Multiple reflections and improvement of edge scattering in GRECO RCS prediction code

Mul iple e lec ions and imp o emen o edge sca e ing in GRECO RCS p edic ion code Juan M. Rius, M.VaII-Ilosse a, Lluis Jo e G up A.M.R., Dp . Teo ia del Senyal Comunicacions, UPC Apdo. 30002, 08080 Ba celona, TI. +34-3-4017219, Fax +34-3-4017232 Abs ac GRECO code o monos a ic RCS p edic ion in eal ime has been ex ended by conside ing mul iple e lec ions be ween su aces and imp o ing he edge di ac ion coe icien s. Mul iple e lec ions a e analysed h ough a e y e icien ay- acing algo i hm based on he g aphical p ocessing echnique. Me hod o equi alen cu en s o edge sca e ing has been imp o ed by Mi zne 's and Michaeli's inc emen al leng h di ac ion coe icien s (ILDC). This communica ion p esen s he gene al ea u es o GRECO code, in pa icula he ad an ages o he new g aphical p ocessing echnique. Emphasis will be placed in he new ea u es o GRECO s ill unpublished: he ay- acing algo i hm and he implemen a ion o inc emen al leng h di ac ion coe icien s. G aphical Elec omagne ic Compu ing (GRECO) Du ing he las ou yea s, he de elopmen o g aphical p ocessing echniques o high- equency monos a ic RCS p edic ion has gi en ise o GRECO code (1), (2), (3). Real- ime compu a ion is achie ed h ough g aphical p ocessing o an image o he a ge p esen a he sc een o a wo ks a ion, using he ha dwa e capabili ies o a 3-D g aphics accele a o . The wo main ad an ages o he g aphical p ocessing app oach o e classical echniques a e: a) Ha dwa e g aphics accele a o emo es hidden su aces and edges: hey do no con ibu e o he su ace o line in eg als when hey a e pe o med by he g aphical p ocessing echnique. b) Reduced CPU ime and RAM equi emen s. They a e independen o a ge elec ical size and complexi y. The main ea u es o GRECO code a e he ollowing: a) The I-DEAS compu e aided design package o geome ic modelling o solids has been used o modelling a ge geome y. The a ge is desc ibed as a collec ion o pa ame ic su aces, de ined wi h wo-dimensional NURBS (non-uni o m a ional B- splines). Pa ame ic su aces equi e less mass s o age memo y ha he ace ing app oach, and adjus mo e accu a ely o he eal a ge su ace. b) Physical Op ics (PO) app oach o pe ec ly conduc ing su aces and Impedance Bounda y Condi ion (IBC) + Physical Op ics o ada abso ben coa ings. c) Me hod o Equi alen Cu en s (MEC) wi h ei he Physical Theo y o Di ac ion (PTD), Mi zne 's o Michaeli's Inc emen al Leng h Di ac ion Coe icien s (ILDC) o pe ec ly conduc ing edges. A compa a i e s udy o he esul s o he h ee kinds o ILDC's will be p esen ed in his communica ion. d) Double e lec ion analysis by geome ic op ics (GO) ay- acing o he i s e lec ion and bis a ic physical op ics o he second. A new and e y e icien ay- acing algo i hm has been de eloped and will be also p esen ed in his communica ion. Ray-T acing Double e lec ions be ween su aces a e analysed by a hyb id GO-PO scheme. The GO e lec ion a he i s su ace assumes ha specula e lec ion occu s, acco ding o s a iona y phase p inciple. The PO e lec ion a he second su ace ensu es ha he co ec sca e ed ield is ob ained when he e is no specula e lec ion o he obse e . Fo each pixel on he a ge su ace, a e lec ed ay is aced along he GO specula di ec ion. The impac o he e lec ed ay wi h ano he su ace is de ec ed on he sc een by ollowing he ay-pa h and compa ing he z coo dina es o he ay wi h ha o he su ace a he same x,y loca ion. In case ha he e is a second e lec ion, he ield sca e ed o he obse e is compu ed using bis a ic PO. Vec o o mula ion o bis a ic GO and PO o espec i ely he i s and second e lec ions allows o ob ain he sca e ing ma ix o he a ge . This scheme is alid o bo h plana and cu ed su aces. In he o me case, he e lec ed ays a e pa allel, which is equi alen o a plane wa e inciden o e he second su ace. In he la e case, he di e gence ac o due o he cu a u e o he su ace is implici in he g aphical ay- acing algo i hm: he numbe o ay- hi s on he second su ace is in e sely p opo ional o he di e gence o he e lec ed ays. Inc emen al Leng h Di ac ion Coe icien s I is well known ha U lm se 's PTD coe icien s a e accu a e o analysing high- equency monos a ic edge di ac ion only when he incidence di ec ion is pe pendicula o he edge, o which monos a ic obse a ion is along he Kelle cone (5). This is he case o he main edge con ibu ion o o al RCS, so ha oblique edges con ibu ion can be usually neglec ed. Fo ha eason, and due also o hei simplici y, PTD coe icien s oge he wi h Physical Op ics cons i u e he mos usual app oach o monos a ic RCS p edic ion. Excellen esul s ha e been ob ained by GRECO code using a e y e icien linea app oxima ion o PTD coe icien s (2), (3). An excep ion o he abo e ule is he analysis o s eal h ai c a , in which specula su aces and edges a e delibe a ely a oided. Fo