EuCAP 2006 - European Conference on Antennas & Propagation

Session: Session 2PP2A - Diffraction, RCS, Diffraction Inverse, Optimisation, Synthesis (07a2)
Type: Poster Antenna
Date: Tuesday, November 07, 2006
Time: 15:30 - 18:30
Room: Agora A

Seq   Time   Title   Abs No
1   00:00   An Approximation for Bistatic Scattering Matrix of a Target above a Ground Plane
Osipov, A.; Kemptner, E.
DLR Microwaves and Radar Institute, GERMANY

The presence of a ground plane may considerably change RCS of a target, which is known as the multipath or ground-plane effect. The change is explained by the reflection of the incident and scattered fields from the ground. The effect is most pronounced when the ground is flat and the surface material is a good reflector (e.g. water or wet soil). Exact numerical account for the ground-plane effect makes the RCS simulations much more computationally expensive because of the need to include a large area on the ground which contributes to the illumination of the target and to the reflection of the field scattered by the target.

This paper proposes a simple approximate formula for the scattering matrix of a target placed above a ground plane. The approximation accounts for electromagnetic interactions between the target and the ground plane, which involve a single reflection from the target and up to two reflections from the ground. It provides the correction for the amplitude, the phase, and the polarization of the scattered signal for both mono- and bistatic configurations and applies to perfectly conducting, absorbing, and dielectric interfaces. To verify the approach, the formula is applied to a test configuration which consists of a sphere and an infinite ground plane [test case no.5, JINA 2004 Workshop]. The accuracy of the approximation is estimated through a comparison with the results obtained with alternative methods (method of moments, ray tracing).

The formula can be easily implemented into PO-based RCS simulation codes to account accurately and rapidly for the ground-plane effect. Practically important configurations include a ship on the see, a motor vehicle on a road, and an airborne vehicle (helicopter, aircraft, missile) above a soil or water surface. The approach can also be useful to simulate the ground-plane effect in outdoor RCS test ranges.

2   00:00   On the Simulation of RCS from Trees and Forests above Real Finite Ground
Olcan, D.; Kolundzija, B.M.
School of Electrical Engineering, University of Belgrade, SERBIA AND MONTENEGRO

We present a numerically efficient technique for simulating RCS from trees and forests. Furthermore, we included other objects positioned (potentially hidden) in forests and the finite real ground below. The exploration of real finite ground plane, forest density and operating frequency is done. We pay special attention to the modeling of the finite real ground with the real-life curvatures. The software tool WIPL-D Pro v6.0 is used for all simulations [1].

The general idea is based on the fact that dielectric rods can be substituted with metallic wires and distributed loadings along them [2]. Such substitution is valid up to the frequency at which rod (wire) cross-section becomes comparable to the wavelength at the operating frequency. The approximate formula for the frequency isa≤lambda/8, where a is the rod (wire) radius and lambdas is the wavelength at the operating frequency. For the real-life trees, by using the formula, RCS from trees can be simulated up to approximately 100 MHz. These frequencies are of special interest for so-called FOPEN (FOliage PENetrating) radars [3]. The results that we present are below this frequency.

However, the same technique can be used and above this frequency if all rods with higher radii are modeled as dielectric bodies and all others as metallic counterparts with distributed loadings. Note that by using this technique the number of unknowns needed for simulation can be reduced for 100 times, while the results are practically the same [4].

On the Fig. 1 is shown tank positioned in the middle of the forest with 50 trees on the flat finite ground of 50 x 50 m2. On the Fig. 2 is shown monostatic RCS for incident plane wave at elevation angle degrees and degrees for tank alone, forest alone, and tank in the forest at 30 MHz.

Fig. 1. Tank in the forest.
Fig. 2. Computed RCS.

Presented technique is shown to be numerically efficient and it opens the possibility of simulating complex scenes using MoM codes.


[1] Branko M. Kolundzija, Jovan S. Ognjanovic, Tapan K. Sarkar, WIPL-D Pro v6.0: Electromagnetic Modeling of Composite Metallic and Dielectric Structures, Software and User Manual, WIPL-D Ltd. 2006.
[2] Branko M. Kolundzija, Antonije R. Djordjevic, Electromagnetic Modeling of Composite Metallic and Dielectric Structures, Artech House, Inc., Boston, 2001.
[3] Anders Sullivan, "Advanced Modeling and Simulation of Low Frequency Foliage Penetrating Radar", U.S. Army Research Laboratory,
[4] Dragan I. Olcan and Branko M. Kolundzija "Precise and Efficient Modeling of Trees with WIPL-D Code", Applied Computational Electromagnetics Society ACES 2004, Syracuse NY, April 2004.

3   00:00   Radar Cross Section of Some Simple and Collected Targets to be Used for Classification
Nicolaescu, I.1; Cernat, M.2
1Military Technical Academy, ROMANIA;
2Transilvania University of Brasov, ROMANIA

The goal of this paper is to analyze the scattering properties of different kind of targets, from simple shapes to collected targets made up of several objects, from 400 MHz to 7400 MHz to be used as patterns in a Ground Penetratin Radar in the classification stage. The data have been collected in an anechoic chamber with a VNA set to work as a Stepped Frequency Continuous Wave Radar. The data are analyzed in frequency and time domain in order to picture the radar cross section dependency of frequency, incident angle, polarization and targets shape. The measurement have been carried out using a bistatic arrangement with two TEM horns for linear polarization and two spiral antennas for circular polarization (fig. 1). The experimental data are compared with some simulation with FEKO (fig. 2 and 3) and with theoretical data in order to work out a calibration procedure. The measured data for different kind of targets: sphere with different diameters (6, 16 and 26 cm), dihedral, trihedral, rectangular plates and collected target have been analyzed in time and frequency domain. For instance the time response of a rectangular plate (49 times 90 cm) is displayed on figure 5. Figure 4 shows the S21 magnitude, which characterizes the RCS of the plate, depending on the position angle of the target and the frequency of the signal. As one can see, for frequencies around 5 GHz the signal received has a minimum value, which is due to the frequency behavior of the spiral antenna. Time response for rectangular plate shows us the distance to the target. The bistatic RCS for the other objects, including object collection has been presented on the paper together with a system calibration procedure. All the measured data has to be used as references for data acquired with stepped frequency continuous wave radar and than included into a pattern recognition data base to be used in the classification stage.

4   00:00   Fast and Accurate Modelling of Large Plane Array Antennas
Chiniard, R.1; Barka, A. B.2; Pascal, O. P.3


Structures of interest are very large planar array antennas built with some hundreds to several thousands sources (approx. dimension:25 lambda² to 1000 lambda²). This kind of antenna is usually studied by classical Floquet approach which has been developed by Amitay, Galindo and Wu during the seventies. Assuming a planar geometry, infinite and periodic in two directions of space, computation domain is reduced to the unit cell corresponding to one primary source. Nevertheless, it cant take into account diffraction by edges of the array. Furthermore, electromagnetic description of the inner part of antenna often remains superficial.

