A 3D Polar Processing Algorithm for Scale Model UHF ISAR Imaging

Transcription

1 A 3D Polar Proessing Algorithm for Sale Model UH ISAR Imaging Christopher J. Beaudoin* a, Andrew J. Gatesman a, Robert H. Giles a, Jerry Waldman a, and William E. Nixon b a Submillimeter-Wave Tehnology Laboratory, University of Massahusetts Lowell, Lowell, MA b U.S. Army National Ground Intelligene Center, 2055 Boulders Road, Charlottesville, VA ABSTRACT In reent years, UH syntheti aperture radar has beome a growing area of interest among the radar ommunity. Due to their relatively long wavelengths, UH systems provide advantages that may not be attainable by mirowave and millimeter-wave radar systems. These advantages inlude exellent target detetion statistis in high lutter environments, wide-area surveillane, and long stand-off ranges. UH systems also have proven synergisti properties with higher frequeny radar systems in appliations suh as topographial mapping. However, the ability to study the harateristis of these lower frequeny radar systems in a ontrolled and systemati environment is diffiult. In this work, a physial sale modeling proess is utilized to generate three-dimensional UH imagery that may be used to study sattering phenomenology at these wavelengths. Dimensionally and dieletrially saled targets and senes are measured in a 6 18 GHz mirowave ompat range to model the baksatter of the full-size target at UH wavelengths. The mirowave ompat radar range and transeiver hardware utilized to model UH radar signature data are briefly desribed. A desription of the image proessor used to generate three-dimensional UH imagery from wide-band/wide-angle data olletions is desribed as well. inally, imagery of radar signature data olleted from a M1A1 Abrams main battle tank model is examined. The high resolution imagery resulting from the wide-band/wide-angle olletion will show that sub-wavelength features of ground targets are resolvable at these wavelengths. Keywords: UH, 3D ISAR, radar, sale-modeling 1. INTRODUCTION 1.1 Appliations of UH SAR In the past 15 years, there has been a renewed interest in UH SAR among the radar ommunity for various problems where high frequeny sensors do not provide an adequate solution. Due to their relatively long wavelengths, UH signals an penetrate optially-dense materials muh more effetively than those of sensors operating at shorter wavelengths. This property makes UH SAR suitable for deteting targets beneath a foliage anopy, whih has been oined the Oliage PENetration (OPEN) problem. 1 Suh sensors are also apable of Ground PENentration (GPEN), thereby allowing detetion of sub-terrain objets. 2 Low frequeny SAR also has demonstrated use in sene hange detetion. 3 This tehnique srutinizes the temporal differenes between two SAR images of an idential sene to determine what sattering enters have moved between the two olletions. It has also been found that UH hange detetion analysis is muh less sensitive to natural temporal deorrelations of the sene (i.e. fluttering leaves and gras than hange detetion analysis onduted at higher frequenies. 3 This harateristi makes UH SAR hange detetion a muh more robust tool in determining movement of vehiles as well as small man-made strutures. Due to their wide-beamwidth, UH SAR an provide wide-area surveillane and therefore an provide hange information over muh larger area than an typially be sanned by a high frequeny SAR. 3,4 urthermore, due to its penetration apabilities, UH systems an provide hange information about targets beneath foliage and sub-terrain objets. 4,5 Radar test beds have also been developed to exploit the synergies between UH and X- band SAR sensors. 6 When used together in an interferometri modality, the sensors an provide a thorough topologial mapping of a forested area. Beause of its penetration apabilities, UH SAR is used to map the topology below the foliage anopy. The X-band SAR sensor, unable to penetrate the foliage anopy, is used to map the topology of the anopy itself. *orrespondene: hristopher_beaudoin@uml.edu; telephone: ; fax: ; web: mail: Submillimeter-Wave Tehnology Laboratory, 175 Cabot Street, Suite 130, Lowell, MA 01854

