Figure 7. The return loss and radiation patterns of the corrugatedhorn are compared to the results of a MM/MOM program inFigures 8 and 9–11, respectively. The results are in very goodagreement.

CONCLUSION

A FDTD algorithm has been presented for modeling bodies ofrevolution containing materials of finite conductivity and arbitrarydielectric constant. This algorithm was applied to the analysis of acorrugated horn and has been validated by comparing the return-loss and radiation-pattern results to those of a MM/MOM tech-nique.

REFERENCES

1. T.G. Jurgens, A broadband absorbing boundary condition for the FDTDmodeling of circular waveguides. IEEE Transactions on MicrowaveTheory and Techniques Symposium Digest, 1995, pp. 35–38.

2. D.B. Davidson and R.W. Ziolkowski, Body-of-revolution finite differ-ence time domain modeling of space-time focusing by a three-dimen-sional lens. Opt Soc Am 11 (1994), 1471–1490.

3. Y. Chen, R. Mittra, and P. Harms, Finite-difference time-domain algo-rithm for solving Maxwell’s equations in rotationally symmetric geom-etries. IEEE Trans Microwave Theory Tech MTT-44 (1996), 832–839.

4. J.G. Maloney, G.S. Smith, and W.R. Scott Jr. Accurate computation ofthe radiation from simple antennas using the finite-difference time-domain method. IEEE Trans Antennas Propagat AP-38 (1990), 1059–1068.

5. A. Taflove, Computational electrodynamics, the finite-difference time-domain method. Artech House, Norwood, MA, 1995.

6. D.C. Wittwer and R.W. Ziolkowski, How to design the imperfectBerenger PML. In Electromagnetics, Taylor and Francis, London, 1996,pp. 465–485.

7. A.P. Zhao and A.V. Raisanen, Application of a simple and efficientsource excitation technique to the FDTD analysis of waveguide andmicrostrip circuits. IEEE Trans Microwave Theory Tech MTT-44(1996), 1535–1539.

© 2002 Wiley Periodicals, Inc.

ELECTROMAGNETIC INVERSION OFIPSWICH OBJECTS WITH THE USEOF THE GENETIC ALGORITHM

Yong Zhou and Hao LingDepartment of Electrical and Computer EngineeringThe University of Texas at AustinAustin, Texas 78712

Received 22 December 2001

ABSTRACT: The genetic algorithm is combined with a moment methodsolver to carry out the shape inversion of two-dimensional metallic ob-jects. The binary bitmap discretization is used in conjunction with geo-metrical median filtering to describe the shape of the object. Results ofthe shape inversion with the use of this algorithm are presented for sev-eral Ipswich objects based on measurement data. © 2002 Wiley Peri-odicals, Inc. Microwave Opt Technol Lett 33: 457– 459, 2002; Pub-lished online in Wiley InterScience (www.interscience.wiley.com). DOI10.1002/mop.10349

Key words: inverse scattering; genetic algorithms; Ipswich data; multi-ple scattering effects

INTRODUCTION

Inverse synthetic aperture radar (ISAR) imaging [1] is a linearizedform of electromagnetic inverse scattering. Although the algorithmis fast and robust in obtaining the approximate shape of an object,it suffers from resolution limitation and image artifacts due tomultiple scattering phenomena. Rigorously solving the electro-magnetic inverse scattering problem, on the other hand, is muchmore challenging. Recently, some researchers have explored theuse of genetic algorithms (GA) together with computational elec-tromagnetic solvers to attack the inverse scattering problem [2–6].This Letter presents results of the use of GA in conjunction with amethod-of-moments (MoM) solver to invert metallic objects fromthe Ipswich measurement data set [7]. Particular attention is fo-cused on concave metallic objects with strong multiple scatteringeffects.

In the inversion of two-dimensional (2D) objects, two types ofgeometrical descriptions have been used: the Fourier-seriesscheme [2,4] and the binary bitmap discretization [3,5]. The Fou-rier-series scheme is very efficient in representing smooth convexshapes. However, it does not work well for objects with highlyconcave shapes or disconnected parts. The binary bitmap discreti-zation is a more general way to represent arbitrary 2D shapes. Itsmain drawback is the larger degrees of freedom required to accu-rately model simple shapes. More recently, cubic B-splines werealso investigated as a way to accurately represent complex shapes[6]. This work uses the binary bitmap approach to discretize thesearch space. To constrain the problem, a geometrical median filteris applied to create more realizable shapes. A cost function isdefined as the difference between the measured and the computedscattered fields from each assumed shape. The inverse problem isthen cast into a minimization problem, and a genetic algorithm isapplied to minimize this cost function. Three Ipswich objects, thetriangular cylinder, the dihedral, and the circular cavity, are in-verted by using this scheme. Results based on both the MoM-simulated field and the measured data are presented.