In order to enhance modelling accuracy, we are interested in analysing inner antenna effects on radiation or Radar Cross Section (RCS) patterns. This is only allowed by the use of rigorous method which cannot reach such areas, as previously noticed. Ten years ago, Mcgrath and Pyati have hybridised Floquet with FEM in a global formalism. When calculating RCS patterns, one can note that Floquet modes depend of the wave incidence. This point makes it necessary to have a total resolution for each incidence.

Now, we intend to develop a full multidomain formalism to mix both Floquet and exact resolution. For periodic structures that we deal with, it makes it possible to separately calculate all the devices constituting the primary source and its feeding circuits before connecting them to the radiating domain. For RCS purposes, once the description of the inner part is achieved, only the last step of the procedure has to be made again for each incidence. An efficient and versatile electromagnetic tool is then obtained and constitutes a significant enhancement considering the rather short CPU times.

2.Theory and validations

The original method proposed here associates multidomain formalism with Floquet modal expansion. Using Floquet formalism, computation domain is reduced to the unit cell. Floquet modal expansion is matched at the cavity aperture with the unit cell behaviour provided by the multidomain approach. By application of an array factor, far field radiation as well as RCS are obtained.

One of the approximation of our development resides in the planar hypothesis of the array. So, at this point, we only have characterized array effect. One strategy to pass this limitation is to consider structure where antenna is placed in. We have made development in this way and we notice a significant increase in the accuracy of our new result compared with rigorous method.

So, we have simulate a lot of numerical tests cases as rectangular guide array or patch array antenna. Besides our method, we have calculate test case with rigorous method and commercial software which are considered as our reference. The following article could describe RCS diagram of an antenna placed on a generic military aircraft. For this case, which is illustrated by fig 1, we combine our method(array effect) with asymptotic method(structure effect).

Fig 1: Aircraft and array antenna modelling

The proposed article is linked with project of a Test case based on array antenna proposed to Workshop JINA 2006.

5   00:00   Retrodirective Surfaces with Loaded Dihedral Corner Reflectors
Schuchinsky, A.; Fusco, V.
Queen's University Belfast, UNITED KINGDOM

Dihedral corner reflectors (DCR) have been extensively used as passive retrodirective devices for more than half a century. However, conventional DCR barely fulfil the requirements of modern space communications, remote sensing and electronic tracking due to a strong angular dependence of their radar cross section (RCS). In this work, we propose a new arrangement called loaded DCRs (LDCR) which consitute the basic elements of retrodirective surfaces (RDS) with high backscattering efficiency (in excess of 80%) and small variations (less than ±2%) across the whole range of illumination angles.

The analysis of LRDS is based upon the physical optics (PO) model, which is sufficient for our purposes. The cross-section of LDCR shown in Fig. 1 represents a basic canonical element of RDS. The DCR is filled by a medium with refractive index n > 1 that decreases a ray incidence angle α to β = arcsin(sin(α)/n), as the refracted ray enters the DCR through a flat interface between two media (line AB in Fig.1). Thus, the incoming rays are more closely confined to the interface normal, that results in the increased efficiency of DCR backscattering of the reflected rays. The ray trace analysis has been performed for a general case of asymmetric LDCR where the faces A0=a and B0=b may be unequal. Fig. 2 displays the effect of n and the aspect ratio b/a on angular dependence of the normalised width of the LDCR aperture (a portion of the AB face providing the backscattering). These results of Fig. 2 demonstrate that even at the moderate values of n=3, the efficiency of backscattering considerably increases and exceeds 80% for |α|≤ 0.2pi, as compared with only |α|≤ 0.062pi at n=1. In the case of asymmetric LDCR, the angle of backscattering maximum also deviates from the normal (α=0), and its value can be varied as required by the specified scattering pattern.

An asymmetric shape of the curves in Fig. 2 for LDCR with unequal a and b suggests that the reflector overall efficiency may be further enhanced in cascaded LDCRs. The latter case also provides an additional degree of freedom due to a variable mutual slant between the individual LDCRs. Comparison of the normalised apertures for the 3 types of cascaded arrangements: flat, convex and concave in Fig. 3 shows a superior performance of the concave configuration.

Further details of the study of the synthetic retrodirective surfaces composed of cascaded LDCRs of different types and the issues of the edge diffraction and specular reflection at the media interface will be addressed in the full paper.

6   00:00   Modeling a mm-Wave Imaging System with a 2.5D BiCGS-FFT Volume Integral Equation Technique
Van den Bulcke, S.1; Franchois, A.1; Zhang, L.2; Stiens, J.2
1Department of Information Technology (INTEC-IMEC), Ghent University, BELGIUM;
2ETRO-TW, Vrije Universiteit Brussel, BELGIUM

In this contribution we present an exact forward solver for a two-dimensional (2D) inhomogeneous dielectric object embedded in a homogeneous background medium. The object is illuminated with a given three-dimensional (3D) time-harmonic incident field. The 3D scattered field is computed in a number of points surrounding the object. The size of the scattering objects can be very large with respect to the wavelength, leading to an extremely high number of unknowns. Therefore a 2.5D configuration is adopted, since it reduces the computational cost while it maintains the capability of accurately studying the system performance.

The vector fields are calculated by discretizing a contrast source integral equation with the Method of Moments. The resulting linear system is solved iteratively with a stabilized biconjugate gradient Fast Fourier Transform (BiCGS-FFT) method [1][2]. Simulation and validation results for a number of test objects are shown.

Simulation results for test objects are compared to measurements performed at the VUB, where a free-space active mm-wave imaging system is being developed. The system presently consists of a mm-wave vector network analyzer [3] operating in the 75 to 300 GHz range. It measures the S-parameters in amplitude and phase with a dynamic range of more than 80 dB. At the transmitting side, a horn antenna emits an incident Gaussian beam, which is focused by a lens at the object location. At the receiving side the scattered field is focused by a lens for image formation at a receiving horn antenna. The total distance between transmitting and receiving sides is typically 75 cm.

[1] X.M. Xu et al., J. Appl. Comput. Electromag. Soc., 17(1), 97-103, 2002.
[2] P. Zwamborn and P. M. Van den Berg, IEEE Trans. Microw. Theory Techn., 39(6), 953-960, June 1991.

7   00:00   An Iterative Procedure for Combining the Advantages of a Multi-Frequency and Multi-Resolution Inversion Algorithm
Franceschini, D.; Donelli, M.; Massa, A.; Tamanini, E.
University of Trento, ITALY