2 The development of stealth tehnology has also ontributed to the trend in the renewed interest of low frequeny radars. Low RCS objets typially exhibit an RCS proportional to the square of the wavelength. This property is attributed to resonant effets at these long wavelengths beause the target sizes are typially on the order of the radar wavelength. Therefore, longer wavelength radars have a better probability of deteting stealthy targets Need for UH Radar Measurement Capability Due to the renewed interest in UH radar researh, a need for high quality, alibrated UH radar data exists. Airborne operational UH radar systems are urrently in use; however, suh systems must ontend with less than ideal operating onditions. Suh examples of these non-ideal onditions are unknown flight path deviations, unorreted systemati errors in the alibration proess, and radio frequeny interferene (RI). urthermore, the onditions required for a partiular study may not be available or feasible. Therefore, suh operational radar systems may not be apable of onduting a ontrolled and systemati study of a partiular problem. Radar automati target reognition (ATR) developers rely on very aurate SAR imagery of targets in order to train identifiation algorithms. 8 Ideally, an entire imagery library of the target in a variety of orientations and artiulations would be available in order to train the algorithm on any possible irumstane in whih the radar may observe the target. Training an ATR algorithm on suh a library of imagery maximizes the likelihood of orretly lassifying a given unknown target. Radar signature libraries of targets do exist for mirowave and millimeter-wave radar systems; however, the available radar signature libraries at UH frequenies are limited. As noted earlier, a major problem faed by operational UH SAR systems is the issue of radio frequeny interferene. 9 The soures of the unwanted signals are typially radio and television stations with whih the radar must share bandwidth. Operational UH systems must ontend with these unwanted signals and as a result, the available sets of data are said to be sparse-band. 20 These sparse-bands of data reate issues in SAR imagery in terms of inreasing image side-lobe levels 20, while the RI signals introdue spurious satterers in the imagery. 10 RI suppression is urrently a topi of ative researh to mitigate these spurious signals and the availability of data not orrupted by suh signals may assist in developing pratial methods. 1.3 Physial Sale Modeling Approah to UH Radar Data Colletions Sine 1981, Expert Radar Signature Solutions (ERADS) under funding from the National Ground Intelligene Center (NGIC) has developed state-of-the-art sale model measurement systems to aquire radar signatures in support of a number of advaned radar appliations suh as automati target reognition (ATR) systems, RAM development, and buried objet detetion. ERADS has developed ompat ranges at 12 GHz 11, 160 GHz 12, 520 GHz 13, and 1.56 THz 14 for aquisition of UH, X-band, Ka-band, and W-band radar imagery of, 1/16 th, 1/35 th and 1/48 th sale model targets and senes. Radar sale modeling requires that the target's geometri and dieletri properties be saled appropriately. Therefore, the omplex dieletri onstant of any nonmetalli omponent of the full sale target at the full sale wavelength must be mathed to the omplex dieletri onstant of the orresponding sale model omponent at the saled wavelength. The University of Massahusetts Lowell Submillimeter-Wave Tehnology Laboratory (STL) has demonstrated the tehnology neessary to tailor the dieletri properties of materials. 15,16 Condutive oatings neessary to simulate the metalli body and omponents of the full sale vehiles have been developed as well. 2. METHODOLOGY 2.1 3D UH Radar Data Colletion Proess A 6-18 GHz ompat range (depited in figure 1a) was utilized to ollet target radar signatures in the sale-model environment. The radar system operates in a stepped-frequeny, pulsed/cw modality and inorporates a large off-axis paraboli refletor to emulate far-field target illumination and monostati baksatter olletion. The refletor is apable of illuminating a 2 ft. by 2ft. by 2ft. volume with uniform planar wavefronts. Currently, the system operates in the linear HH and VV polarization hannels with a planned upgrade to polarimetri measurement apability.

