ABSTRACT Full-Polaimetic Analysis of MERIC Ai Tagets Data C. Titin-Schnaide, P. Bouad ONERA Chemin de la Hunièe et des Joncheettes 91120 Palaiseau Fance Cecile.Titin-Schnaide@onea.f, Philippe.Bouad@onea.f This pape addesses the detailed analysis of full polaimetic ada images, obtained fom eal data, by using the Polaimety theoy paametes. The expeimental gound based ada station MERIC has been designed at ONERA to pefom full polaimetic measuements on non-coopeative in flight aiplanes. The fist pomising esults of an analysis caied out fom a MERIC full-polaimetic ISAR image of a line ae pesented. 1.0 INTRODUCTION The theoy of polaization has been studied [1] fo seveal decades. Howeve, its implementation has been delayed while waiting fo technological pogess. At pesent, expeimental high esolution ada can povide full-polaimetic data with the equied magnitude and especially phase accuacy. Some full polaimetic aibone SAR adas have aleady been developed. Full-polaimetic SAR images analysis (poduced fom RAMSES data, fo example), has shown pomising esults egading the vegetation classification and the analysis of motionless gound tagets. Fo In-flight taget studies, 2D-ISAR ada imaging is a well-established method giving the eflectivity distibution of taget scattees. Full-polaimetic ISAR imaging will be intoduced and discussed. It will be shown that Polaimety povides additional infomation about scattees electomagnetic behaviou. The full-polaimetic gound based ada station MERIC has been designed to measue in-flight tagets [4], in ode to ceate full-polaimetic data base. The analysis of a civilian aicaft is pesented to illustate Polaimety potentiality. 2.0 ISAR FULL-POLARIMETRIC IMAGING 2.1. Rada images Rada tagets can be split into two main classes depending on how elementay mechanisms add in the esolution cell. If they add incoheently, scatteing mechanisms ae epesented by andom vaiables and the statistical (o geneal) theoy of polaization is applicable. This is the case fo lage natual aeas like foests, fields, meadows... Pape pesented at the RTO SET Symposium on Taget Identification and Recognition Using RF Systems, held in Oslo, Noway, 11-13 Octobe 2004, and published in RTO-MP-SET-080. RTO-MP-SET-080 39-1
If they add coheently, electomagnetic scatteings ae coheent and the deteministic theoy of polaization is applicable. This is mainly the case fo man-made o atificial tagets like aeoplanes, tucks, ailways... Rada images of these tagets ae chaacteized by a small numbe of bight scatteing centes. 2.2. Point Object Model A common assumption fo ada atificial ada tagets is the Point Object Model (POM). Accoding to this model, any taget is descibed by a collection of isotopic point scattees. Polaimetic measuement give access to the taget backscatteed matix [S]. In the POM fame, this matix can be epesented by a sum on N elementay scatteing matices [s i ], phase shifted accoding to the scattees locations x i : j2k x [ S]( k ) = [ s i i ] e i= 1, N 2πf whee k = is the wave vecto depending on fequency f and incidence angle. c Fo any ada system, the image [ I]( x) is obtained though a Fouie Tansfom: [ I]( x) = [ S]( k ) e j 2k x Assuming the elementay matices [s i ] do not vay with fequency and oientation, the image is given by: whee δ (x ) is the Diac distibution. [ I]( x) = [ s i= 1, N i ] δ ( x x In pactice, measuements ae ecoded ove a limited fequency bandwidth and ove a bodeed incidence domain. Theefoe, the Point Spead Function (PSF) G x x ) eplaces the Diac distibution: ( i dk i ) [ I]( x) = [ s i i = 1, N ] G( x x i ) This equation shows that the esulting image can be consideed as the complex sum of each point scattee image. Bight scatteing centes ae no longe point centes. They have a stetch in space chaacteized by the PSF. The same elementay scatteing matix is associated with all pixels in the vicinity of a point scattee with a stength given by