GA SCHEME

In an inverse problem involving metallic objects, the measuredscattering field Emea from the object is known, but the shape andsize of the object are not. The method-of-moments solution basedon the electric field integral equation is applied to obtain therigorously computed scattered field Ecal from each assumed shape.To evaluate the performance of each shape, the cost function is

Contract grant sponsor: Office of Naval Research; Contract grant number:N00014-98-1-0615

Figure 1 Ipswich measurement setup

Figure 2 Real shapes of Ips009, Ips004, and Ips011

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 33, No. 6, June 20 2002 457

defined as the root-mean-square (RMS) error between Emea andEcal (normalized with respect to Emea).

A genetic algorithm is applied as the searching tool tominimize the cost function. In our GA implementation, theinitial generation is produced randomly and each object shape isencoded into an N�N binary array, with ones representingmetal and zeros representing free space. A 2D median filter isused as a low-pass filter to eliminate unrealistic shapes consist-ing of isolated cells. With a fixed window size of M�M, themedian filter slides through every cell of the binary array andsets the cell to one if the sum of the cell values within thewindow is greater than or equal to M2/2 and zero otherwise. Themedian filter is applied once every several generations so thatthe isolated cells are cleared from time to time, while the newfeatures created by the mutation and crossover operations havea chance to survive in the population.

The cost function for each member is then calculated, and theshapes with low cost values are selected as parents to produce thenext generation. A two-point crossover scheme involving threeselected parents is used. The process selects three parents anddivides each parent into three parts. The three parent shapes arethen intermingled to produce three children shapes. This crossoverscheme exhibits a more disruptive characteristic for regenerationthan the conventional one-point crossover. It serves to counteractagainst the median filtering effect. The mutation operation, whichis applied to the individual array cells, inverts the cell according toa preset mutation rate. The selection, cross-over, and mutationprocess is iterated until the lowest cost function in the population

reaches a sufficiently small threshold or when the cost functiondoes not decrease any further.

RESULTS

The Ipswich measurement data was taken at a single frequency of10 GHz in the bistatic configuration. There were a total of 36transmitter positions around the object and 18 receiver locationsfor each transmitter position (Figure 1). Figure 2 shows the shapesand sizes of three metallic Ipswich objects selected for inversion,namely, the triangular cylinder, the dihedral, and the circularcavity. They are labeled as Ips009, Ips004, and Ips011, respec-tively. For Ips009 and Ips011, the electric field is parallel to theaxis of the target. For Ips004, the electric field is perpendicular tothe axis of the target.

Imaging results for these targets were first generated withthe use of the traditional Fourier imaging method [1]. The datawere placed into the k space, as shown in Figure 3. They werethen interpolated onto a rectangular grid and 2D fast Fouriertransformed into the image domain. The resulting images areshown in Figure 4. In the results corresponding to the dihedraland circular cavity, image artifacts due to multiple scatteringcan be observed. For the dihedral, the multiple scattering causesstrong artifacts outside the body. For the circular cavity, themultiple scattering effect makes it hard to see the opening of thecavity.

The GA inversion algorithm was first tested using MoM-simulated field data as the input. In all of the reconstructions, thenumber of chromosomes in the population was set to 100 and thecrossover and mutation rates were set to 0.8 and 0.2, respectively.The search area was chosen to be 15�15 cm for Ips004 and12�12cm for Ips009 and Ips011. The number of cells within thisarea was set to 20�20. The reconstructed results in Figure 5(a)show the final inverted shapes of the three objects. The final shapesare in fairly good agreement with the real shapes. The final RMScosts for the three objects were found to be 3%, 38%, and 18%,respectively. The dihedral and the circular cavity contain strongmultiple scattering, and yet their inverted shapes closely resemblethe correct objects.

Next, the inversion algorithm is applied to the actual measureddata. Figure 5(b) shows the final reconstructed shapes. As can beseen, the inverted shape is good for the triangular cylinder, whichhas no multiple scattering effects. For the dihedral, the recon-structed shape is not continuous, but is quite similar to the realobject. The circular cavity shows the most discrepancy with thereal shape. The exterior and the opening of the cavity are correctlyinverted, while the interior part of the cavity shape is not assatisfactory.

Figure 3 Measured data in k space

Figure 4 Imaging results for three Ipswich objects

458 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 33, No. 6, June 20 2002

Interestingly, in all three inversions, it was found that the finalshape obtained by GA has a lower cost value than that of the exactshape (38% vs. 58% RMS error for the triangular cylinder; 82%vs. 92% for the dihedral and 55% vs. 73% for the circular cavity).This indicated that a mismatch exists between the measured fieldand the MoM-simulated field. This difference is believed to havedriven the GA to zoom onto a shape that is similar to the exactshape but has a lower cost value.