3 Target Mehanial Staging Azimuth (Rotation) Axis Transeiver Hardware Paraboli Refletor Elevation (Goniometer) Axis (a) (b) () igure 1: Data olletion methodology (a) mirowave ompat radar range (b) 2D Az-El target sanning stage () data olletion geometry. urthermore, the ompat radar range inorporates a 2D azimuth-elevation (Az-El) mehanial sanning stage (shown in figure 1b) whih is used to orient a free-spae 1/35 th sale target at a variety of angles. The UH data olletion system samples the target s omplex baksatter phasor, Φ, at every frequeny step, over a speified range of azimuth and elevation illumination angles, thereby providing three-dimensional data olletions. The data olletion sample arrays are defined by the following: fb fb f ( p) = f + p f p = 0,1,2 K 1 (1a) 2 ψ a a ( q) = + q q = 0,1,2 K 1 2 a a () s = ψ + s s = 0,1,2 K 1 ψ 2 ψ Equation (1) defines the sample arrays speifying the frequeny, azimuth, and elevation loations f(p), (q), and ψ(, respetively, at whih the target s baksatter phasor Φ(f,,ψ) is sampled during the data olletion proess. The parameters f b, a, and ψ a represent the total span of the 3D data olletion in frequeny, azimuth, and elevation angle, respetively, while f,, and ψ represent the enter frequeny, azimuth, and elevation angles of the aperture. The uniform sample inrements in frequeny, azimuth, and elevation angle are given by f,, and ψ, respetively, while p, and s are the sample indies of the respetive dimensions. The parameters f b, a, ψ a, f,, ψ, f,, and ψ are referred to as the data olletion parameters and the olletion of Φ(f,,ψ) is referred to as the radar signature data. The (x t,y t,z t ) oordinate system shown in figure 1 is referred to as the target-fixed system as it defines the oordinate geometry that is fixed to the body of the target under measurement. 2.2 Wide-Band/Wide-Angle 3D ISAR Image ormation Proessor The polar format algorithm (PA) is used here to develop the 3D image formation proessor in whih the radar signature data are proessed. The PA has been applied widely for use in monostati SAR imaging of instrumented and operational data olletions. 17,18 In essene, the algorithm provides an elegant tehnique of formatting oherent radar data olleted under plane wave illumination over a wide angular aperture suh that they may be interpreted as the spatial ourier ψ ψ f (1b) (1)

4 transform of the target s 3D refletivity distribution. After the appropriate formatting of the data, a multidimensional ourier transform proess is performed to provide a reonstrution of the target s refletivity distribution. This method provides a geometrially aurate reonstrution (from the available data) of the target refletivity distribution in the ase when the inident wavefronts are planar aross the breadth of the target and the baksattered wavefronts are sampled in the far-field. The ompat radar range onfiguration utilized in the data olletion proess (shown in figure 1a) ensures that both requirements are satisfied. Based on the data olletion diagram shown in figure 1, the target-fixed spatial frequeny loations of the samples of Φ(f,,ψ) an be represented as 19 : t t x t = y t z k = 2k ( p) ( p) sin os ( p) ( ( q) ) os( ψ ( ) ( ( q) ) os( ψ ( ) ( ()) sin ψ s (2a) 2πf = (2b) where t is the ourier spae vetor defining the loation of the data sample at the target-fixed spatial frequeny oordinates t x, t y, and t z. The salar k(p) is the wavenumber of the eletromagneti wave having frequeny f(p). The aquired radar signature data Φ(f,,ψ) are said to reside in a volume in 3D ourier spae (figure 2a). In order to failitate the ISAR image proessing, the 3D polar proess aperture shown in figure 2a is transformed from the target-fixed spatial frequeny oordinates ( x t, y t, z t ) to the radar-fixed spatial frequeny oordinates ( x, y, z ). The transformation maintains a fixed rotational orientation of the 3D proess aperture in the ( x, y, z ) oordinate system, regardless of the enter azimuth and elevation angles and ψ, thereby simplifying upoming proessing tasks. The oordinate transformation an be viewed as a 2D rotation of the 3D proess aperture by the enter azimuth and elevation angles, and ψ and is given by the following: = x y z = 2k ( p) os( ψ ( ) sin( ( q) ) ( ψ () s ) sin( ψ ) + os( ψ ( ) os( ψ ) os( ( q) ) ( ψ () s ) os( ψ ) os( ψ ( ) sin( ψ ) os( ( q) ) sin [ ] sin. (3) A diagram of the 3D proess aperture in the radar-fixed spatial frequeny oordinate system is shown in figure 2b. Ultimately, the rotation of the 3D proess aperture auses the image reonstrutions to revolve about the radar-fixed oordinate system in response to varying the enter azimuth and elevation angles, and ψ, of the 3D proess aperture. 