the PSF. If the scattees ae fa enough fom each othe, thei PSF do not intefee and the tue elementay matices [ s i ] ae obtained at locations x i. A taget is theefoe descibed by a set of point scattees whose elementay scatteing matices and locations ae known. In pactice, the scatteing matix of a given scattee is always moe o less distoted by the scatteing matix of the othe scattees. The highe is the esolution, the smalle is the PSF and the less distoted ae the elementay scatteing matices. A 2D ISAR image is a pojection of the 3D scattee distibution onto a 2D plane. Some diffeent scattees can then be confused. This poblem inceases fo the 1D epesentation: a ange pofile being the 39-2 RTO-MP-SET-080
pojection on the line of sight of the 3D distibution of scattees. So in this case a lage numbe of scattees can be mixed togethe. 2.3 ISAR imaging To build the ISAR image of a moving taget with the equied tansvesal esolution, the ada has to tack the taget in ode to acquie measuements duing a sufficiently long duation. Each complex ange pofile thus acquied must be aligned with the peceding pofile using a complex coelation method. Phase distotion due to the tanslation motion of the moving taget is compensated using the DSA (Dominant Scattee Algoithm) method. The pinciple of this method is to select the bight scattee showing the least amplitude vaiation as a efeence point, At ada wavelengths, the etuned signal is dominated by backscatteing fom featues like cones, edges and suface discontinuities The objective of ada classification based on classical ISAR imaging is to conside athe the locations and RCS level of scattees than taget shape. Full polaimetic ada data makes it possible to also use electomagnetic mechanisms ceating the scattees. 3.0 POLARIMETRIC PARAMETERS The natue of deteministic mechanisms can be chaacteised by seveal sets of polaimetic paametes. These sets ae globally equivalent. Howeve thei sensitivity to electomagnetic popeties can be diffeent. 3.1. Sets of polaimetic paametes It is well known that deteministic mechanisms ae descibed by a 2 by 2 complex matix: the scatteing matix. Unde the ecipocity postulate and given its absolute phase is ineffective fo descibing the physical mechanism, it depends on five independent paametes. Seveal sets of paametes have been poposed in the liteatue: The Fok paametes set: Accoding to [1] the back-scatteing matix of any deteministic mechanism can be mathematically epesented by seveal opeatos: [ S] = e iψ [ σ 0 ] iτ [ σ 2 ] iτ [ σ 2 ] iψ [ σ 0 ] e [ Sd ] e e whee: i2 = ν 1 0 S d ] µ e 2 4ν and whee the fou Pauli matices ae noted [ σ j ], j = 0, 3. 0 ( tgγ ) e [ i It depends on the five Polaization Fok angles: ψ, τ, γ, ν, µ The vaiation anges of the Polaization Fok paametes ae as follows: π 2 < ψ < π 2 π 4 < τ < π 4 π 4 < ν < π 4 0 < γ < π 4 The oientation angleψ gives the tilt of the taget vesus the hoizontal polaization, in the plane pependicula to the ada line of sight. The symmety angleτ indicates the symmety ate vesus an axis o a plane (if τ is low the scattee is symmetic and if it is high it is not symmetic). The skip angle ν gives infomation about the paity of the numbe of scatteings (if ν is low this numbe is even, if ν is RTO-MP-SET-080 39-3
high it is odd). The polaizability angle γ povides infomation about the ability of the scattee to polaize the waves on a paticula polaization (if γ is low the scattee is polaizing and if γ is high it is not). The Huynen paametes set: This set contains nine eal paametes [1]: the oientation angle ψ and the disoiented (oientation extacted) Mulle matix paametes: 2A 0, B0 + B, B0 B, C, D, E, F, G In the deteministic case, these paametes ae linked by fou elations: 2 2 2 A0 ( B0 + B ) = C + D 2 A 0 E = DG 2 2A 0 ( B0 B) = G 2 A 0 F = CG All these paametes ae homogeneous to a powe. The span is an invaiant quantity (independent of any polaization base