Session:  Session 3A07A  Diffraction, RCS, Inverse Diffraction (08g) 
Type:  Oral Antenna 
Date:  Wednesday, November 08, 2006 
Time:  08:30  12:20 
Room:  Gallieni 2 
Chair:  
Cochair:  
Remarks: 
Seq  Time  Title  Abs No  
1  08:30 
An Effective Orbit Estimation Algorithm for a Space Debris Radar Using the QuasiPeriodicity of the Evaluation Function
Isoda, K.; Sakamoto, T.; Sato, T. Kyoto University, JAPAN 1.Introduction
2.The quasiperiodicity of the evaluation function 3.A fast orbit estimation algorithm using the quasiperiodicity We have experimentally clarified that the phase rotation p_{i} is dominant for the local shape of the evaluation function. Therefore, in the local search, we fix other parameters to find the optimum p_{i} in (1). Once we find the local peak, we jump to the next area and update all the parameters.
We apply this algorithm to the experimental data.
Fig. 2 shows an application example of the proposed method to real data for the H2A rocket booster, whose RCS is 27.6 m^{2},
which gives the peak SNR of 0.53dB higher than the conventional method.
The error of the estimated parameters are substantially reduced to 140 m for r1 and 3.9 m/s for vd, respectively. References 

2  08:50 
RCS Predictions for Stealthy Wind Turbines
Matthews, J.; Lord, J.; Pirollo, B. BAE Systems, Advanced Technology Centre, UNITED KINGDOM
Due to the international demand for renewable energy sources, many countries are realising the importance of wind power. As a consequence, a great quantity of windfarms, consisting of increasingly large turbines, are being developed. Due to the large physical size of wind turbines, many objections are raised as the wind farm presents an electrically large obstacle at typical radar frequencies. In some countries, 50% of wind farm planning applications raise objections due to proximity to a radar installation. These objections are understandable, particularly for safety critical radar (Air Traffic Control, Defence) but objections are often raised without a complete understanding of the problem. In order to mitigate this problem, the interaction of wind turbines and radar systems must be understood. A final objective is to create a tool capable of quantifying the impact of proposed wind farms on radar installations. A useful tool in understanding the effect of wind turbines on radar systems is computational modelling. A critical aspect of this is to understand the electromagnetic scattering behaviour of the windturbine in terms of RadarCrossSection (RCS) and Doppler signature. Typical windturbines have rotating aerodynamic blades which are 4060m long, (with 100m blades being considered in the future) which produce a significant Doppler return. The tower is even larger and produces a large static return. There is also scattering from the nacelle, and interaction between each component. At the radar frequencies considered in this study, 3GHz and 10GHz, the electrical size of the turbines, together with features such as aerodynamic surfaces, present a challenge in electromagnetic modelling.
This paper reports the development of modelling techniques to predict the RCS and Doppler spectrum from windturbines. A review of suitable modelling techniques is presented, including both inhouse and commercial tools. Detailed CAD models of the turbine structure, provided by windturbine manufacturers are used. The total RCS from the structure is decomposed to highlight the areas which contribute most significantly to the scattering crosssection. RCS and Doppler spectra will be presented for different orientation angles. Finally, recommendations for application of stealth technologies for different parts of the turbine will be discussed, with a prediction of efficacy.


3  09:10 
Efficient SIE/VIE Scattering Analysis of Ferroelectric, Inhomogeneous Materials with High Permittivity for Microwave Applications
Avdikos, G. K.^{1}; Zervos, T.^{2}; Anastassiu, H. T.^{3}; Uzunoglu, N. K.^{4} ^{1}School of Applied Mathematics & Physics, National Technical University of Athens, GREECE; ^{2}Institute of Informatics & Telecommunications, NCSR "Demokritos", Athens, GREECE; ^{3}Hellenic Aerospace Industry, GREECE; ^{4}School of Electrical & Computer Engineering, National Technical University of Athens, GREECE This paper investigates the scattering behavior of large, ferroelectric inhomogeneous bodies with high permittivity, varying linearly along one dimension (xaxis). One of the salient features of such materials is their capability of changing their dielectric permittivity, and hence their operational characteristics, by applying a constant bias field. They are very useful in microwave, phased array and scattering applications, mostly in conjunction with E and H plane horn antennas. Mathematical modeling of their scattering properties is based on either Surface or Volume Integral Equation (SIE and VIE) formulations. In order to approximate the linear variation of the permittivity, a staircase scheme is utilized, and the dielectric slab is decomposed into a number of homogeneous, pencillike sections (figure 1). The Radar Cross Section (RCS) and the induced currents are computed by increasing the number of sections until their values converge (figures 2 and 3). In general, RCS convergence is achieved faster. In the SIE case, the number of unknowns is generally low, but rises dramatically with the number of sections and the problem complexity may become computationally prohibitive. VIE with tetrahedral discretization is also invoked, provided that the total number of unknowns is tractable. The advantage of VIE over SIE is that the unknowns practically do not depend on the number of slab sections. For the cases where large systems arise (for high dielectric permittivity or high frequency of incident electromagnetic wave), fast methods are employed to overcome the computational bottleneck. Appropriate numerical quadrature integrations are employed to determine the currents and farfield parameters. Several lossy and lossless, linear and ferroelectric materials are investigated, most of them being used in applications involving microwave resonators.
Acknowledgments: The Project is cofunded by the European Social Fund (75%) and National Resources (25%) (Herakletus) 