17 This is the so alled inverse syntheti aperture radar (ISAR) proessing modality (i.e. a fixed antenna illuminating a rotating target). Appliation of a ourier transform to the samples of the target s baksatter phasor Φ( x, y, z ) having loations desribed by equation (3) produes a reonstrution of the target s 3D refletivity distribution. In the interest of omputational effiieny, the ISAR image reonstrution proess is arried out by first performing a 3D interpolation of the data samples onto a 3D Cartesian grid. A 3D fast ourier transform (T) proess is then applied to the interpolated samples to provide a reonstrution of the target s 3D refletivity distribution D Cartesian Grid Constrution As shown in figure 2b, the Cartesian grid (box) is irumsribed onto the available 3D proess aperture suh that the entire aperture is inluded within the grid. Determining the boundaries of the Cartesian volume is a matter of analyzing the 3D geometry of the situation depited in figure 2b for an arbitrary set of f b, f, ψ a, ψ, and a. Beause of the oordinate system transformation desribed by equation (3), a fixed rotational orientation of the 3D proess aperture with respet to the ( x, y, z ) oordinate system is maintained, regardless of the data olletion parameters. The boundaries of the Cartesian volume irumsribing the 3D proess aperture are given by the quantities, xmin, ymin, zmin, xmax, ymax, and zmax and are determined through a geometrial analysis of figure 2b whih is outside the sope of this paper. The 3D Cartesian sample

5 Cirumsribed Cartesian Volume (a) (b) igure 2: 3D polar proess aperture in (a) target-fixed and (b) radar-fixed spatial frequeny oordinates. grid is then defined by set of arrays desribing the sample loations in the x, y and z dimensions limited by the boundaries in the respetive dimensions. The x, y, and z 3D Cartesian grid sample loations are given by: x max x min x ( u) = x min + u x u = 0,1,2 K 1 (4a) x y max y min y () v = y min + v y v = 0,1,2 K 1 (4b) z z max z min ( w) = + w w = 0,1,2 K 1 z min z y y z. (4) In equation (5), x (u), y (v) and z (w) are the 3D Cartesian grid sample loations in the x, y, and z dimensions, respetively, while x, y, and z symbolize the sample intervals and u, v, and w are the sample loation indies of the respetive dimensions. In order to preserve the spetral ontent of the polar formatted samples in the Cartesian grid, the sample intervals x, y, and z are determined by the data olletion sample inrements f,, and ψ as given by: x z + 2 π f = (5a) 4π f = (5b) + 2 π f ψ (5) = where f + is the maximum frequeny at whih data are olleted as is determined by equation 1a.

6 D Interpolation Proess The 3D interpolation method developed in this work implements a one-dimensional sin funtion interpolator 17 in the three separate spatial frequeny dimensions to generate samples on the irumsribed 3D Cartesian grid defined by equation (5). Analysis of equation (3) reveals that the 3D proess aperture may be deomposed into individual elevation-ut planes (i.e. data olleted at fixed (q ) in eah of whih the samples lie on a polar raster. Two-dimensional interpolation of polar raster samples onto a retangular grid in onjuntion with the PA has been desribed in the literature. 17 or a given elevation-ut plane, the data samples are first interpolated along the wavenumber lines (i.e. fixed ψ( and (q) ) to obtain output samples loated at the desired y loations given by equation (5b). The samples produed by the y interpolation are then interpolated along the z diretion (i.e. fixed y (u) and (q) ). The result of this z interpolation positions the output samples at the desired z loations given by equation (5). This 2D interpolation proess is repeated in eah elevation ut plane. The final x interpolation is performed at eah ( y (u), z (w)) oordinate in the Cartesian grid and plaes samples between the adjaent elevation-ut planes suh that they are loated at the desired x loations given by equation (5a). The 3D array of samples resulting from the x interpolation are then o-loated with the 3D Cartesian grid. 3. RESULTS 3D radar signature data were olleted on the 1/35 th sale model M1A1 Abrams main battle tank shown in figure 3. The M1A1 Abrams model is onfigured in the travel-mode (transport) position, and is affixed with Identifiation riend or oe (I) panels. The data were olleted in the VV polarization hannel with frequeny parameters f = f b = 342 MHz, and f = 3.43 MHz over a 360 span in azimuth angle, with ψ = 45, ψ a = 72, and = ψ = 2. 