The realization of a reliable microwave imaging system requires the solution of some typical drawbacks arising from the intrinsic limitations concerned with every inverse scattering problem, such as the non-linearity and the ill-posedness of the mathematical model as well as the presence of an upper bound in the essential dimension of data. Such drawbacks can be partially suppressed by considering multifrequency acquisition setups [1] [2], even though the increase of the computational burden and the frequency dependent behavior of the materials have to be carefully taken into account.
Although an effective processing of a single frequency noiseless dataset may allow a faithful retrieval of the contrast function, the measurement errors limit the accuracy of the reconstruction. Therefore, it is possible to effectively benefit from a wider number of independent data from multifrequency measurements in order to reduce the ill-posedness and improve the robustness against false solutions [2]. For these reasons, algorithms able to exploit frequency diversity have been developed and assessed ([1] [2] and the references therein), analyzing the optimum trade off between the choice of the number of frequencies and the unavoidable increase of the computational burden for the simultaneous numerical processing.
On the other hand, the amount of non-linearity turns out to be reduced when low working frequencies are used. However, the information content collectable from the scattering data is reduced [2] and it does not allow an accurate spatial resolution of the scenario under test. On the contrary, the multiple-scattering effects, and consequently the non-linearity of the problem, are enhanced when higher frequencies are used, but a more detailed description of the object can be looked for. Starting from these considerations, this paper presents a new multifrequency approach able to suitably exploit the information content at different frequencies through an effective multi-resolution strategy. In more detail, the unknown scatterer distribution is represented by means of a multi-resolution expansion where each level of resolution is adaptively tuned taking into account the corresponding frequency of the scattering experiment. Moreover, such a frequency-adaptive discretization is integrated into a multi-scaling technique [3] in order to iteratively define the optimal trade off between reconstruction accuracy, information content of the data and the step-by-step acquired information on the scenario.
[1] K. Belkebir, R. Kleinmann, and C. Pichot, "Microwave imaging- Location and shape reconstruction from multifrequency scattering data," IEEE Trans. Microwave Theory Tech., vol. MTT-45, pp. 469-475, 1997.
[2] O. M. Bucci, L. Crocco, T. Isernia, and V. Pascazio, "Inverse Scattering Problems with Multifrequency Data: Reconstruction Capabilities and Solution Strategies," IEEE Trans. Geosci. Remote Sensing, vol. 38, pp. 1749-1756, 2000.
[3] S. Caorsi, M. Donelli, D. Franceschini, and A. Massa, "A new methodology based on an iterative multi-scaling for microwave imaging," IEEE Trans. Microwave Theory Tech., vol. 51, pp. 1162-1173, 2003.

8   00:00   Scattering and Absorption of Electromagnetic Waves on Inhomogeneous Bodies
Panchenko, B.; Panchenko, B.; Gisatullin, M.; Glotov, E.
Ural State Technical University, RUSSIAN FEDERATION

We use the dyadic Green functions and orientated resistances and admittances for investigation of electromagnetic wave scattering on magneto dielectric stratified spherical structures. It is investigated the fields of scattering, the fields in different sheets of structure, energetic properties scattering and absorption, transformation of fields polarization. The optical theorem and electrostatic solution of problem are used for verification of general solution.

Some cases particular of general solution are considered in detail:

1. Scattering waves on dielectric and semicondacting thin screens;

2. Absorption of electromagnetic waves on six-layers structure modeling the head of men-user of mobile phone;

3. Scattering on spherical structure from materials with negative index of refraction;

4. Numerical optimization of scattering behaviors for considered directions.

The paper offers a numerical dates and the results are discussed. Most interesting results are connected with scattering on spherical structure from materials with negative index of refraction (double negative DNG). It is imported to note same properties of this structure: minimization of radar cross-section, increase of total coefficient of diffraction, axle symmetry diagram of scattering.

9   00:00   3D Inverse Scattering by Level Set with Zero Capacity Connecting Set. Wave Guide Optimization by Zone
Dubois, P.1; Dedeban, C.1; Zolésio, J.-P.2
1France Telecom, FRANCE;

10   00:00   Antenna Characteristics in Microwave Imaging for Breast-Cancer Screening
Rubaek, T.; Meincke, P.
Technical University of Denmark, DENMARK

In recent years, the use of microwave imaging for breast-cancer screening has gained the interest of an increasing number of research groups. Apart from being non-ionizing, the use of microwaves as an alternative or supplement to the commonly used X-ray mammography is desired due to the ability of the microwaves to detect cancer in the breasts of younger women. The microwave-imaging system considered in this paper consists of a metallic hemisphere which is to be positioned against the chest wall, enclosing the chest. 32 antennas are positioned on the inside of the hemisphere which acts as the ground plane for the antennas. The hemisphere has a radius of 15 cm and the data is collected at 5 GHz using a multi-static setup in which the antennas, in turn, act as the transmitting antenna while the S parameters of the transmitting antenna and each of the 31 receiving antennas are measured.

In this paper, the microwave-imaging system will be simulated using a method-of-moments program in a free-space setup with the purpose of illustrating the importance of including the antenna characteristics in the imaging algorithm. To this end, a new linear inversion algorithm that includes the antenna characteristics in the form of the spherical-wave spectra of the antennas has been derived. The algorithm is based on the first-order Born approximation, assuming that the scattered field is linearly dependent on the incident field through the unknown object function. Although a more advanced, non-linear imaging algorithm is to be used for screening for breast cancer, the difference in the results of the new algorithm and a more simple linear imaging algorithm, in which the antennas are assumed to be ideal dipoles, clearly illustrates the importance of including the antenna characteristics in the imaging algorithm.

In the new algorithm, the integral equation obtained from the linearized scattering model is cast into the discrete form P o = s, with the unknown object function given by o. This ill-posed matrix equation can be solved using standard techniques such as the truncated singular-value decomposition or the Tikhonov algorithm.

When the new algorithm is applied, the imaging procedure has two steps. First, the spectrum of each of the antennas in the imaging system is determined. This is done by running a simulation of the system with no scatterer in it and calculating the field on a full sphere inside the metallic hemisphere for each antenna. The spectrum of the antenna can then be calculated using the orthogonality of the spherical-wave functions. After determining the spectrum for each antenna, the matrix P is constructed. This step needs only to be done once for the imaging system and the matrix P may be stored and used for imaging in the following measurements.
Second, the matrix equation is solved. Since the matrix P is dependent only on the imaging system and not on the scatterer, a singular-value decomposition of the matrix may be created and stored. Once the singular-value decomposition is known, the matrix equation can be easily solved.

Compared to the more simple algorithm, the new algorithm shows a clear improvement in the image quality.

11   00:00   Convex Hull Detection of a Scattering System Embedded in an Inhomogeneous Background
Capozzoli, A.; D'Elia, G.; Vinetti, P.
University of Naples Federico II, ITALY

Inverse Source (IS) and Inverse Scattering (ISC) are relevant topics in applied electromagnetics: the determination of the number, the position, the shape and the electromagnetic parameters of a scattering system, from the knowledge of the radiated field on an observation domain, is of interest not only from the theoretical point of view, but also in practical applications. In particular, the detection of voids and reinforcements in concrete, the detection of mines or underground cavities from electromagnetic field data require the solution of an inverse problem.

Unfortunately, the solution of the full inverse problem can be quite complex: the inversion algorithms are heavily affected by the ill-conditioning and typically require a huge numerical computational burden, which sometimes become unaffordable. Furthermore, when the solution is sought for by local optimizing an objective functional, the presence of local optima can lead to false solutions and make the approach unreliable.

Therefore, the efficiency and the effectiveness of the inversion algorithms can be improved by any sort of a priori information on the investigated object: a good estimate of the region containing the scattering system can significantly improve the performances. On the other side, in some applications the interest is focused on finding the smallest region wherein the scatterers are located.

To meet the above needs, a simple and effective technique to evaluate the convex hull of the scattering system, without solving the whole inverse problem, has been introduced in [1] in the case of a 2D geometry, for homogenous backgrounds, and experimentally validated in [2].

