William H. Weedon t, Weng Cho Chew and Chad A. Ruwet Department of Electrical and Computer Engineering University of Illinois, Urbana, IL 61801

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1 A STEP-FREQUENCY RADAR SYSTEM FOR BROADBAND MCROWAVE NVERSE SCATTERNG AND MAGNG NTRODUCTON William H. Weedon t, Weng Cho Chew and Chad A. Rwet Department of Electrical and Compter Engineering University of llinois, Urbana, L Step-freqency radar (SFR) is an attractive alternative to implse radar for obtaining broadband time-domain scattering data [1]. Throgh the se of an inverse Forier transform, the SFR freqency-domain {magnitde and phase) data may be converted into a synthetic time-domain plse. Time-domain inverse scattering imaging techniqes [1-7],, sed in conjnction with SFR data collection, may be sed to generate images of the permittivity and condctivity profiles of scattering objects, and can provide a sefl diagnostic and investigative tool. Step-freqency radar systems may be sed in microwave nondestrctive evalation (NDE) for detecting voids and defects in concrete strctres sch as bildings, bridges, dams, and tnnels, and asphalt pavements sch as roads and aircraft rnways. Step-freqency radar may also be sed in grond-penetrating radar (GPR) for detecting and identifying bried ndergrond objects, sch as toxic waste canisters, grondwater contaminants and polltants, land mines, tility pipes, mineral deposits, bedrock formations and other lithographic strctres. The chief advantages of SFR over implse radar are the higher signal-tonoise ratio attainable de to narrowband electronics and the availability of extremely stable signal sorces, reslting in increased measrement accracy and stability [1,8-10]. This allows for the removal of many sorces of systematic (non timevarying) measrement error inclding the freqency-dependent magnitde and phase variations of connectors, transmission lines, directional coplers, amplifiers and antennas. The disadvantage of SFR measrement systems, however, is that the data collection time is generally increased. For high-resoltion microwave imaging applications, the increased measrement time can be jstified since is sally additional time reqired to process the data. Both linear diffraction tomography (DT) algorithms [12-14] and nonlinear inverse scattering algorithms may be sed to process the scattering data. Diffraction tomography takes into accont the fact that microwaves, nlike x-rays, do not travel in straight lines. However DT ignores another wave phenomenon known as mltiple scattering [14]. The only general method to inclde both the diffracting and mltiple scattering effects of the waves in an image reconstrction is to se an iterative nonlinear inverse scattering algorithm [1-7,16-20]. Another important advantage of nonlinear inverse scattering is that the procedre imposes few constraints on the sensor configration. Most DT algorithms place severe constraints on the sensor configration, sch as the reqirement that sensors be separated by a t Crrently with the Center for Electromagnetics Research, Northeastern University, Boston, MA t Crrently with National nstrments, nc., Astin, TX. Review of Progress in QlOitative Nondestrctive Evalation, Vol. 14 Edited by D.O. Thompson and D.E. Chimenti. Plenm Press. New York

2 Data N HP 8510B Network Analyzer (.5-18 GHz) Port 2 (RX) Port 1 (TX) RX Microwave Switch (DC-8 GHz) Compter Workstation TX Microwave Switch (DC-18 GHz) Broadband Antenna Array (2-12 GHz) Scattering Objects Figre 1. Block diagram of prototype step-freqency radar (SFR) broadband inverse scattering measrement system. maximm of one half wavelength. Other algorithms are also limited to monostatic measrement configrations. The reslts presented in this paper are processed sing the distorted-born iterative method (DBM) [4] and the local shape fnction (LSF) method [2]. Both the DBM method and LSF method are nonlinear iterative time-domain inverse scattering algorithms. The DBM algorithm reconstrcts an image of either the permittivity or condctivity profile of an inhomogeneos scatterer, whereas the LSF method is sed to reconstrct metallic scatterers. Reconstrctions of varios metallic and dielectric scattering objects inclding metallic rods, glass rods and plastic PVC pipes from real measrement data collected in or laboratory are shown. MCROWAVE MEASUREMENT APPARATUS Description of the SFR System A block diagram of basic components of the prototype step-freqency radar measrement apparats is shown in Figre 1. The system consists of a broadband switched antenna array, an HP 8510B atomated network analyzer, microwave switches and controller, and an optional broadband amplifier. The entire measrement system is atomated and controlled by a compter workstation. Cstom software was written in the C programming langage to control the measrement apparats via an EEE-488 (GPB) interface. The HP 8510B atomated network analyzer serves as both the transmitter and receiver and allows s to collect both amplitde and phase information by stepping throgh varios freqencies. Broadband Switched Antenna Array The broadband switched antenna array sed to perform the scattering measrements, shown in Figre 2, contains 11 identically fabricated 2-12 GHz tapered slotline, or Vivaldi, antennas arranged in a linear array, and two DC-18 GHz SP6T microwave switches that are compter controlled. One switch is connected to 5 ar- 644