change) epesenting the total RCS back-scatteed by the taget: span = 2 2 2 ShH + ShV + SvH + SvV = 2A0 + ( B0 B) + ( B0 + 2 B) A featue vecto valid fo identification (independent of total powe infomation) is obtained though the unit span nomalization: A + ( B + B) + ( B B) 1 2 0 0 0 = The Huynen paametes can be witten [1] as a function of the Fok paametes. Then, it is easy to maximise each Huynen paamete. Figue 1 a, b, c, d, e, f, g contains the combs obtained when paametes 2A 0, B0 + B, B 0 B, C, D E, F, G ae espectively maximised. One can notice that maximising any geneato paamete 2A 0, B 0 + B and B0 B leads to a comb with only one peak (1a, b, c). The maximum of any othe paamete coesponds to a comb with thee equal peaks (1d, e, f, g, h). Theefoe, the unit span constaint leads to a set of eight chaacteistic featue combs (figue 1) with eithe one peak (equal to 1) o thee equal peaks (equal to ½). The vey good continuity fom one featue comb to anothe is an impotant advantage fo a classification algoithm based on coelation between measued and efeence combs. In pactice, most of the analysed scatteing centes ae symmetical ( τ 0 ). Theefoe, we often have: E = F = G = 0. Only the five fist combs of figue 1 ae fequently found. The main electomagnetic mechanisms ae: Specula eflection on a smooth suface locally spheical o on a plate. In this case the dominating paamete is 2A 0 (figue 1a). Scatteing on a shap edge o on a long and thin wie descibed by a comb looking like figue 1d. A maximum value of paamete C coesponds to thee equal peaks fo 2A 0, B B + 0 and C. 39-4 RTO-MP-SET-080
(1a) (1d) (1f) 2A 0 =1 (1b) 2A 0 =B 0 +B =C=1/2 (1e) B 0 +B =B 0 -B =E=1/2 (1g) B 0 +B=1 (1c) 2A 0 =B 0 +B =D=1/2 B 0 +B =B 0 -B =F=1/2 (1h) B 0 -B=1 2A 0 =B 0 -B =G=1/2 Figue 1 : the eight chaacteistic combs A diffeence between the two local cuvatues is chaacteized by an incease of paamete D. A maximum value of D coesponds to thee equal peaks fo 2A 0, descibes the quate-wave dephasos accoding the sign of D. B 0 + B and D (figue 1e). It The maximum of paamete F is descibed by thee equal peaks (figue 1g). It coesponds to helices accoding the sign of F. 4.0 POLARIMETRIC ANALYSIS OF AN AIRCRAFT A specific softwae has been designed at ONERA to assist polaimetic analysis of full-polaimetic ada images. In paticula, it can be used to calculate and show the image of any polaimetic paamete fo any selected aea. Seveal ecognition methods can be used to impove the analysis (based on a compaison between eithe scatteing matices o combs of Huynen paametes ). As an example, esults obtained fom a full-polaimetic analysis of a civilian aicaft measued by MERIC ada, ae pesented. The chosen aicaft is a Mac Donnel Douglas MD 82 in take-off phase. A photo (figue 2) gives an idea of the aicaft pesentation with egads to the ada duing the measuements. The RCS images of the fou (eceive)/t(ansmit) polaizations hh, hv, vh and vv ae given in figue 3. About ten main bight spots appea vey clealy. The geat similaity between the hv and vh images (in accodance with the ecipocity postulate) can be seen. These fou images show that co and coss polaized images must be taken into account. The bight spot aeas ae defined by selecting all pixels with span geate than a given level. In figues 4 to 7, the eliminated pixels ae indicated in light geen. Images of the Huynen paametes 2A0 (Figue 4) and B0+B (Figue 5) show that these paametes ae vey disciminating. The highe values (in wam colous) of paamete 2A0 indicate the suface mechanisms locations. On the othe hand, the highe values (in wam colous) of paamete B0+B show the double-bounce aeas. The analysis can be efined by calculating the comb of Huynen paametes fo vaious selected vaiable size aeas. This kind of analysis allows us to identify numeous scattees. Automatic ecognition algoithms can be applied on each pixel to obtain a classified image: a set of mechanisms ae stoed in the efeence memoy. The most likely mechanism of the efeence memoy RTO-MP-SET-080 39-5
