Figure 5 Simplified ship-like target

about 1�10 smaller than that of the conventional ray-tracingmethod.

The second example is a simplified ship-like target, asshown in Figure 5. We compute the RCS from � � 0 to� � 360 in 721 equal-spaced incident directions at 10 GHzfrequency. Figure 6 shows the RCS comparison of our resultsŽ . Ž .solid line with the measured results circle . Again, excellentagreement is found between the two results. In the multireso-lution grid algorithm, the number of initial ray tubes and the

Ž .tolerance value are set to 25 � 50 and 0.003 m � ��10 ,respectively. The number of ray tubes for the conventionalray-tracing method is set to 333 � 666. As shown in Table 1,our algorithm is approximately 30 times faster than theconventional ray-tracing method.

CONCLUSION

In this letter, the multiresolution grid algorithm is presentedand applied to the RCS calculation. Numerical results showexcellent agreement with the measured one. The efficiency incalculation time is case dependent. However, the calculationtime is not greater than that of the conventional ray-tracingSBR. In our numerical results, the proposed algorithm yieldsapproximately 10�30 times faster results.

Ž .Figure 6 Comparison of our results solid line and measuredŽ .results circle for the simplified ship-like target, VV polarization,

10 GHz frequency

REFERENCES

1. D.P. Bouche, F.A. Molinet, and R.A.J. Mittra, Asymptotic andhybrid techniques for electromagnetic scattering, Proc IEEE 81Ž .1993 , 1658�1684.

2. J.M. Rius, M. Ferrando, and L. Jofre, High-frequency RCS ofcomplex radar targets in real-time, IEEE Trans Antennas Propa-

Ž .gat 41 1993 , 1308�1319.3. D. Klement, J. Preissner, and V. Stein, Special problems in apply-

ing the physical optics method for backscatter computations ofŽ .complicated objects, IEEE Trans Antennas Propagat 36 1988 ,

228�237.4. H. Ling, R.C. Chou, and S.W. Lee, Shooting and bouncing rays:

Calculating the RCS of an arbitrarily shaped cavity, IEEE TransŽ .Antennas Propagat 37 1989 , 194�204.

5. T.G. Griesser and C.A. Balanis, Backscatter analysis of dihedralcorner reflectors using physical optics and the physical theory of

Ž .diffraction, IEEE Trans Antennas Propagat AP-35 1987 ,1137�1147.

� 2001 John Wiley & Sons, Inc.

MICROWAVE HOLOGRAPHIC 3-DRENDERING SYSTEM USINGA REDUCED-SIZE PLANARARRAY ANTENNAHala Elsadek,1 HeshamEldeeb,1 Franco De-Flaviis,1 Luis Jofre,1

Esmat Abdallah,2 and Essam Hashish31 Department of Electrical and Computer EngineeringUniversity of California at IrvineIrvine, California 92697-26252 Microstrip DepartmentElectronics Research InstituteDokki, Giza 12622 Egypt3 Department of Electronics and CommunicationFaculty of EngineeringCairo UniversityCairo, Egypt

Recei�ed 5 January 2001

ABSTRACT: A compact rendering system for establishing a three-( )dimensional 3-D pointer is possible by combining microwa�e hologra-

phy with microstrip antenna arrays to enter 3-D coordinates of a point inspace into computer memory. To obtain the reduction in system size, newsolutions are proposed in both the holographic reconstruction algorithmsand the recei�ing planar array antenna. � 2001 John Wiley & Sons,Inc. Microwave Opt Technol Lett 29: 397�402, 2001.

( )Key words: microwa�e holography; 3-D pointer mouse ; planarmicrostrip array antenna; antenna size reduction; slit insertion

1. INTRODUCTION

The first microwave hologram was produced at Bell Labora-� �tories in 1950 1 . We utilize this idea to design a dynamic

Ž .system for a 3-D pointer. Using this new pointer mouse , theoperator can create and draw, point by point or on a multi-point basis, any 3-D graph or object that exists physically oreven virtually, and can save it in computer memory. After-wards, this can be used in information reduction, scaling,interpolation, image compression, and 3-D data acquisition,generating a body-fitted grid system for computer simulation,data animation, or pattern recognition of objects in 3-Dspace. We can envision applying this 3-D image processing inmany fields of applications, such as computer-aided design in

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 29, No. 6, June 20 2001 397

medicine and robotics where true spatial information rendersimportant assistance.