3D UH ISAR imagery was generated from the radar signature data olletion utilizing the wide-band/wide-angle 3D ISAR image formation proessor desribed in setion 2.2. igures 4 and 5 display several projetions of the 3D UH imagery generated from the M1A1 Abrams radar signature olletion. The data were proessed over the full radar bandwidth and elevation aperture with ψ = 45 and utilized an azimuth aperture a = 72 at = 120 (figure 4) and = 180 (figure 5) to form the imagery. Based on the proessing parameters, the peak to null mainlobe width of the wide-band/wide-angle imaging system s impulse response funtion 18 is 0.44 meters in the range dimension and 0.37 meters in ross-range and height dimensions. The ISAR imagery shown in figures 4 and 5, therefore, exhibit 0.44 meter range resolution and 0.37 meter ross-range and height resolution. We note here that the data are olleted over a wavelength span of meters. In figures 4 and 5, the positive ross-range (x) axis is shown in red, positive range (y) axis in white, and positive height (z) axis in blue. Also note that the radar propagates in the diretion of the positive y axis in the radar-fixed oordinate system. As suh, the x-z projetion represents the front aspet view of the 3D ISAR image at azimuth/elevation view angle = 0, the y-z projetion represents the side aspet view at azimuth view angle = 90, elevation view angle = 0, while the x-y projetion represents the top aspet view at azimuth view angle = 0 and elevation view angle = 90. igures 4d and 5d display arbitrary views of the imagery at the aspet angles aptioned in the respetive figures. The imagery in figures 4 and 5 differ somewhat from traditional 2D ISAR imagery by the manner in whih the image intensities are displayed. Beause of the three-dimensional nature of the RCS intensity distributions whih have been rendered to the two-dimensional images shown in figures 4 and 5, the peak of the sattering enters are masked by the threedimensional ideal point satterer image response (i.e. impulse response funtion of the system). One may visualize a onstant intensity level in the imagery, enoded by onstant olor, as a surfae whih enompasses the higher intensity surfaes within. As suh, the surfaes of onstant intensity must be peeled bak in order to reveal surfaes of higher intensity. The proess of peeling bak the onstant intensity surfaes, however, has the unfortunate effet of reduing the image s overall dynami range. Therefore, a trade-off must be made between display of the image s dynami range and visualization of the sattering enters at the ore of the imagery. or this reason, 8 db ( dbsm) of dynami range is shown in figures 4 and 5 in order to allow visualization of the target s main sattering features. The low level intensity in the imagery is represented by the olor green whih is sueeded by the olors yellow and orange then by the high level intensity signified by the olor red. Through lose srutiny of the imagery, one may observe higher level olors behind the low level green surfaes. Considering the relatively long wavelengths used in the 3D UH ISAR imaging experiment, the imagery shown in figures 4 and 5 provide resolution suffiiently high enough to isolate individual sattering features ontributing to the target s 3D refletivity distribution. In omparing the ISAR imagery of figure 4 to the orresponding photo of the M1A1 at the equivalent azimuth view angle (figure 3a), various distint physial features of the MBT an be assoiated to the sattering behavior shown in the imagery. As shown in figure 4, the high resolution imagery allows identifiation of the seven exposed

7 Commander s Cupola Turret Panels Smoke Extrator I Panel Side Skirt Reverse Lights (a) (b) igure 3: 1/35 th sale model M1A1 Abrams MBT in travel mode with I panels at (a) 120 azimuth aspet and (b) 180 azimuth aspet poses as viewed by the radar during data olletion wheels of the tank, eah of whih has a meter diameter. urthermore, the imagery also reveals the asymmetri spaing of the rear wheel as observed in figure 3a. This feature is a main distintion between US and Russian-made MBT s. The two edges of the flat plate running lengthwise with the tank s body, formed by the side skirt shielding the wheels, are also resolved in the imagery. Beause the sattered waves are redireted from the baksatter diretion by the skirt s plate at this enter azimuth/elevation angle, a shadow spanning the length of the skirt an be observed in figures 3a, 3b, and 3d between the two edges of the plate. Also shown in the imagery is a tapered elongation of this plate s top edge at the front of the tank in response to the orresponding struture shown in figure 3a. The small plate-like I panel affixed to the illuminated side of the tank s turret also generates a shadow in figures 4a, 4 and 4d. The illuminated panel on the front of the tank s turret also possesses a planar surfae whih appears brightly in the imagery. In this partiular aspet view, the sattered waves from this surfae are direted bak toward the radar making the surfae visible at this proess aspet angle. The opposing panel of the turret appears as a shadow in the imagery as the sattered waves are primarily direted away from the radar. We also note that sub-wavelength features omprising the tank suh as ommander s upola, the reverse lights, and the smoke extrator loated in the enter of the annon s barrel are well-resolved in the imagery. 