This communication aims to extend the above mentioned approach to a new, more complex, scenario involving heterogeneous scattering systems, embedded in a non-homogeneous backgrounds. The underlying theory, based on the concept of the local spectral content of an electromagnetic field, has been properly reformulated, and is briefly discussed in the communication.

To validate the approach and estimate its performances, an extensive numerical analysis has been performed, by referring to a 2D geometry, in the cases of linear and circular scanning observation domain. The field data to be inverted have been simulated by means of a commercial CAD to make the analysis as close as possible to a real world one, and the cases of metallic and dielectric scatterers have been considered. Some typical results will be presented and discussed.

[1] O. M. Bucci, A. Capozzoli, G. DElia, "Determination of the convex hull of radiating or scattering systems: a new, simple and effective approach", Inverse Problems, 18 No.6, December 2002, pag. 1621-1638.

[2] O.M. Bucci, A. Capozzoli, C. Curcio, G. D'Elia, "The experimental validation of a technique to find the convex hull of scattering systems from field data", Antennas and Propagation Society International Symposium, Vol. 1, June 22-27 2003, pp.539-542.

12   00:00   Electromagnetic Inversion of Amplitude-Only Data through a Two-Step Strategy
Franceschini, G.; Franceschini, D.; Donelli, M.; Azaro, R.; Massa, A.
University of Trento, ITALY

The diffusion of microwave imaging techniques in many different fields, such as biomedical and industrial diagnostic, is due to their capability of a qualitative and quantitative analysis of the dielectric properties of the scenario under test. However, these methodologies present some drawbacks related to the ill-posedness and the highly non-linear nature of the arising inverse scattering problem. Another non-trivial point is the amount of collectable information that is limited to an upper-bound depending on the geometrical and physical characteristics of the system even if multi-illumination, multi-view and multi-frequency systems are used. Moreover, the data acquisition requires complex and expensive hardware setups especially if the phase distribution is required. As a matter of fact, holographic and interferometric techniques, generally used in optical applications, give the phase information starting from amplitude-only data, but they require undesired additional post-processing.

In order to realize a reliable and cost-effective imaging apparatus, different strategies have been recently developed (see [1] and references therein) for the inversion of phaseless scattering data. Up to now, two main categories of approaches have been proposed. The former recast the original amplitude-only data retrieval as a standard inverse scattering problem after the reconstruction of the phase information. Alternatively, ad-hoc strategies have been presented for directly reconstructing the dielectric properties of the scatterers from phaseless information.

In such a framework, this contribution proposes an innovative two-step strategy. The first stage determines the phaseless data for the state equation starting from the measurement of the incident field in a limited number of locations in the observation domain. Then, a successive step is aimed at dealing with a phaseless-data reconstruction. In order to fully exploit the limited amount of collectable information without attempting to complete the amplitude-only scattering data, a suitable multi-scaling algorithm is used. Moreover, the local minima problem is addressed by means of a Particle Swarm-based hill-climbing optimization [3]. Such a two-step strategy considerably simplifies the measures collection both in terms of measurement setup and acquisition time.

A selected set of numerical and experimental results will be presented in order to verify the impact of the lack of the phase information and quantify the achievable reconstruction accuracy with respect to reference full data problems.


[1] L. Crocco, M. DUrso, and T. Isernia, "Inverse scattering from phaseless measurements of the total field on a closet curve," J. Opt. Soc. Am. A, vol. 21, Apr. 2004.
[2] S. Caorsi, M. Donelli, D. Franceschini, and A. Massa, "A new methodology based on an iterative multiscaling for microwave imaging," IEEE Trans. on Microwave Theory Tech., vol.51, pp. 1162-1173, Apr. 2003.
[3] J. Robinson and Y. Rahmat-Samii, "Particle swarm optimization in electromagnetics," IEEE Trans. on Antennas and Propagat., vol.52, pp. 771-778, Mar. 2004.

13   00:00   Fuzzy-Logic Reasoning for Estimating the Reliability of Noisy Data in Inverse Scattering Problems
Casagranda, A.; Franceschini, D.; Benedetti, M.; Massa, A.
University of Trento, ITALY

The electromagnetic noise unavoidably corrupts inverse scattering data even though collected in a controlled-environment. Hence, the effectiveness of inversion strategies is strongly affected because of the intrinsic ill-posedness and ill-conditioning of the problem in hand mainly caused by the limited amount of information collectable from the scattering experiments [1]. Generally, microwave imaging algorithms do not consider or partially address the issue of the reliability of the data. On the contrary, this work aims at highlighting that the level of reliability of the field measurements strongly affects the effectiveness of the retrieval process. Consequently, a direct evaluation of the data reliability in terms of a mathematical model or numerical values ("objective knowledge") would be really useful. Unfortunately, the amount of equivalent noise on the scattering data is usually available as "subjective knowledge", difficult or complex (and expensive) to be quantified using traditional mathematics or in terms of experimental rules. Therefore, it is generally neglected. However, unlike standard mathematics, the fuzzy theory [2] [3] seems to be an useful tool for exploiting such an information and for extracting the "clean" information-content coming from noisy data.

Accordingly, an unsupervised approach for taking into account the presence of the noise has been presented in [4] where crisp inputs are suitably mapped into crisp outputs employing the Fuzzy-Logic operations based on fuzzy concepts and rules. By so doing, the fuzzy-logic system is able to define suitable regularization parameters that weight the scattering data according to their degree of truth.
In order to assess the benefits of the integration of the fuzzy logic operations into reference inverse scattering techniques, selected numerical experiments have been considered In particular, a multi-step iterative algorithm [5] has been used for adaptively optimizing the resolution level and properly exploit the information content of the fuzzy-processed data.


[1] O.M. Bucci and T. Isernia, "Electromagnetic inverse scattering: Retrievable information and measurement strategies," Radio Sci., vol. 32, pp. 2123-2138, Nov.-Dec. 1997.
[2] L. A. Zadeh, "Fuzzy Sets," Information and Control, vol. 8, pp. 338-353, 1965.
[3] J. M. Mendel, "Fuzzy logic system for engineering: a tutorial," IEEE Proc., vol. 83, pp. 345-377, Mar. 1995
[4] A. Casagranda, D. Franceschini, and A. Massa, "Assessment of the reliability and exploitation of the information content of inverse scattering data through a fuzzy-logic-based strategy - preliminary results," IEEE Geosci. and Remote Sensing Letters, vol. 2, pp. 36-39, Jan. 2005.
[5] S. Caorsi, M. Donelli, D. Franceschini, and A. Massa, "A new methodology based on an iterative multiscaling for microwave imaging," IEEE Trans. Microwave Theory Tech., vol. 51, pp. 1162-1173, Apr. 2003

14   00:00   Microwave Tomography of Breast Cancer: A Feasibility Study
D'Urso, M.1; Catapano, I.2; Crocco, L.2; Morabito, A.3; Isernia, T.3
1University, ITALY;
3Universita' Mediterranea di Reggio Calabria, ITALY

Traditionally, in a microwave tomography problem one looks for a quantitatively accurate description of the electrical and geometrical characteristics of an assigned domain from the knowledge of a set of incident fields and measures of the corresponding total or scattered fields (both in amplitude and in phase) on a generic surface lying outside the region under test. The development of accurate and reliable techniques for solving this kind of problems is an important challenge because of their potential applications in applied geophysics, non invasive subsurface monitoring and non destructive testing and diagnostics. Recently, several papers have been published dealing with the possibility of applying microwave tomography approach based procedures to biomedical application, such as for example the breast cancer imaging.