4  09:30 
Three Dimensional Complex Permittivity Reconstruction by Means of NewtonType Microwave Imaging
De Zaeytijd, J.; Franchois, A.; Eyraud, C.; Geffrin, J. M. Ghent University, BELGIUM This contribution treats the microwave imaging of threedimensional (3D) inhomogeneous (lossy) dielectric objects embedded in a homogeneous background medium. The goal is to reconstruct the 3D complex permittivity distribution within a given inversion domain from measurements of the scattered field which are taken in a number of points surrounding the domain for multiple incidences and possibly for multiple frequencies. The non linear inverse scattering problem is solved in terms of the optimization of a cost function that involves the discrepancy between the measured and the calculated scattered field. We only optimize for the complex permittivity hence the fields in the inversion domain are eliminated by solving a forward problem in each iteration. Two versions of the wellknown FFTmethod for solving the volume integral equation are implemented. One is the weak form formulation of Zwamborn and van den Berg (IEEE transactions on microwave theory and techniques, 40(9), 17571766, 1992) and the other is a stronger form in which only the electric flux density is expanded in rooftop functions and where no averaging whatsoever is used. Moreover the latter code is able to use the Multilevel Fast Multipole Algorithm (MLFMA) to further speed up the computation and reduce the needed memory in some cases of large geometries. The effect of both methods on the reconstruction results is compared. Newtontype optimization techniques, such as GaussNewton and quasiNewton algorithms with line search, are applied to the inverse problem and compared. The standard leastsquare cost function is used and a regularization technique to alleviate the illposedness of the problem is investigated. Reconstructions from simulated data are presented for some 3D objects in the configuration of the bistatic microwave measurement setup of Institut Fresnel, France (J.M. Geffrin et. al., Inverse Problems, 21, S117S130, 2005), where the transmitter and receiver can be moved on part of a spherical or a cylindrical surface surrounding the object. From measurements on 3D objects, already carried out in this configuration, a realistic noise level is estimated and applied to the simulated data. 

5  09:50 
Alternative Current Expressions for Overcoming Shadowing Treatment Arising in the Physical Optics Approach
Cátedra, F.; Delgado, C. Alcalá University, SPAIN The Physical Optics (PO) method has been widely used when analysing electrically large EM problems. It considers only the illuminated parts of the geometry for computing the scattered fields, assuming null currents in the shadowed parts of the bodies under analysis. However, the shadowing problem can be even more problematic than the field calculation itself, specially when dealing with curved surfaces in complex geometries and multiple interactions, where many eclipse effects may appear. In these cases, illuminated regions must be obtained by using expensive minimization algorithms. The set of illuminated regions must be accurately determined, which implies many raytracing intersection tests. In this communication, an alternative treatment of the PO currents is considered. New electric and magnetic current expressions are proposed from the Equivalence Principle in order to bypass the shadowing problem. The currents calculated this way can be expressed in terms of current modes, providing an efficient storage and field calculation. A combination of these currents with some acceleration techniques, such as the angular ZBuffer or quasianalytical integration procedures, makes possible to maintain the PO efficiency when analysing simple cases, greatly improving it in more complex environments. 