3 Figre 2. Photograph of broadband switched antenna array containing 11 identical broadband Vivaldi antennas and two microwave switches enclosed in a polystyrene hosing. 80.0cm ~ R=40.0cm 8.0cm r , + : Object : L J grid Figre 3. Arrangement of transmitters (T), receivers (R) and object grid for new switched antenna array. ray elements while 6 elements are connected to the other. Hence, the array may be configred via compter control to operate as either an 11-element monostatic array or a mlti-bistatic array consisting of 30 different measrements. The switches atomatically terminate the antenna elements at 50 n when they are switched off, redcing the copling among the elements. The antenna elements and microwave switches are enclosed in a polystyrene hosing. The arrangement of the transmitters and receivers for the new switched antenna array is shown in Figre 3. The 11 antenna elements are separated by 8.0 cm, giving a total baseline of 80.0 cm. This baseline length was chosen with the goal in mind of resolving objects at a range of R = 40.0 cm. 645

4 NONLNEAR NVERSE SCATTERNG MAGNG Both the DBM and LSF inverse scattering imaging techniqes have been discssed extensively in the past, and their formlation will not be repeated here. However, for the prposes of completeness, we will give a fnctional description of the algorithms. The varios steps in the data processing of the measrement data sing both the DBM and LSF algorithms are smmarized in the flow diagram of Figre 4. The switch on the left indicates that either measred data or compter generated scattering data (synthetic data) may be sed in the inverse scattering algorithm. The algorithm begins with specification of the initial parameters, which are set to zero becase we wish to se a minimal amont of a priori information. Using the crrent compter model, forward scattering data are generated and sbtracted from the measred data. This difference is then sed to compte a measre of the residal field error. f the difference is below a specified tolerance, the crrent model parameters are displayed on a graphics workstation. f the field error is not below a specified tolerance, the field error is sent to a conjgate gradient optimization procedre which retrns an pdate to the model parameters. The process is repeated ntil a convergent soltion is attained. RESULTS Metallic Object Reconstrctions The measrement geometry sed in the SFR data collection is shown in Figre 3. The object space consisted of a 35 x 35 sbgrid. The grid space and time step sizes sed in the FDTD forward solver were ~x = 2.5 mm and ~t = 5.5 ps. Figres 5 and 6 show the reslting images after the LSF inverse scattering algorithm was applied to the measred scattering data from two metallic cylinders. Figre 5 is for the case when the cylinders were aligned horizontally with respect to the array, and Figre 6 is for the vertical alignment case. n both cases, the cylinders were separated by 3.2 cm, and the cylinders each had a diameter of 4.5 mm. Dielectric Object Reconstrctions Metallic objects are more difficlt for inverse scattering algorithms to image than dielectric objects becase the inverse scattering problem is more nonlinear for metallic objects. However, dielectric objects are more difficlt to measre becase the scattered field prodced by a dielectric object is mch weaker than that of a metallic object. We present reconstrctions of dielectric objects below to demonstrate that accrate scattering data can be collected from dielectric objects and that high-qality images may be generated. Figres 7 and 8 show reconstrctions of plastic PVC pipes of diameters 2.7 cm and 4.8 cm, respectively. Both of these pipes were located in an air backgrond. The DBM permittivity optimization algorithm was sed for both cases. For both pipes, high qality images were prodced. The bottoms of the pipes are not reconstrcted as well as the tops becase scattering data were collected from the top only. Figre 9 shows a DBM permittivity reconstrction of an empty glass gradated cylinder of diameter 5.25 cm located in air. CONCLUSONS A prototype step-freqency radar imaging system has been designed and bilt. The SFR imaging system has applications in nondestrctive evalation and grond-penetrating radar. A calibration procedre involving the se of a calibration target was presented to remove plse distortions de to the antennas as well as transmission lines, connectors, amplifiers and directional coplers. t was shown that the calibration procedre does an excellent job of removing plse distortions, 646