Breast cancer is still a common cause of death in women. Early detection is an important part of effective treatments, and mammography is currently used to screen for breast cancer. While sensitive to tumors, mammography has indeed limitations in distinguishing amongst malignant and benign tumors.

Because of the very high difference, at microwave frequencies, of the electromagnetic properties of the malignant tissues with respect to the normal ones, microwave tomography has been proposed and studied as a possible effective tool in this context. As a matter of fact, microwave tomography can provide information that is complementary to mammography, as the resulting images indicate the differences in the electrical properties of the breast tissues, which also allows, at least in principle, to discriminate amongst the different types of tumors

On the other side, it is simple to understand that the reconstruction capabilities of the inverse scattering procedure (which is the core of a microwave tomography problem) play a key role, as a non accurate reconstruction may lead to either false alarms or lack of detection.

In the recent years, many different measurement configurations and solution procedures have been proposed and analyzed.

In this communications, first with reference to the canonical 2D case and then to the more complex 3D geometry, we show the usefulness of some theoretical tools which allow a somehow optimal design of the measurement set-up for an accurate imaging. In particular, by reasoning on the electromagnetic characteristics of the coupling medium, the desired space resolution and the degree of non-linearity of the underlying inverse scattering problem, useful criteria can be derived for an optimal choice of the working frequency and of the electromagnetic characteristics of the matching liquid.

Then, we compare the reconstruction capabilities of two inversion methods: the recently introduced Contrast Source-Extended Born inversion method and the traditional and widely used Contrast Source inversion scheme. It will be show how, by properly acting on the degrees of freedom of the problem, type of immersion liquid, working frequency and so on, it is possible to achieve good reconstructions and to accurately discriminate between different types of tumors when they are contemporary present.

15   00:00   The Multi-frequency Diagonalized Contrast Source Method for Electromagnetic Inversion
Casagranda, A.1; Abubakar, A.2; Franceschini, D.1; Massa, A.1; van den Berg, P. M.3; Habashy, T. M.2
1University of Trento, ITALY;
2Schlumberger-Doll Research, UNITED STATES;
3Delft University of Technology, NETHERLANDS

Inverse scattering problems deal with the determination of the constitutive parameters of the unknown objects embedded in a known background medium. In the frequency-domain approaches, the configuration is illuminated by a single frequency wave-field and the scattered field is measured in an observation domain outside the inaccessible investigation domain. The inversion of the collected data is a well-known to be non-linear and ill-posed. Furthermore, the retrievable information is limited. In order to overcome such drawbacks, a multi-frequency approach can be used by exploiting the Maxwellian dispersion relationships. However, besides the need of requiring multi-frequency acquisition facilities, the use of the set of multi-frequency data significantly increases the computational burden of the inversion process.

In a recent work, Abubakar et al. [1] proposed two computational effective strategies for the solution of the inversion problem. Such methods, called Diagonalized Contrast Source Inversion (DCSI) methods, are based on: (a) the source-type integral equation formulation [2], (b) a robust iterative method for Born inversion [3] and (c) the diagonal approximation of the scattering operator [4]. In particular, instead of solving the non-linear problem, a three-linear-step procedure is carried out significantly reducing the overall computational time. The preliminary numerical results reported in [1] highlight the effectiveness of these approaches as well as the favorable trade-off between complexity and reconstruction accuracy. In order to further improve the resolution of the inversion scheme, this paper combines the DCSI-based approaches with a multi-frequency strategy. Towards this end, both hopping and multiple-frequency processing have been implemented and the obtained results point out an extension of the range of validity of the diagonalization in comparison with that of single-frequency versions.


[1] A. Abubakar, T. M. Habashy, P. M. van den Berg and D. Gisolf, "The diagonalized contrast source approach: an inversion method beyond the Born approximation", Inv. Problems, vol. 1, pp. 685-702, 2005.
[2] T.M. Habashy, M.L. Oristaglio and A.T. de Hoop, "Simultaneous nonlinear reconstruction of two-dimensional permittivity and conductivity", Radio Science, vol. 29, pp. 1101-1118, 1994.
[3] A. Abubakar, P.M. van den Berg and S. Semenov, "A robust iterative method for Born inversion", IEEE Trans. on Geosci. Remote Sensing, vol. 42, pp. 342-354, 2004.
[4] T.M. Habashy, R.W. Groom and B. Spies, Beyond the Born and Rytov approximations: A nonlinear approach to electromagnetic scattering, Journal Geophysical Research, vol. 98, pp. 1759-1775, 1993.

16   00:00   High Electromagnetic Field Measurement by Using Target Diffraction
Vauchamp, S.; Diot, J-C.; Lalande, M.; Andrieu, J.; Jecko, B.

I. Introduction

XLIM (French research institute based at the University of Limoges) has just launched a new project which is called Michelson project and whose the concept has been patented. The objective is to measure an electromagnetic field in a selected place. A target is illuminated by a incident field which must be measured. This field is diffracted by this target in different directions. A receiving antenna is placed at a given location and recovers the diffracted field at this place. The purpose is to come back to the incident field which lights up the target from the voltage measured on the receiving antenna output. To obtain the incident field, a global transfer function of this system must be calculated before. One of many possible applications of this system is the measurement of high power which could be destructive for traditional receiving systems. Moreover this system doesnt disturb much the field in the zone of the measurement.

II. Principle of Michelson Project

Experimental setup is shown on Figure 1. The target is illuminated by the incident field ei(t) which must be measured. This field is diffracted by this target in different directions and according to different polarizations. A receiving antenna is placed at a location so that it is protected from the high field source. This antenna receives the field ed(t) which is diffracted by the target. The voltage vr(t), picture of receiving field, is measured by a sampler connected to the antenna output. hc(t) is the transient transfer function of target and depend on the direction of the incident field which radiates the target (vector i), the direction of diffracted field by the target (vector d), the distance R between target and receiving antenna, the polarization of field ei(t). hr(t) is the transient transfer function of the receiving antenna. From these functions, the global transfer function of this system hg(t) can be calculated by simulation, analytic calculation or experimental measurements. Thus we can link the field ei(t) that we want to know and the measured voltage vr(t).

III. Experimental Results and Prospects

To validate the Michelson concept, preliminary tests were realized with UWB (Ultra Wide Band) pulses and with a low level source. These first tests, with a metallic flat plate and a metallic sphere as targets, have allowed to validate the Michelson concept compared to results obtained by a classical electric field sensor.

To protect the receiving antenna from the source, we work actually on targets which are able to depolarize the incident field such as the dihedral corner reflector. The magnetic field can be measured also with this system with targets which are sensitive to this field, such as loops.

To increase the precision of the measurement we are envisaging to work with a receiving antennas array. Thus we could obtain a better gain and a better directivity in reception, and the signal noise ratio would be improved.