For practical purposes, an investigation volume of 1 m �1 m � 1 m is defined, and the different electrical and geo-metrical system parameters are considered. As a workingfrequency, we propose S-band or C-band operation as a goodcompromise between positioning accuracy and the number ofelements. Using a conventional imaging system with an FFT� � Ž .2 , a planar surface holographic plate of about 2 m � 2 mhad to be considered, making the system size unsuitable inpractice for some applications. Instead, using the reducedsystem proposed here, a planar antenna of 1 m � 1 m can beused, while keeping the location capabilities of about 1 mmŽ .� �100 in accuracy unchanged. The objective geometry of0the final practical system is shown in Figure 1.

To check the different parameters of the system, a firstprototype of a planar array with a limited number of ele-

Ž .ments 2 � 2 has been fabricated and measured. The proto-type has been tested at different frequencies with a reduced

Ž .holographic plate size of 10 cm � 10 cm , and its positioningcapabilities have been tested in a reconstruction volume ofŽ .10 cm � 10 cm � 10 cm . In this paper, we present theresults at 2.23 GHz with positioning capabilities of 1 cm.Antenna array systems using size reduction techniques aresimulated theoretically and measured experimentally. Excel-lent agreement between the results is reached. The designedantenna system is used to generate the hologram at differentpositions. The reconstruction here is done by a correlationtechnique, which is free from the � �2 hologram’s grid size0

� �criterion that exists in the conventional FFT technique 2, 3 .Illustrating the virtual retrieved image of these holograms, wecan see that the 3-D coordinates of any point within therequired investigation volume can be captured and saved inmemory. Needless to say, the extension of our system repre-sented here has no limitations, either in array surface, orreconstruction volume, or operating frequency.

2. MICROWAVE HOLOGRAPHY RECONSTRUCTIONALGORITHM

The digital hologram data are retrieved by a computer simu-� �lation model 3 called the correlation technique, which is

Ž .Figure 1 Objective geometry of the final 3-D pointer mousesystem

based on the following equation:

Ž .cos kRi� Ž .� � � � I 1Ý Ýi i� � Ri�� �

where � is the retrieved image, I is the intensity of a gridi �

point on the hologram plane, and R is the distance be-i�Ž .tween the hologram plane’s grid point � and reconstruction

Ž . Ž .point i . The procedure in Eq. 1 basically inspects whetherŽ .or not the point i is a part of the original object. This is

accomplished by using the correlation between the hologramŽ .intensity and the factor P � cos kR �R which repre-i� i� i�

sents the hologram of the point source. If the intensity I�coincides with the pattern P generated by the point sourcei�

Ž .at i , the correlation � becomes large, and hence the pointiŽ .i has a large probability of being included in the originalobject. On the contrary, if I does not coincide with the P ,� i�

Ž .then � becomes small, and point i may not be included iniŽ .the original object. By changing i over the 3-D space and

drawing the structure of � , it should coincide with theioriginal object pattern. This method does not suffer from the

� �FFT limitations 2, 3 , so the hologram sampling grid separa-tion can be less than � �2, and the holographic plate size0can approach the transversal section of the reconstructionvolume.

( )3. 3-D POINTER MOUSE SYSTEM

� �The proposed 3-D mouse system is illustrated in Figure 2 4 .The mouse unit itself works as hand agent that contains apassive reflecting dipole antenna with a modulating diode atŽ . � �1 kHz with its power supply feed 5 . This unit is attached tothe operator’s hand to locate its movements. The illuminatorŽ .transmitter dipole antenna is fixed in a certain cornerwithin the reconstruction volume. When the user clicks onthe hand agent at the required position in space, the switch isclosed, allowing modulation of the illumination signal at thediode marked point at a low-frequency level. Modulating thediode at a low-frequency rate results in modulating thescattered field, which is proportional to the local field atthe corresponding mouse location. The mouse’s plate con-

Ž .tains the receiver microstrip antenna array that measuresŽthe modulated object’s scattered signal which carries the

.amplitude and phase information of the point position . Adetailed discussion of this array design and implementation ispresented in the next section. The object signal interfereswith the reference signal in the panel unit to form the

Ž .interference pattern hologram . The hologram data are de-modulated and digitized through an analog-to-digital con-verter in the same unit. Digital data are interfaced to thecomputer and retrieved in it through a hologram reconstruc-

Ž � �.tion driver it can be software or hardware 6 that is called a3-D mouse card. Finally, the retrieved point is drawn on thescreen, if needed, with any graphics software.

