarizations

An efficient method to include frequency-dependent materials in
finite difference time domain calculations based on the recursive
evaluation of the convolution of the electric field and the
susceptibility function has previously been presented. The method has
been applied to various materials, including those with the Debye,
Drude, and Lorentz forms of complex permittivity, and to anisotropic
magnetized plasmas. Previous demonstrations of this approach have been
confined to total field calculations in one dimension. In this paper the
recursive convolution method is extended to three-dimensional scattered
field calculations. The accuracy of the method is demonstrated by
calculating scattering from spheres of various sizes composed of three
different types of frequency-dependent materials

The principles of ray optics and, in more detail, some selected applications of ray techniques to electromagnetics are reviewed briefly. It is shown how a systematic use of matrix representation for the wavefront curvature and for its transformations simplify the handling of arbitrary pencils of rays and, consequently, the field computations. The same methods apply to complex rays which give a means of describing the effects of reflections and refractions on Gaussian beams. The relations of ray optics to other disciplines are also briefly discussed.

A summary of the development and verifications of a computer code,
RECOTA (return from complex target), developed at Boeing Aerospace for
calculating the radar cross section of complex targets is presented. The
code utilizes a computer-aided design package for modeling target
geometry in terms of facets and wedges. It is based on physical optics,
physical theory of diffraction, ray tracing, and semiempirical
formulations, and it accounts for shadowing, multiple scattering and
discontinuities for monostatic calculations

The radar cross-section patterns of lossy dihedral corner
reflectors are calculated using a uniform geometrical theory of
diffraction for impedance surfaces. All terms of up to third order
reflections and diffractions are considered for patterns in the
principal plane. The surface waves are included whenever they exist for
reactive surface impedances. The dihedral corner reflectors examined
have right, obtuse, and acute interior angles, and patterns over the
entire 360° azimuthal plane are calculated. The surface impedances
can be different on the four faces of the dihedral corner reflector;
however, the surface impedance must be uniform over each face. Computed
cross sections are compared with a moment method technique for a
dielectric/ferrite absorber coating on a metallic corner reflector. The
analysis of the dihedral corner reflector is important because it
demonstrates many of the important scattering contributors of complex
targets including both interior and exterior wedge diffraction,
half-plane diffraction, and dominant multiple reflections and
diffractions

Simulation Environment for the EM Design of Modern Ship

- Shipedf

ShipEDF. Simulation Environment for the EM Design of Modern Ship. Pisa, Italy: IDS Ingegneria dei Sistemi
S.P.A.

Radar Reflectors for Cruising Sailboats: Why They Work, What the Limitations Are and How to Evaluate Them

- P Gallman

Gallman P. Radar Reflectors for Cruising Sailboats: Why They Work, What the Limitations Are and How to
Evaluate Them. Los Angeles, CA, USA: Ulyssian Publications, 2005.

Calculation of electromagnetic scattering from large and complex targets and obtaining their inverse synthetic aperture radar images

- B Yılmaz

Yılmaz B. Calculation of electromagnetic scattering from large and complex targets and obtaining their inverse
synthetic aperture radar images. MSc, Mersin University, Mersin, Turkey, 2008.