5 Measred Data (Freqency-Domain) nitial E(r)=} Parameters o(r) =0 '--_,------' y(r )=0 Calibration Filter Compter Generated Data (Time-Domain) Compter BE(r), Bo(r), &y(r) Model Parameter Update E(r), o(r), y(r) Compte Forward Scattering Soltion Ez.n( ) + Compte Residal Field Error Conjgate Gradient Optimization, , 1 Frechet Transposed 1 : _ 9'p~r!~0.: _:, , 1 Frechet 1 : Derivative: 1 Operator N Display Model Parameters E(r), o(r), y(r) Figre 4. Block diagram of processing of measred and compter simlated scattering data. and allows an accrate prediction of the scattered field plse shape from arbitrary targets with a FDTD forward modeler. The operating freqency band of 2 GHz to 12 GHz sed in or system was chosen for laboratory measrements of test objects in air, and shallow penetration NDE applications. For other NDE and GPR applications, the choice of operating freqency wold clearly depend on the backgrond medim, the desired depth of investigation, and the reqired object resoltion. The antenna size, and hence operating freqency band of the prototype system presented here cold be scaled p or down to meet a desired application. 647

6 16 Original Object hape Fnction Recon trction 16 E 18 J20 co 1ii E ~20 1ii 22 24~ 24 ~ ~ ~ o 2 4 Tran ve e Axi,cm Transverse Axi, cm Figre 5. Original object and shape fnction reconstrction of two metallic cylinders of diameter 4.5 mm aligned horizontally with separation 3.2 cm. Original Object Shape Fnction Recon trction E E J20 t,i :a Tran ver e Axi,cm Tran verse Axis, cm Figre 6. Original object and shape fnction reconstrction of two metallic cylinders of diameter 4.5 mm aligned vertically with separation 3.2 cm. 648

7 REFERENCES 1. W. H. Weedon, "Broadband microwave inverse scattering: Theory and experiment." Ph.D. dissertation, University of llinois at Urbana-Champaign, W. H. Weedon and W. C. Chew, "Time-domain inverse scattering sing the local shape fnction (LSF) method," nverse Probl., vol. 9, pp , M. Moghaddam, "Forward and inverse scattering problems in the time domain." Ph.D. dissertation, University of llinois at Urbana-Champaign, M. Moghaddam, W. C. Chew, and M. Oristaglio, "Comparison of the Born iterative method and Tarantola's method for an electromagnetic time-domain inverse problem," nt. J. maging Syst. Technol., vol. 3, pp , M. Moghaddam and W. C. Chew, "Nonlinear two-dimensional velocity profile inversion sing time domain data," EEE Trans. Geosci. Remote Sensing, vol. 30, Jan M. Moghaddam and W. C. Chew, "Stdy of some practical isses in inversion with the Born iterative method sing time-domain data," EEE Trans. Antennas Propagat., vol. 41, no. 2, pp , A. Tarantola, "The seismic reflection inverse problem," in nverse Problems of Acostic and Elastic Waves (F. Santosa, Y. H. Pao, W. Symes, and C. Holland, eds.), SAM, Philadelphia, G. H. Bryant, Principles of Microwave Measrements. London: Peter Peregrins Ltd., J. A. Landt, "Typical time domain measrement configrations," in Time Domain Measrements in Electromagnetics (E. K. Miller, ed.), New York: Van Nostrand Reinhold, R. Lawton, S. Riad, and J. Andrews, "Plse & time-domain measrements," Proc. EEE, vol. 74, pp , W. H. Weedon, W. C. Chew, and C. A. Rwe, "Step-freqency radar imaging for NDE and GPR applications," in SPE Proceedings: Advanced Microwave and Millimeter Wave Detectors, vol. 2275, (San Diego, CA), A. J. Devaney, "A filtered backpropagation algorithm for diffraction tomography," Ultmson. maging, vol. 4, pp , A. J. Devaney, "A compter simlation stdy of diffraction tomography," EEE Tmns. Biomed. Eng., vol. BME-30, pp , A. C. Kak, "Compterized tomography with x-ray, emission and ltrasond sorces," Pmc. EEE, vol. 67, no. 9, pp , W. C. Chew, Waves and Fields in nhomogeneos Media. New York: Van Nostrand, Y.-M. Wang and W. C. Chew, "An iterative soltion of two-dimensional electromagnetic inverse scattering problem," nt. J. maging Syst. Technol., vol. 1, pp , R. E. Kleinman and P. M. van den Berg, "Nonlinearized approach to profile inversion," nt. J. maging Syst. Technol., vol. 2, pp , N. Joachimowicz, C. Pichot, and J.-P. Hgonin, "nverse scattering: an iterative nmerical method for electromagnetic imaging," EEE Trans. Antennas Propagat., vol. AP-39, no. 12, pp , W. C. Chew and G. P. Otto, "Microwave imaging of mltiple condcting cylinders sing local shape fnctions," EEE Microwave Gided Wave Lett., vol. 2, pp , Jly G. P. Otto and W. C. Chew, "Microwave inverse scattering-local shape fnction imaging for improved resoltion of strong scatterers," EEE Trans. Microwave Theory Tech., vol. 42, no. 1, pp ,