Note that the diode modulation step can be replaced bydirectly connecting the transmitting dipole antenna to theoperator’s hand mouse unit, which will be connected to thegenerator through an RF cable with the cost of a movable RFconnection. In this case, the microstrip antenna directly re-ceives the mouse-radiated signal. The selection between thetwo models depends on the application.

4. PLANAR MICROSTRIP ANTENNA

4.1. Holographic Recording Plate. A microstrip antenna arrayis the best candidate for satisfying the hologram recording

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 29, No. 6, June 20 2001398

process requirements because of its light weight, small size,low cost, directive beam, and narrow bandwidth which aresuited to this monofrequency application. Its planar or con-formal configuration allows it strong capabilities to bemounted on any device or wall surface to cover any experi-mental required area. A rectangular patch element is suitablefor this application due to its simple structure, which allowsintegration with any feed or matching network. It has a lowscattering field cross section compared to other common

� �shapes, such as circular and triangular patches 7 . Also, ithas a sufficient receiving area to handle the required holo-gram information.

4.2. Con�entional Antenna. As a reference for the holo-graphic plate illustrated in Figure 1, a 2 � 2 element array ofa microstrip rectangular patch with proximity aperture cou-pling was designed and fabricated. The initial interelementdistance was 0.6� . Special attention has to be taken in0reducing the interelement coupling effect since we need tosample as accurately as possible without any neighboringinterference effect. The antenna array was analyzed by thefinite-element method and fabricated with a photolitho-graphic technique. Scattering parameters were measured us-ing an HP8510c network analyzer. Figure 3 shows a compari-son between the simulated and measured values at 2.23 GHzfor the input impedance and the mutual coupling, and illus-trates very good agreement.

4.3. Antenna Size Reduction with Slit Insertion Procedure. Inorder to match the size requirements of the proposed recon-struction system, we have to reduce the antenna conventionaldimensions described in the previous section to about onefourth of their conventional value. This procedure is done by

Ž .cutting a slit see Fig. 4 at an adequate position of the patchsurface with adequate length and width. We select an in-verted H-shape slit because it can effectively minimize the

size of the microstrip antenna from a half wavelength to aquarter wavelength without any overlap with the feed aper-

� �ture or feed line 9 . The slit decreases the resonant fre-quency because the current has to flow around the slit so theelectrical equivalent length of the current path becomes

Ž .longer. Figure 5 b shows the antenna’s current flow pathŽ .after the slit insertion, while Figure 5 a shows the patch-

equivalent circuit around the TM dominant mode. The slit10� �is only a line, so by Wheeler’s equivalent-volume concept 9 ,

its effect can be modeled by inserting a transverse magneticwall of zero thickness into the microstrip patch. By calculat-ing the effect of this magnetic wall, we know the value of theinductance line. Relating the above concept to transmission-line theory, the inductance of the inverted H-shape slit can berepresented by the formula

jXSV Ž .Z � j2� fL � 2S SH 2

Ž . Ž .2where L � h� ��8 2 l �W is the inductance of theSH 0 SHperpendicular slit on the feed line, and where h is thesubstrate thickness, l the slit length, W is the patch width,SH

Ž .X � Z tan kl �2 is the inductance of the slit parallel toSV 0 SVthe feed line with Z the average characteristic impedance of0microstrip lines of widths W � 2 l , l , and k is theSH SVwavenumber.