4. SUMMARY AND CONCLUSIONS The ative role of the UH SAR sensor in present-day remote sensing appliations requires that suh systems be studied in-depth in order to fully exploit the sensor s apabilities. In this work, we have used a 6-18 GHz sale model radar signature data olletion system to generate UH radar signature data on a free spae tatial target. A 3D ISAR image formation proessor used to reonstrut the 3D refletivity distribution of a target from its radar signature data was also presented. inally, high resolution 3D ISAR imagery generated from a freespae radar signature data olletion of an M1A1 Abrams MBT demonstrated the feasibility of studying UH SAR using the desribed radar sale-modeling and image proesses. Considering the eletromagneti sattering proesses taking plae during a wide-bandwidth, wide-angle radar signature data olletion, it is oneivable that satterer persistene through the entire data olletion aperture may limit the resolution ahievable by the imaging system. That is, the shorter the persistene of a given satterer through the data olletion proess, the more oarsely that satterer is resolved. The UH ISAR imagery presented in this work demonstrates that high resolution an be attained in a long wavelength imaging system if wide-bandwidth, wide-aperture olletions are

8 feasible. This outome is most likely a result of the eletromagneti sattering regime in whih the measurements takes plae. Beause the wavelengths used in UH SAR are on the order of the size of the target, the target and its features experiene Rayleigh and resonane sattering phenomena. In this sattering regime, sattering amplitude is largely independent of illumination angle 7 and this being the ase, satterers tend to persist throughout the data olletion aperture. Suh a rationalization may explain why satterer persistene does not limit the ahievable resolution in the long-wavelength, wide-angle imaging senario desribed in this work. In an attempt to validate this hypothesis, one may onsider generating ISAR imagery from a radar data olletion of the idential target in a short wavelength system where low frequeny sattering phenomena are longer prevalent and analyze the relationship between satterer resolution and the extent of the data olletion aperture. ACKNOWLEDGEMENTS The authors wish to thank Mr. Mihael Coulombe and Mr. Thomas Horgan at the Submillimeter-Wave Tehnology Laboratory for their onsiderable efforts in the development of the radar system used to ondut this signature olletion. REERENCES 1. M. Davis, P.G. Tomlinson, and R.P. Maloney, Tehnial hallenges in ultra-wideband radar development for target detetion and terrain mapping, Proeedings of the IEEE Radar Conferene, M.I. Mirkin, C.. Lee, T.O. Grosh, B.E. Hedges, S. Ayasli, K. Kappra, and K. Sturgess, Results on ground penetration SAR phenomenology from June 1993 Yuma experiment, Proeedings of the IEEE Radar Conferene, L.M. Ulander, W.E. Pierson, M. Lundberg, P. ollo, P. rolind, and A. Gustavsson, Performane of VH-band SAR hange detetion for wide-area surveillane of onealed ground targets, Proeedings of the SPIE, Vol. 5427, G.J. Moussally, R.W. ries, and R. Bortins, Ground-penetrating syntheti-aperture radar for wide-area airborne minefield detetion, Proeedings of the SPIE, Vol. 5415, A. Andrews, J. Ralston, and M. Tuley, Researh on Ground-Penetrating Radar for Detetion of Mines and Unexploded Ordnane: Current Status and Researh Strategy, Institute for Defense Analysis, IDA Doument D- 2416, Log: H , D.L. Shuler, J. Lee, and G. De Grandi, Measurement of Topography Using Polarimetri SAR Images, IEEE Transations on Geosiene and Remote Sensing, Vol. 34, No. 5, L. Neng-Jing, Radar ECCMs new area: anti-stealth and anti-arm, IEEE Transations on Aerospae and Eletroni Systems, Vol. 31, No. 3, L.M. Novak, S.D. Halversen, G.J. Owirka, and M. Hiett, Effets of Polarization and Resolution on the Performane of a SAR Automati Target Reognition System, The Linoln Laboratory Journal, Vol.8, No. 1, R. Goodman, S. Tummala, and W. Carrara, Issues in Ultra-Wideband, Widebeam SAR Image ormation, Proeeding of the IEEE Radar Conferene, L. Nguyen, T. Ton, D. Wong, and M. Soumekh, Adaptive Coherent Suppression of Multiple Wide-bandwidth RI Soures in SAR, Proeedings of the SPIE, Vol. 5427, 2004.