17   00:00   Resonances of Complex Shape Scattering Objects: Modelling by Resonant Circuits
Chauveau, J.; de Beaucoudrey, N.; Saillard, J.
IREENA, Polytech'Nantes, FRANCE

In resonance domain, the radar scattering response of any object can be modelled by its natural poles of resonance, with the formalism of the Singularity Expansion Method (SEM). The mapping of poles gives useful information in order to discriminate radar targets. In this paper, we propose to use resonant circuits modelling to characterize the resonance behaviour of complex shape targets from the quality factor. We present results exhibiting the advantage of this Q parameter.

The Singularity Expansion Method [C.E. Baum, in Transient Electromagnetic Fields, L.B. Felsen, Ed., New York: Springer-Verlag, 1976] has been introduced in order to characterize the electromagnetic response of structures. This method was stimulated by observation of typical transient temporal responses of various scatterers, which behave as a combination of damped sinusoids. Conversely, in the frequency plane, each damped sinusoid corresponds to one pair of complex conjugate poles.

To illustrate the concepts of SEM, it is interesting to compare resonance phenomena of radar targets with a RLC resonant circuit. Equation (1) gives the RLC transfer function A(w), which is also valid for any resonator, mechanical as well as electrical. For Q > 1/2, roots of the denominator of A(w) are complex conjugate poles s1,2 given by equation (2).

Scattering response of a target can be modelled as a sum of a few resonators. For canonical targets (sphere, cylinder, dipole ) poles are distributed over branches joining fundamental pulsation of resonance and corresponding harmonic pulsations. Previously [J. Chauveau et al, APS-URSI, New Mexico Albuquerque, July 2006], we have shown that the representation in {w0 ; Q} clearly brings out the resonance behaviour of canonical targets.

A complex shape target can often be modelled by a combination of canonical objects (Fig. 1) with poles of resonance distributed over some distinct branches, each one being associated to the corresponding canonical object. Fig. 2 is the mapping of poles in the complex plane. Fig. 3 presents the evolution of Q-factor as a function of w0 and allows to distinguish and to classify elementary components of the target from the quality of their resonance.

18   00:00   Rigorous Closed-Form Formulas for the Scattering from Plane Angular Sectors with Conical-Section Boundaries
Vallecchi, A.
University of Florence, ITALY

The scattering from flat surfaces with curved boundaries has recently deserved considerable interest in the context of the accurate prediction of the radar cross section of realistically modelled complex targets. Earth observation by remote sensing also involves the investigation of transmission through and scattering from assemblages of randomly oriented particle scatterers, such as the leaves of vegetation and the ice crystals formed in clouds at high altitude, to deduce information about the targeted scene from measured data. Since taking into account the size, shape, and orientations of the scatterers as well as multiple scattering interactions requires extensive computing, the simplest applicable formulas are needed to represent the elemental particle scattering.

The physical optics (PO) is a well established approximation in the computation of backscattering in the high-frequency region, and its validity has been assessed when the dimensions of the scattering object is large compared with the wavelength. However, as a main drawback of the PO approach, a double integral over the surface of the disk must be evaluated numerically. Even though such an integration can be convert into a line integral extended over the rim of the plate by applying Green's Theorem, its accurate evaluation may require a large number of segment subdivisions, which directly influences the required computational time. So far, completely closed-form PO scattered field expressions are only available for elliptical disks (M. A. Karam, Appl. Opt., vol. 37, pp. 1666-1673, 1998) and for polygons through Gordon's formula (W. B. Gordon, IEEE Trans. Antennas Propagat., vol.23, pp. 590-592, 1975).

In this contribution, a closed-form solution for the far zone scattering from either dielectric or metallic angular sectors characterized by a conical-section contour, that is, an arc of ellipse, parabola, or hyperbola, and whose size is large with respect to the wavelength, is deduced based on a PO approximation for the induced currents. The scattered field is expressed in terms of incomplete cylindrical functions which, like other special functions, possess known integral representations, recurrence relations, convergent and asymptotic series expansions; as a result, the field can be efficiently computed by resorting to specific approximate expressions in terms of elementary functions. The appeal of the proposed solutions especially lies in the fact that they can be applied in conjunction with Gordon's result to evaluate the scattering from large complex planar objects with curved boundaries, which can be modelled as composite geometries formed by a juxtaposition of polygons and angular sectors or segments, as the summation of a number of discrete contributions, with very reduced computational complexity as compared to the standard PO representation. Furthermore, it appears that these results can also be applied to the derivation of analytical expressions for the scattering amplitude from dielectric objects of canonical forms in the framework of the generalized Rayleigh-Gans approximation, which is commonly used to compute the backscattering from vegetation canopies mainly consisting of leaves smaller or comparable to a wavelength, and the more general case of arbitrary plate thickness by following the same approach as in D. M. L. Vine et. al., J. Opt. Soc. Amer., vol. 73, pp. 1255-1262, 1983.

19   00:00   Currents Reconstruction with High Resolution Using the fft Iterative Method and Spectrum Replies
Sanchez Escuderos, D.; Baquero Escudero, M.; Rodrigo Peñarrocha, V.M.; Vico Bondia, F.
Universidad Politecnica de Valencia, SPAIN

The design of an antenna involves a lot of steps from the definition of its purpose and its initial idea to its manufacture. This last step is the most critical because the transformation between the simulations and the real antenna is not as good as it could be desirable. The material and machine tolerances are limited, what affect the resulting antenna and therefore its radiated field. The discovery of the differences of this real antenna with regard to the ideal could help us to improve it for obtaining the desirable results. This could be achieved looking at the equivalent currents of the antenna reconstructed from the available data, i.e. the measurement of its radiated field, usually in the near field region. Moreover, this effort is not only valid for discovering problems in the manufacturing process, but also it could help us to know if there have been any mistake in the designing process or in the feed of the antenna, for example.
The most common algorithm for obtaining the equivalent currents from the radiated field in the near region consists of three steps: The first one transforms the near field to far field, the second one obtains the plane wave spectrum from the far field and the last one calculate the near field in the plane of interest. With this field is easy to obtain the equivalent currents using the principle of equivalence. This process, that has been the followed by us for this paper, implies that the equivalent currents are obtained on a plane and the antenna must have a plane shape in their main direction of interest for their better study.
The process described previously works well if we don't need a good resolution. If we need to distinguish points separated less than 1 wavelength, it doesnt let us to differentiate it. This is because the only part of the spectrum achievable with this method is the visible part. To improve the precision we add zeros (zero padding), but this doesn't improve the resolution.
In this paper we propose increase the resolution of the reconstruction not adding zeros in the spectrum, but using a technique for extrapolating the spectrum. This, an fft iterative method, let us to obtain some parts of the spectrum unachievable with the traditional method. The rest parts, needed for a good precision and resolution, are obtained using the property of periodicity of the spectrum appeared on arrays antennas. With these two methods the resolution achievable improves up to 0.5 wavelengths. As an example, we show the currents for an antenna formed by 25 elements separated 0.5 wavelengths reconstructed with the traditional method and with our improvement.