The discussed slit shape is inserted in the rectangularpatch of Section 4.1. The antenna surface is reduced by ratioof 62.5% with substrate permittvity, � � 2.55 for the feedrlayer and � � 2.33 for the patch layer, respectively, and thersubstrate height is 1.58 mm in both cases. The patch di-

Ž .mensions become L � 3 � W � 1.5 cm , the horizontalŽ Ž .. Žslit is 0.25 � .05 cm W�6 Xl �5 , the vertical slit is 1.5 �SH

.0.075 cm , and the interelement distance is 0.3� .0The major problem of adding the slits with their induc-

tance effect is the difficulty of matching with the feed and

Figure 2 3-D mouse system with modulating diode

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 29, No. 6, June 20 2001 399

Figure 3 Comparison between simulation and experimental scat-tering parameters of 2 � 2 H-plane coupling rectangular patch phasearray at 2.23 GHz, dielectric constant � � 2.55 for patch and feedrlayers, h � 0.158 cm for feed and 0.0787 for patch, element size � 4� 3 cm, aperture � 0.155 � 1.3 cm, and feedline width � 0.23 cm

Ž .with stub length � 1.2 cm after aperture edge: a self S parame-i iŽ . Žters, and b mutual S parameters dashed lines are experimentali j

.results

obtaining a good antenna radiation pattern and gain. Tosolve this problem and obtain approximately the same an-tenna characteristics as before inserting the slit, a shorttuning stub of length l and width w is connected to thes s

Ž . � �patch, as illustrated in Figure 4 a 10 . The stub dimensionsare l � 0.65 cm, w � 0.6 cm. Its position is on the patchs sedge, offset from the patch center by a half of the feedlinewidth. This perturbed cavity or short tuning stub is used inconjunction with the proximity coupling to oppose the sliteffect and provide enhanced element matching without anyexcessively thick substrate problems or metallic post and pinfabrication problems. Figure 6 illustrates the experimentalresults of a 2 � 2 array with a 62.5% surface reduction ratioand an interelement distance of 0.3� . From a comparison0

Žwith Figure 3, the array performance input impedance and.mutual coupling is approximately the same since the change

in coupling parameters S is in the range of a few decibels,i jwhich does not affect our holographic image recordingaccuracy.

Ž .Figure 4 a Proximity aperture-coupled rectangular patch antennaŽ .with slit insertion and matching stub. b layout of 2 � 2 reduced-size

array antenna

5. VIRTUAL IMAGE RECONSTRUCTION RESULTS

To verify our idea, the hologram is generated at differentpoints within the operator’s hand reconstruction volume us-ing a microstrip reduced-size antenna array. The hologramplate size is 10 cm � 10 cm. The reconstruction volume is10 cm � 10 cm � 10 cm in the x-, y-, and z-directions,respectively. As examples, a hologram is generated for points

Ž . Ž .at positions 4 cm, 4 cm, 12 cm and 9 cm, 9 cm, 9 cm ,respectively. Figure 7 shows the 3-D representation of theretrieved point image at these positions. From the figure, it isseen that we could capture the 3-D coordinates of a pointwithin the object reconstruction volume.

One of the main problems in all indoor antenna applica-tions is the reflection from the surroundings that adds noisedegrading the received field signal. This problem, which couldbe important in a whole multipoint 3-D object simultaneousreconstruction application, is not severe in our image process-ing here since the object is a single point. On the other hand,we use a software filter to eliminate this noise and obtain

� �clear retrieved point coordinates 8 .It is worth mentioning here that the holographic system in

Figure 2 can be used for simultaneously identifying multiple

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 29, No. 6, June 20 2001400

Ž .Figure 5 a Equivalent circuit of single-element reduced-size rect-Ž .angular patch antenna. b Current flow path on antenna surface

with an inverted H-shape slit

Figure 7 Retrieved image of one-point holography at frequency ofŽ .2.23 GHz with hologram size of 10 � 10 and grid sampling � �30

Ž . Ž . Ž . Ž .with the point position at a 4, 4, 12 and b 9, 9, 9

Figure 6 Experimental results of 2 � 2 reduced-size antenna array at 2.23 GHz. Top: mutual coupling scattering parameters.Bottom: self-scattering parameters

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 29, No. 6, June 20 2001 401

Figure 8 Reconstructed image of two-point hologram at 2.23 GHzŽ . Ž .with point positions at 50 cm, 50 cm, 9 cm , 70 cm, 70 cm, 9 cm and

with hologram size 1 m � 1 m

points, colors, or materials using different modulating fre-quencies for every selected feature. Figure 8 is a simulationexample for a two-point reconstruction with a hologram size

Ž .of 1 m � 1 m and point positions at 50 cm, 50 cm, 9 cm andŽ . Ž70 cm, 70 cm, 9 cm , respectively. The resolution minimum

.object point separation is found empirically to be about � ,0while the accuracy is related to the number of array antennaelements.