9 11. C.J. Beaudoin, Development of a 1/35 th Sale VH/UH ar-ield RCS Imaging System Used to Investigate Sattering and Imagery of Tree Obsured Targets, M.S. Thesis, University of Massahusetts Lowell, M. J. Coulombe, T. Horgan, J. Waldman, J. Neilson, S. Carter, and W. Nixon, "A 160 GHz Polarimetri Compat Range for Sale Model RCS Measurements, Antenna Measurements and Tehniques Assoiation (AMTA) Proeedings, Seattle, WA, M. J. Coulombe, T. Horgan, J. Waldman, G. Szatkowski, and W. Nixon, "A 520 GHz Polarimetri Compat Range for Sale Model RCS Measurements, Antenna Measurements and Tehniques Assoiation (AMTA) Proeedings, T. M. Goyette, J. C. Dikinson, J. Waldman, W. E. Nixon, and S. Carter, ully Polarimetri W-band ISAR Imagery of Sale-Model Tatial Targets Using a 1.56 THz Compat Range, Proeeding of SPIE 15 th Annual Inter. Symp. on Aerospae/Defense, Simulation, and Controls, Vol. 4382, A. J. Gatesman, T. M. Goyette, J. C. Dikinson, J. Waldman, J. Neilson, and W. E. Nixon, Physial sale modeling the millimeter-wave baksattering behavior of ground lutter, Proeeding of the SPIE, Vol. 4370, R. H. Giles, A. J. Gatesman, J. itz-gerald, S. isk, and J. Waldman, "Tailoring Artifiial Dieletri Materials at Terahertz requenies, The ourth International Symposium on Spae Terahertz Tehnology, C.V. Jakowatz, D.E. Wahl, P.H. Eihel, D.C. Ghiglia, and P.A. Thompson, Spotlight Syntheti Aperture Radar: A Signal Proessing Approah, Kluwer Aademi Publishers, Boston, D.L. Mensa, High Resolution Radar Cross-Setion Imaging, Arteh House, In., Massahusetts, C. Beaudoin, A. Gatesman, M. Clinard, J. Waldman, R. Giles, and W. Nixon, Physial Sale Modeling of VH/UH SAR Colletion Geometries, Proeedings of the IEEE Radar Conferene, K.W. orsythe and A.. Yegulalp, Waveforms, Signal Proessing and Performane of Sparse-Band Syntheti Aperture Radar, MIT Linoln Laboratory, Projet Report PR-15, 2001.

10 (a) (b) () (d) igure 4: 3D UH VV ISAR imagery of the M1A1 Abrams MBT at = 120, ψ = 45 : (a) x-z (front) projetion (b) y-z (side) projetion () x-y (top) projetion and (d) arbitrary projetion at azimuth = 5 elevation = -30 referened to the radarfixed oordinate system.

11 (a) (b) () (d) igure 5: 3D UH VV ISAR imagery of the M1A1 Abrams MBT at = 180, ψ = 45 : (a) x-z (front) projetion (b) y-z (side) projetion () x-y (top) projetion and (d) arbitrary projetion at azimuth = -20 elevation = 15 referened to the radarfixed oordinate system.