(accoding to an appopiate ule of compaison) is allocated to each pixel. The algoithm can be based equally well on eithe a compaison between scatteing matices [2] o on a compaison between Huynen paametes combs. A classified image is pesented on the ight pat of Figue 6 and Figue 7. The mechanisms ae epesented by a specific colomap: Suface mechanism ("S") in blue, Double-bounce o dihedal type mechanisms ("Dd") in ed. The dipole type mechanisms indicating lengthened tagets ("Dp") ae efeenced in yellow. Positive o negative quate-wave dephasos devices ("Q ± ") in puple and mauve colous. Two intemediate mechanisms ae intoduced: cylinde ("C") between suface mechanism and dipole; lengthened dihedal cone ("DdL") between dihedal and dipole. Among nonsymmetical tagets, the ight and left helices ("H ± ") ae associated with white and black. The light gey ("X") o dak gey ("Y") colous indicate symmetic and non-symmetic unecognized mechanisms espectively. Numeous scattees geneating suface (ight pat of figue 6) and double-bounce mechanisms (ight pat of figue 7) have been ecognized. On the left pat of figues 6 and 7, identified mechanisms locations ae indicated. Suface scattees ae identified in blue and geen on figue 6. They ae located on: the end of the tail flat (1), the left (2) and ight (3) engines, the fuselage (4), (6), (8), the end of the wing (5), the opposite pat of the fuselage (7). Double-bounces ae identified on figue 7. They indicate the following inteactions: udde - ight pat of the hoizontal tail flat (1), udde - left pat of the hoizontal tail flat (2), back of ight engine (3), tailing edge flap contol systems casing - undeside of ight wing (4),(5),(6), fuselage - back of the ight wing (7), fuselage - font of the ight wing (8), fuselage antennas (9),(10), (11). 5.0 CONCLUSION Like all man-made tagets, aicaft ada images ae chaacteized by a collection of bight scattees. Conventional 2D-ISAR imagey can detemine thei location and RCS. Full-polaimetic ISAR imaging povides access to exta infomation about the electomagnetic mechanisms that ceates them. This study, caied out on eal data povided by MERIC full-polaimetic ada, shows that a lot of infomation can be obtained using Polaimety. Mechanisms like specula eflection on plate o on cuved suface, edge diffaction, double-eflection, suface waves, suface discontinuity. can be ecognized. Futue measuements that will be povided by MERIC station can be used to build a full-polaimetic database of ai tagets. Fom this database, suitable methods of automatic taget ecognition will be 39-6 RTO-MP-SET-080
poposed and tested on fully o patially eal polaimetic data, in ode to assess the usefulness of Polaimety. 6.0 REFERENCES [1] Huynen J.R., "Phenomenological theoy of ada tagets". Phd Thesis, 1970 [2] Cameon W.L., Leung L.K., "Identification of elemental polaimetic scattee esponses in highesolution ISAR and SAR signatue measuements", Second intenational wokshop on ada polaimety, Nantes, Septembe 1992. [3] Titin-Schnaide C., Deuillet P., "Analyses polaimétiques haute ésolution de mesues de cibles ada en laboatoie", JIPR, Nantes, mas 95 [4] Titin-Schnaide C., Attia S.," Calibation of the MERIC Full-Polaimetic Rada: theoy and implementation ". Aeospace Science and Technology August 2004 7.0 GLOSSARY MERIC : Moyen Expéimental pou la Reconnaissance et l Identification des Cibles RAMSES : Rada Aéopoté Multi Spectal d Etude des Signatues RTO-MP-SET-080 39-7
Figue 2 : MD82 pictue in taking off phase Figue 3 : fou-polaimetic RCS ISAR images 39-8 RTO-MP-SET-080
Figue 4 : 2A0 paamete image Figue 5 : B0+B paamete image RTO-MP-SET-080 39-9
1 5 3 2 4 6 7 8 12 34 6 7 8 5 Figue 6 : suface mechanisms analysis 1 2 3 4 5 6 7 8 9 10 2 1 3 4 5 6 7 8 910 Figue 7 : double-bounce mechanisms analysis 39-10 RTO-MP-SET-080