6. CONCLUSION

A special method for investigating a 3-D mouse or a 3-Dpointer was described. With this method, a hologram is easilyestablished for any point within the designed reconstructionvolume at low cost. Studies of the receiving microstrip arraywere done theoretically and verified experimentally. An im-provement in the hologram size is accomplished by reducingthe receiving antenna size. The image is retrieved by acorrelation algorithm in which we can reduce the hologramsize while keeping the same information content in an un-changed reconstruction volume. Research is currently beingdone to obtain additional array surface reduction ratios byimproving the number of elements in order to reach thecommercially applicable 3-D rendering system.

REFERENCES

1. S.H. Lee, Computer generated holography: An introduction,Ž .Appl Opt 26 1987 , 4350.

2. C. Pichot, L. Jofre, G. Peronnet, and J. Bolomey, Active mi-crowave imaging of inhomogeneous bodies, IEEE Trans Anten-

Ž .nas Propagat AP-33 1985 , 416�425.3. H. Eldeeb and T. Yabe, A fast method for an efficient recon-

Ž .struction in computer holography, J Plasma Fusion Res 71 1995 ,331�335.

4. H. Elsadek, H. Eldeeb, M. Ueda, J. Horikushi, and T. Yabe,Using microwave holography and microstrip antenna for 3D

Ž .mouse investigation, Int J Electron 81 1996 , 178�198.5. W.C.Y. Lee, Mobile communications engineering, Theory and

applications, McGraw-Hill Telecommunications, 1997, chap. 8.6. T. Yabe, T. Ito, and M. Okazaki, Holography machine HORN-1

for computer aided retrieval of three dimensional image, Japan JŽ .Appl Opt 32 1993 , 261�263.

7. J.R. James and P.S. Hall, Handbook of microstrip antennas,Peter Peregrinus Ltd., London, England, 1989.

8. H. Elsadek, H. Eldeeb, J. Horikushi, and T. Yabe, An efficienttechnique for constructing microwave holograms with use ofmicrostrip antenna and retrieval of its digital form, Microwave

Ž .Opt Technol Lett 14 1997 , 227�233.9. X.X. Zhang and F. Yang, Study of a slit cut in microstrip antenna

Ž .and its applications, Microwave Opt Technol Lett 18 1998 ,297�300.

10. D.M. Pozar and B. Kaufman, Increasing the bandwidth of mi-crostrip antenna by proximity coupling, Proc Inst Elect Eng 32,Ž .1987 , 368�369.

� 2001 John Wiley & Sons, Inc.

AN ESTIMATION OF POWERTRANSMISSION THROUGH A DOUBLYCLAD OPTICAL FIBER WITH ANANNULAR COREP. K. Choudhury1 and Roger A. Lessard21 Satellite Venture Business LaboratoryFaculty of EngineeringGunma UniversityKiryu 376-8515, Gunma, Japan2 Department of PhysicsFaculty of Science and EngineeringLaval UniversityQuebec City, P.Q. G1K 7P4, Canada

Recei�ed 9 January 2001

ABSTRACT: An estimation has been made of the distribution of power( )o�er different modes through the guiding region of an optical fiber withan annular core. The general expression for the power in the guidingregion is deri�ed under the use of a scalar field approximation, and thepower pattern is plotted against the dimensionless core parameter forthree lowest azimuthal model indexes. The analysis is rigorous in thesense that no approximation is used to determine the field functions.� 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 29:402�405, 2001.

Key words: optical fibers; electromagnetic wa�e propagation

INTRODUCTION

For years, investigators have endeavored to study opticalfibers and waveguides with several kinds of cross-sectionalgeometries, and also, with materials having different electro-magnetic properties, keeping in view their possible applica-tions in the areas of integrated optics and telecommunica-

� � � �tions 1�12 . Investigations of guides with parabolic 4, 5 and� �circular 9 bendings were presented by Choudhury et al., and

certain unusual properties were observed. For example, theabsence of a well-defined discreteness of modes and thepresence of mode-bunching properties were observed in thecase of parabolically deformed guides, whereas for circularlydeformed guides, a kind of mode proliferation was noticed.

� �Power patterns of such guides were also reported 15, 16 .

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 29, No. 6, June 20 2001402