6  10:40 
Analysis of the Potentialities and Limitations of the Integration between the IMSA and the Level Set Method for Inverse Scattering
Benedetti, M.^{1}; Lesselier, D.^{2}; Massa, A.^{1}; Lambert, M.^{2} ^{1}University of Trento, ITALY; ^{2}CNRSSUPELECUPS 11, FRANCE
Because of the limited amount of information collectable form the scattering experiments and the intrinsic instability of standard inverse scattering problems, it is quite difficult and in several cases almost impossible to achieve reliable and satisfactory (in terms of resolution accuracy) reconstructions of the inaccessible scenario under test without recurring to an effective exploitation of the apriori information or and iterate use of the scattering data. As a matter of fact, the necessary spatial resolution would require a significant and independent set of data nonavailable due to the bandlimited nature of the scattered field although multifrequency or multiillumination/multiview setups would used. Moreover, the large ratio between problem unknowns and independent field samples causes the presence of the local minima in the cost function defined in the arising optimization problem. In order to contemporarily address these drawbacks, recent developments reported in literature suggest splitting the original problem in a series of successive subproblems according to the general strategy of 'divide and conquer'. Then, each partial solution is profitably used as initialization for solving the successive problem, which turns out to be more and more close to the original one even though characterized by a reduced complexity because of the information on its solution acquired at the previous steps. In such a framework, Massa et al. proposed in [1] a pixelbased approach (called Iterative MultiStep Approach  IMSA) which improves at each step the resolution accuracy in a subset of the whole investigation domain by considering a more detailed multiresolution description of the unknown scatterer profile.
[1] A. Massa et al, "A new methodology based on an iterative multiscaling for microwave imaging,'' IEEE Trans. Microwave Theory Tech., vol. 51, pp. 11621173, 2003. 

7  11:00 
Shape Reconstruction Algorithms for Buried Conductors and Voids
Pierri, R.^{1}; Soldovieri, F.^{2}; Leone, G.^{3} ^{1}Seconda Universita' di Napoli, ITALY; ^{2}IREACNR, ITALY; ^{3}Università Mediterranea di Reggio Calabria, ITALY
Proposed topic A22 Scattering, inverse scattering, microwave imaging The problem of localizing and reconstructing the shape of a buried object by means of electromagnetic waves is relevant in a wide class of applications, such as ground penetrating radar, remote sensing. In this framework, the tomographic approach is particularly interesting because it allows to achieve a spatial map of the geometric features of the region under investigation. Here, we address the inverse scattering problem of recovering the position and the shape of unknown objects starting form the knowledge of scattered field once a known electromagnetic field impinges on the region under test. We consider objects buried in a homogeneous halfspace, whose dielectric properties are known, separated by a planar interface and the scattered field is collected at the airsoil interface. We refer to "strong scatterers" representative of both perfect conductors and voids or cavities provided that in the latter case the soil permittivity is sufficiently larger than the freespace one. The inversion algorithm searches for the unknown contour of the current density induced on the object surface. In particular, we move under the Kirchhoff or Physical Optics (PO) approximation which allows to simplify the problem. Accordingly, a linear inverse problem is faced and the Singular Value Decomposition (SVD) tool is exploited for analyzing and solving it. It has been already pointed out how, in free space inverse scattering problems, this linear PO based inversion scheme can be fruitfully employed beyond the validity of the PO approximation, that is, in the resonance region and for interacting scatterers [1] and the inversion approach has been experimentally validated with measurements collected in controlled conditions [2]. In this paper we extend the solution approach for perfect conductors buried in the halfspace geometry and deal with the assessment and the improvement of the performances of the inversion algorithm. Next, we extend the approach to the reconstruction of the shape of voids embedded in an halfspace by resorting to a distributional model similar to the one used for the perfect electric conductors. In particular the contour is searched for as the support of the surface magnetic equivalent current density modelled still according to the Kirchhoff approximation [3]. Reconstructions will be given for multiple conductors and voids in realistic measurement configurations. [1] R. Pierri, A. Liseno, R. Solimene, and F. Soldovieri," Beyond Physical Optics SVD Shape Reconstruction of Metallic Cylinders", IEEE Trans. Antennas and Propagation , vol.. 54, pp. 655665, 2006. [2] F. Soldovieri, A. Brancaccio, G. Leone, R. Pierri," Shape Reconstruction Of Perfectly Conducting Objects By Multiview Experimental Data", IEEE Trans. Geoscience and Remote Sensing, vol. 43, no. 1, pp. 6571, Jan. 2005. [3] A. Liseno, R.Pierri," Imaging of voids by means of a physicalopticsbased shape reconstruction algorithm", Journal of the Optical Society of America A, vol. 21, n. 6, pp. 968974, Jun. 2004. 