Figure 1. Currents reconstruction with the traditional method (a) and with our improvement (b)

This work has been supported by Spanish Ministerio de Educación y Ciencia under FPI research fellowship programme (TEC2004-04866-C04-01), cofinanced by the European Social Fund (ESF)

20   00:00   Microwave Links Used as Electromagnetic Raingauges: A Real Time Pilot Experiment in Italy
D'Amico, M.1; Mannucci, G.2; Pinotti, M.1
1Politecnico di Milano, ITALY;
2ARPA Lombardia, ITALY

All hydrological models need information about the spatial distribution of the rainfall, the exact amount and distribution of which are not known and can only be estimated from measurements on the ground (e.g. raingauges) or in the air (e.g. radars). Extrapolation from raingauge data into spatial distributions has long been understood to be as highly speculative. Radar data give the spatial distribution and provide a good basis for short term forecasts necessary for any kind of control and warning, but have their deficiencies in terms of quantitative reliability.

An innovative method of estimating rainfall is via the attenuation it causes to a ground-based microwave link. This provides measurements of path averaged rainfall. It can provide also data on a much finer time scale (virtually continuous) than will either a radar or a raingauge. To investigate the potential of this new technique the European Commission funded the MANTISSA (Microwave Attenuation as a New Tool for Improving Stormwater Supervision Administration) project in Framework V.

In the MANTISSA project extensive experimental campaigns were carried out to assess the potential of the method. However, all the analyses were done "a posteriori·", i.e. not in real time.

Since rain rate is derived from microwave attenuation, it is essential that attenuation data are cleared from contributions due to multi-path and gases present in the atmosphere (especially water vapour), i.e. the "baseline" attenuation level. To this purpose, it is essential to correctly identify "dry" and "wet" periods. A wrong classification of a wet period marked as dry would lead to great inaccuracies in rain rate estimation, since it would result in a overestimated baseline attenuation level, thus leading to an underestimation of the rain rate. Wet and dry periods can be easily identified with a "a posteriori" analysis, or if ancillary equipment is available (i.e. rain sensors or rain gauges); real-time operation, on the contrary, can be quite challenging.

In this contribution we will present the first results of a pilot experiment (funded by ARPA, Agenzia Regionale per la Protezione dellAmbiente, a body of Regione Lombardia) where a real-time technique is applied; data are collected and sent using a GPRS link to the ARPA`s Monitoring Centre, and processed in real time to extract rain rate. Wet periods are identified in real time from the time series of attenuation, using a procedure that does not exploit ancillary equipment. Estimated rain rate is then compared with data collected by co-located tipping bucket raingauges.

21   00:00   A Novel Method for Electromagnetic Target Classification Using the MUSIC Algorithm: Applied to Small-Scale Aircraft Targets
Secmen, M.; Sayan, G. T.
Middle East Technical University, TURKEY

This paper introduces a novel target classification method applied to small-scale aircraft targets using the multiple signal classification (MUSIC) algorithm to extract resonance features from the late-time scattered field data. This method provides high accuracy rates even for extremely noisy data and it needs feature fusion at only a few different target aspects for classifier design.

Late-time scattered signals of a target consist of damped sinusoidal components directly associated with system poles, which provide an excellent feature set for target classification due their aspect and polarization independent nature. The MUSIC algorithm is a well-known tool to extract the parameters of undamped/damped sinusoidal signal components in the presence of noise. The direct determination of target poles, especially their real parts, from scattered data by using the standard MUSIC algorithm becomes a difficult task as the noise power increases. In the proposed method, a matrix called as "MUSIC spectrum matrix (MSM)" is generated over the complex frequency plane to represent the relative strengths of damped sinusoidal components in a given scattered signal to estimate the dominant pole values for the given target within a specific bandwidth at the specified aspect. For the classifier design, such MSMs are computed for each candidate target at distantly selected reference aspects. As the scattered data of a target are strongly aspect-variant, target poles may be excited at different strengths at different aspects, hence the reference MSMs may differ from each other. To minimize the classification ambiguity resulting from this aspect dependency and to maximize target's overall pole information for higher classification accuracy, a "fused MSM (FMSM in short)" is generated for each target by superposing the individual reference MSMs. The FMSM of a target is the main classifier feature in the proposed method. Then, at the real-time recognition phase when a test target sensed at an arbitrary aspect, the MSM computed from the test data is compared to the FMSM of each candidate target. The maximum correlation coefficient computed in this process indicates the classification label for the test target.

Performance of the proposed classifier method is demonstrated for a target set of four small-scale aircrafts scaled by a factor of 100 and modeled by perfectly conducting straight thin wires. Backscattered data for these targets are numerically generated over the frequency range of zero to 1024 MHz with 4 MHz steps for the aspect angle of phi=5, 10, 15, 22.5, 30, 37.5, 45 and 52.5 degrees with theta=60 degree. Out of these eight different aspects, four of them (phi=5, 15, 30, 45 degrees) are chosen to construct the reference database and to design the classifier. Targets' time domain responses are first computed for the noise-free case at all aspects and then the noisy responses are synthesized at the signal-to-noise ratio (SNR) levels of 10, 5, 0 and -5 dB. The classification results turned out to be very satisfactory as shown in Table 1 below that the accuracy rate is 91 percent even for the SNR level of -5 dB. Details of the classifier design and the testing procedure will be given in the full paper.

SNR10 dB5 dB0 dB-5 dB

Table 1. The correct classification rates for different SNR values.
22   00:00   3D Electromagnetic Imaging Methods for Objects Detection
Ia, D.1; Ferrieres, X.2; Masmoudi, M.3

We are interested by an inverse scattering problem. A domain filled with some dielectric or metallic objects is illuminated by an electromagnetic wave, the scattered field is measured by a set of sensors located outside the domain, we wish to locate and caracterize these objects. There are many expected applications like mine detection, security(objects in baggages, people counting in a room), non destructive control in general.

In a first time we are looking for locating the objects. The methods called "time reversal methods" in the temporal domain or DORT in the frequency domain are well known for acoustic, we propose to study them for electromagnetism. Let $(E(x,t),H(x,t))$ a solution of the Maxwell equation then $(E(x,-t),H(x,-t))$ is solution too. By the way, physically, if the time is reversed the wave will propagate by the same way. Then if we record the scattered field and we re-emit it time reversed, the wave will focalize on the scatterers and we can locate the sources. Numerically the time reversal is easy to compute, experimentally, we need an important number of antennas and a fast generator wich can return the time reversed signals, wich is yet a research problem...

Once that first localization done, we want to improve these results firstly by searching for the best localization as possible until finding the shape of the scatterers and the electromagnetic nature of the objects. Using optimization methods seems needed. These methods have an important numerical cost which make them expensive and unusable in 3D, that's why we restrict the search on a smaller domain. We first propose an acceleration of the Gauss Newton method using a DORT method coupling. The use of the eigenvectors as incident wave is used to improve the information obtained in the measured scattered field. The new set of measurements is easy to compute thanks to the linearity of the field with respect to the sources. We have then a cost function depending on a number of sources equal to the number of scatterers obtained by studying the eigenvalues obtained by the DORT method, the improvement is important in 3D. The idea of using these sources is general and can be adapted to many methods.