Note also that the RMS error listed above was particularlyhigh for the dihedral. It was found that the agreement betweenthe measured data and the MoM-computed data for this shapewas good in the field amplitude. However, a relatively largephase difference exists (even after adjusting for the rotationcenter) between the two results. The MoM results were alsochecked against other targets in the Ipswich data set, and thephase agreement was found to be good. It is therefore concludedthat the phase data for Ips004 is suspect. As an alternative,inversion based on only the amplitude of the fields was per-formed. The reconstructed shape is shown in Figure 6. Thequality of the reconstruction is close to that of the MoM-simulated data shown in Figure 5(a).

CONCLUSION

A genetic algorithm was combined with a moment-method solverto carry out shape inversion of the Ipswich measurement data. Abinary bitmap discretization was used in conjunction with a geo-metrical median filter to describe the shape of the object. It wasfound that the algorithm could deal with objects containing strongmultiple scattering effects.

REFERENCES

1. D.L. Mensa, High resolution radar imaging. Artech House, Dedham,MA, 1981.

2. C.C. Chiu and P.T. Liu, Image reconstruction of a perfectly conductingcylinder by the genetic algorithm. IEE Proc Microwave AntennasPropagat 143 (1996), 249–253.

3. T. Takenaka, Z.Q. Meng, T. Tanaka, and W.C. Chew, Local shapefunction combined with genetic algorithm applied to inverse scatteringfor strips. Microwave Opt Technol Lett MTT-16 (1997), 337–341.

4. Z. Qian and W. Hong, Image reconstruction of conducting cylinderbased on FD-MEI and genetic algorithms. IEEE Antennas PropagationSoc. Int. Symposium Digest, 1998, Vol. 2, pp. 718–721.

5. M. Pastorino, A. Massa, and S. Caorsi, A microwave inverse scatteringtechnique for image reconstruction based on a genetic algorithm. IEEETrans Instrum Meas IM-49 (2000), 573–578.

6. K. Barkeshli, M. Mokhtari, and N.M. Amiri, Image reconstruction ofimpenetrable cylinders using cubic B-splines and genetic algorithms.IEEE Antennas Propagation Soc. Int. Symposium Digest, 2001, Vol. 2,pp. 686–689.

7. R.V. McGahan and R.E. Kleinman, Second annual special session onimage reconstruction using real data. IEEE Antennas Propagat. Mag.39(2) (1997), 7-–9.

© 2002 Wiley Periodicals, Inc.

COMPACT PLANAR INVERTED-FPATCH ANTENNA FOR TRIPLE-FREQUENCY OPERATION

Fu-Ren Hsiao and Kin-Lu WongDepartment of Electrical EngineeringNational Sun Yat-Sen UniversityKaohsiung 804, Taiwan

Received 16 November 2001

ABSTRACT: A novel compact planar inverted-F patch antenna withtwo shorted branch strips for triple-frequency operation at about 900,1800, and 2450 MHz is presented. The antenna has compact dimensionsof 5.5 mm in height and 7.5 � 24 mm2 in area. The two shorted branchstrips are printed on an FR4 substrate, and supported above a groundplane by plastic posts. In addition, the longer branch strip, which con-trols the operations at about 900 and 1800 MHz, is printed on bothsides of the FR4 substrate, leading to the reduction in antenna dimen-sions. On the other hand, the shorter branch strip, printed on one sideof the FR4 substrate only, controls the operation at about 2450 MHz.Details of the antenna design and experimental results are presentedand discussed. © 2002 Wiley Periodicals, Inc. Microwave Opt TechnolLett 33: 459–462, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10350

Key words: antennas; planar inverted-F antennas; multifrequency an-tennas

1. INTRODUCTION

Planar inverted-F patch antennas have been shown to be promisingcandidates for applications in wireless communications. Manydual-frequency designs for operations at about 900 and 1800 MHzhave been demonstrated [1–6]. As for achieving triple-frequencyoperation, mainly for operations at 900, 1800 (or 1900), and 2450MHz, many fewer designs are available in the open literature [7,8]. The designs shown in Reference 7 mainly use three differentshorted patches to achieve three separate resonant frequencies. InReference 8, a meandered shorted patch with two shorting stripshas been demonstrated to achieve three resonant frequencies at

Figure 5 Inversion of three Ipswich objects (a) inversion based onMoM-simulated field; (b) inversion based on measured complex field

Figure 6 Inversion of the dihedral based on only the amplitude of themeasured data

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 33, No. 6, June 20 2002 459