8  11:20 
Efficient RCS Calculation of Fighter on a PC Using Maximally Orthogonalized Higher Order Basis Functions
Sumic, D.^{1}; Kolundzija, B.^{2} ^{1}WIPLD d.o.o., SERBIA AND MONTENEGRO; ^{2}Dept. of EE, University of Belgrade, SERBIA AND MONTENEGRO
Topic: Radar cross section The proposed approach is to apply maximally orthogonalized HOBFs, combined with doublediagonal system preconditioning, in order to enable use of iterative solvers, as will be explained in the paper. Analyzed fighter model was built using bilinear quadrilateral patches over which higher order polynomial expansions of currents were defined. This model, 12 meters in length, was simulated on up to 1.39 GHz, in which case its length was 55 wavelengths. The excitation was a plane wave coming at an elevation angle of 60 degrees. By subdividing patches whose side length was over a specified threshold, we controlled the maximum order of expansion on all patches in the model. Smaller subdivision threshold resulted in more patches, lower orders of expansion defined on them, and a larger number of unknowns. On the other hand, lower orders of expansion enabled faster iterative solver convergence. In each case, iterative solver was demanded to decrease the residuum to a level that guarantees good results agreement with the direct solver. Fig 1 shows the duration of simulation for iterative solutions with different subdivision thresholds as well as direct solution with threshold set at 2 wavelengths. Detailed results will be presented in the paper. For example, it will be shown that at 1.39 GHz (29699 unknowns) iterative system solution needs 17 times less operations than the direct one. The total simulation time (including matrix fillin and postprocessing) in this case is 8.3 times shorter than in case of direct solver.
Radar cross section of the airplane is shown in Fig 2. It was calculated in 3601 directions in the incident plane at the frequency of 1.39 GHz, while the current distribution over the surface was calculated in 1,344,000 points. This required 29699 unknowns, occupying 8 GB of RAM, and was done in less than 4 hours on 1.4 GHz Opteron processor under Linux. 

9  11:40 
Microwave Imaging: Reconstructions from AspectLimited Real Data
Chatelee, V.; Aliferis, I.; Dubois, A.; Dauvignac, J.Y.; Pichot, C. LEAT, Universite de Nice  Sophia Antipolis, UMR 6071 CNRS, FRANCE The problem examined here is the quantitative tomographic reconstruction of an unknown object from real data. We consider the case of freespace experiments where a set of ultrawideband antennas, located along a horizontal line, successively illuminate a cylindrical object whose length is large compared to the largest wavelength used. The scattered field is measured along the same line under a multifrequency, multiincidence, multistatic, aspectlimited configuration. Real data are collected in an anechoic chamber from the socalled SIMIS (Synthetic Impulse Microwave Imaging System) that uses an array of eight ultrawideband Vivalditype ETSA antennas [1] associated with a vector network analyzer [2]. The total field, corresponding to the sum of the incident (in the absence of target) and scattered (contributed by the target) fields, is measured over a large frequency band (28 GHz). The scattered field is obtained either by a differential measurement (with/without the object) or by excluding the early time response (gating in the timedomain). Reconstructions are performed using a biconjugate gradient nonlinear inversion algorithm [3] associated to an edgepreserving regularization technique [4]. The incident field of the Vivaldi antennas is numerically computed and incorporated into the reconstruction process [5]. References:
[1] E. Guillanton, J.Y. Dauvignac, C. Pichot, and J. Cashman. A new design tapered slot antenna for ultrawideband applications. Microwave and Optical Technology Letters, 19(4):286289, November 1998. 

10  12:00 
Detection of Multiple Defects in Industrial Products by means of a NonDestructive Microwave Approach
Benedetti, M.^{1}; Donelli, M.^{1}; Pastorino, M.^{2}; Rosani, A.^{1}; Massa, A.^{1} ^{1}University of Trento, ITALY; ^{2}University of Genoa, ITALY The detection of defects or cracks inside products is a keyproblem in many industrial processes to be addressed by means of noninvasive (and of course nondestructive) inspection techniques. In such a framework, the effectiveness of tomographic approaches based on the use of interrogating microwaves has been demonstrated in inspecting dielectric or conductive materials. However, the solution of a NDT/NDE problem through inverse scattering techniques is still illconditioned and nonlinear. On the other hand, it should be noticed that a lot of apriori information on the scenario under test is available and such an information can be effectively employed for reducing the problem unknowns and to improve the detection/reconstruction results. In [1] Caorsi et al. proposed a global optimization technique based on the so called "Free Space Green Function" (FGA) aimed at detecting a single unknown defect inside a known homogeneous host medium. A suitable defined Genetic Algorithm (GA) procedure allowed the exploitation of the apriori information for determining the geometric parameters of the defect (i.e., the position, the size and the orientation) and its electromagnetic properties.
A further improvement of the FGAapproach was achieved in [2] by introducing the numerical computation of the "Inhomogeneous Green's Function" (IGA) for limiting the region of interest to the area occupied by the crack thus enabling more accurate reconstructions and a significant reduction of the overall computational burden [3]. References
[1] S. Caorsi, A. Massa, and M. Pastorino, "A crack identification microwave procedure based on a genetic algorithm for nondestructive testing," IEEE Trans. Antennas Propagat., vol. 49, pp. 18121820, Dec. 2001. 