23   00:00   A Robust and Fast Imaging Algorithm without Derivative Operations for UWB Pulse Radars
Kidera, S.; Sakamoto, T.; Sato, T.
Graduate School of Informatics, Kyoto University, JAPAN


UWB pulse radar systems have high potential for high-resolution imaging in indoor environments. We have already proposed a fast imaging algorithm, SEABED based on a reversible transform BST between the received signals and the target shape. However, the image obtained by SEABED deteriorates in a noisy environment because it utilizes a derivative of received data. In this paper, we propose a robust imaging method by generalizing the SEABED.

Conventional Method

We utilize a mono-static radar system. We assume a target which has a clear boundary, and is expressed as a single valued and continuous function. We define (x,y) as a point on the target boundary. An omni-directional antenna is scanned along x axis. X is the x coordinates of the antenna location, and Y is the range, which can be measured by the output of the matched filter, as shown in Fig. 1. The curve (X,Y) is called a quasi wavefront. SEABED estimates the target image with a reversible transform BST between the target boundary and the quasi wavefront. However, the image of the SEABED deteriorates in a noisy environment because it utilizes dY/dX in the BST.

Proposed Algorithm

To solve this problem, we propose a robust imaging method with an envelop of circles. We define S as an interior set of a circle whose center is (X,0) and radius is Y, for each (X,Y). We define δ S U and δ S I as a boundary points on an union and an intersection set of S. We have proven that a target boundary δT can be expressed as
δ TSU (d2y/dx2 > 0)
δ TSI (d2y/dx2 < 0)
δ SU and δ SI express envelopes of circles obtained by (X,Y), as shown in Fig. 2. By utilizing this relationship, we estimate the target boundary as an envelope of circles. Also we confirm that we can correctly select δ SU or δ SI with the characteristic of quasi wavefronts. This method transforms the group of points (X,Y) to the group of points (x,y) without the derivative dY/dX. Therefore it can realize a stable imaging even in a noisy environment.

Performance Evaluation

Figs.1 and Fig.2 show the estimated points with SEABED and the proposed method, respectively. Here we set the sampling number to 101, and add white noise to the true quasi wavefronts, whose standard deviation is 0.005 wavelength. We confirm that the estimated image of SEABED deteriorates, and cannot reconstruct the outline of the target boundary due to the noise. On the contrary, the image obtained by the proposed method is stable and precise.
This is because the proposed method does not spoil the information of the inclination of the estimated image. The calculation time of this method is within 0.2 sec for Xeon 3.2 GHz processor, which is short enough for realtime operations.

24   00:00   An Edge-Preserving Stabilization for a Fast 3-D Imaging Algorithm with a UWB Pulse Radar
Sakamoto, T.1; Kidera, S.1; Sato, T.1; Sugino, S.2
1Kyoto University, JAPAN;
2Matsushita Electric Works, Ltd., JAPAN

1. Introduction
The UWB(Ultra Wide Band) pulse radar is a promising candidate for the environment measurement for rescue robots because they work even in dense smoke. Radar imaging is known as one of ill-posed inverse problems, for which various algorithms have been proposed. Their computation time is too long because they are based on iterative methods, which is not acceptable for the realtime operation of robotics. We have already proposed a fast imaging algorithm SEABED for UWB pulse radars. The SEABED algorithm has a weak-point that it is not robust for noisy data obtained by experiments. In this paper, we propose a stabilization algorithm for SEABED algorithm, which preserves edges of a target shape.

2. System Model and SEABED algorithm
We assume a mono-static radar system in this paper. An omni-directional UWB antenna is scanned on a plane. We express the surface of the target in the real space with the parameter (x,y,z). These parameters are normalized by the center wavelength l. s(X,Y,Z) is the received signal at the antenna location (x,y,z)=(X,Y,0), where we define Z with time t and speed of the radiowave c as Z=ct/(2l). We define a quasi-wavefront Z(X,Y) which is a equi-phase surface extracted from s(X,Y,Z). SEABED algorithm is based on a reversible transform IBST. IBST describes the target shape (x,y,z) with the quasi-wavefront (X,Y,Z) as


x = X - Z ZX
y = Y - Z ZY
z = Z(1-ZX2-ZY2)1/2

3. Proposed Stabilization Algorithm
We can obtain the target image by calculating the right-hand side of the IBST. However, the formulas include derivative operations, which are sensitive to noise. We show an application example of SEABED algorithm to the experimental data. Fig. 1 shows the true targets shape used in our experiment. The metallic cone target is difficult to smooth because it includes both of an edge and a smooth surface. Fig. 2 shows the estimated target shape with the conventional SEABED algorithm with a smoothing after applying the IBST. In the figure, we see that the surface still contains random components while the edge is distorted by the smoothing.
In order to resolve the problem of the conventional SEABED algorithm, we apply the smoothing to the quasi-wavefront in place of the real image. We have analytically derived the upper bound for the maximum eigenvalue of the Hesse matrix of the quasi-wavefront (X,Y,Z). We adaptively change the correlation length of the smoothing based on the upper bound. Fig. 3 shows the estimated target shape with our proposed algorithm. The proposed algorithm preserves the edge while the random components are suppressed well.

Fig. 1. True target shape used in our experiment.

Fig. 2. Estimated target shape with the conventional SEABED algorithm (within 0.1 sec).

Fig. 3. Estimated target shape with our proposed algorithm (within 0.1 sec).

25   00:00   Acceleration of Total Field' s Reconstruction for Visualization of Scatterer Surface
Zaridze, R.; Tabatadze, V; Kakulia, D; Ghvedashvili, G; Saparishvili, G
Tbilisi State University, GEORGIA

Variety of methods exist of the body' s shape reconstruction by means of irradiation by the field with the wave of significantly less wavelength then the body' s sizes. The proposed method can be used even when the wavelength is comparable to the body' s sizes.

This paper will present the algorithm for the shape and position of a latent body reconstruction using the restored electromagnetic field. The main problem is to reconstruct the scattered field by E and H fields data obtained on some surface in vicinity of the body. Solution of this problem based on the MAS algorithm which uses converging waves functions more than once was presented in [1, 2]. Problem was reduced to solving of the system of linear equations that requires some computational and time resources. New approach consists in application of the equivalent currents and charges conception for converging fields. The algorithm of equivalent sources selection from holographic data also will be presented. In these papers will be included mainly dealed with the visualization of the scattered field singularities in three-dimensional case. The visualization of the body immerged into a dielectric media may be achieved if the dielectric media is transparent for particular frequency of the incident wave.

In order to determine the latent body' s shape more precisely it should be exposed to the radiation from the different directions and in several frequency ranges. The quality of restoration - i.e. resolution is strictly dependent on the number of frequencies used. Additional objective of the paper is to optimize this number. It seems that it is enough to use 5-7 frequencies making up one octave for the satisfactory results.

Contactless determination of shape and position is important in vast number of applications in different branches of science and technology, such as Applied Electrodynamics, Tomography, Medicine (for investigation of the internal organs), Archeology (for the study of fragile archeological samples), Military Engineering (for detection of explosive substances) etc. Application of different methods is necessary for verification of the observing results. Sometimes when a direct contact to the body is undesirable, dangerous, or impossible at all such methods are the only possible way of investigation.