igo ous analysis o oblique edges i is necessa y o use MEC wi h some kind o inc emen al leng h di ac ion coe icien s, which a e co ec o obse a ion ou side he Kelle cone (5). Usually Mi zne 's ILDC (5) ha e been chosen o his pu pose in a numbe o RCS p edic ion codes bu , on he o he hand, hey a e singula o some obse a ion di ec ions (6). This p oblem has been o e come by Michaeli's ILDC (6), which emo e mos o he singula i ies o Mi zne 's and, in pa icula , a e ini e o all monos a ic obse a ions. The main d awback o Michaeli's ILDC is a a he complex o mula ion, e en o he monos a ic case, which makes eal- ime RCS p edic ion di icul o GRECO code. Resul s An in e es ing RCS p oblem which includes con ibu ions om bo h double e lec ions and edge di ac ion is he 900 dihed al p oposed a Ma seille'92 RCS wo kshop (4). The geome y o he objec is shown in ig. 1. No ice he monos a ic sweep along he bisec o plane, q = 450, ins ead o he plane pe pendicula o he dihed al aces, 0 = 90°. This unusual sweep makes he con ibu ion o oblique edges mo e impo an han ha o su ace e lec ion, becoming an excellen es o he accu acy o he di e en kind o edge di ac ion coe icien s. Figu e 2 shows he RCS om single and double su ace e lec ions compu ed by a double PO+PO su ace in eg al compa ed o he p edic ions o he GO+PO ay- acing echnique implemen ed in GRECO code. No ice ha o g azing incidence he la e is a ew dB unde he PO+PO esul , due o he ac ha mos GO ays specula y e lec ed on a ace o he dihed al do no hi he o he one, while o hese ays PO p edic s non-null sca e ed ields ha each he o he ace o he dihed al. The esul s o GRECO code using he h ee kinds o edge di ac ion coe icien s oge he wi h he ay- acing algo i hm a e shown in ig. 2 ( hick line plo s). These esul s ha e been 386 iso II.. -e~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4 " -:I Side iow Fig. 1: Dihed al, 1= 1.5 X, h= 2.25 x. a = 9 RCS sweep along bisec o plane. RCS Es 0 10 20 30 40 50 60 e Fig. 2: Con ibu ion o single and double su ace e lec ions o RCS o he dihed al. Resul s o PO+PO double su ace in eg al (dashed line) compu ed by gaussian cuad a u e, and GO+PO ay- acing (solid line) compu ed by he g aphical p ocessing echnique (dashed line). 100 20 140 16" 3 a ILDC MiChoe i compa ed wi h he compac ange measu emen s o S. Mish a, pe o med a he Canadian Space Agency ( hin line plo ). I should be no ed ha he e a e wo main sou ces o e o in he GRECO code analysis o his objec : he elec ical size is no la ge enough o he high equency me hods o be accu a e and he e exis s an impo an con ibu ion o su ace-edge in e ac ions ha a e no aken in o accoun by GRECO. The bes esul s o 00 pola isa ion a e ob ained wi h U im se s PTD o Michaeli s ILDC, excep o some di ec ions o obse a ion whe e Mi zne s ILDC a e mo e accu a e. In he case o ZZ pola isa ion, he beha iou o Mi zne s ILDC is wo se han ha o PTD o Michaeli s ILDC. Conclusions GRECO code has been imp o ed by he implemen a ion o a GO- PO g aphical ay- acing algo i hm o analysis o mul iple su ace e lec ions and Michaeli s ILDC o oblique edge di ac ion. The esul s o a 90° dihed al wi h oblique monos a ic incidence ha e been compa ed o RCS measu emen s. The e o s due o he no la ge elec ical size o he objec and he su ace-edge in e ac ions deg ade signi ican ly he accu acy o he esul s. Howe e , i can be no iced ha e en in hese ad e se condi ions, GRECO is able o p edic he app oxima e le el o he RCS, o he deg ee o accu acy usually equi ed when complex ada a ge s a e analysed. The conclusion o he compa ison be ween he h ee kinds o di ac ion coe icien s is he ollowing: al hough Mi zne s o Michaeli s ILDC a e in heo y mo e accu a e han U im se s PTD o analysing oblique edges, he imp o emen o e PTD is no signi ican when o he unp edic ed con ibu ions o RCS a e p esen , which is always he case o complex ai c a . Mo eo e , he con ibu ion o oblique edges is e y a ely signi ican agains ha o pe pendicula su aces o edges, so ha he linea app oxima ion o PTD coe icien s p esen ed in (2) and (3) is p obably he mos e icien app oach o eal- ime monos a ic RCS p edic ion. Acknowledgmen s This wo k has been suppo ed by he Spanish "Comisi6n In e minis e ial de Ciencia y Tecnologia" (CICYT) unde he p ojec : TIC 88-288E. Re e ences (1) Juan M. Rius, M. Fe ando, L. Jo e, "GRECO: G aphical Elec omagne ic Compu ing o RCS P edic ion in Real Time", IEEE An ennas and P opag. Magazine, Ap il 1993 (2) Juan M. Rius, M. Fe ando, L. Jo e, "RCS o Complex Rada Ta ge s in Real Time", accep ed o publica ion in IEEE T ans. on An ennas and P opag. (3) Juan M. Rius, "Seccion ec a de blancos ada complejos en iempo eal", Doc o a e Thesis Disse a ion, Uni e si a Poli ecnica de Ca alunya, July 1991. (4) "SER Ma seille-92, d udes compa a i es de Su aces Equi alen es Rada de co ps in ini emen conduc eu s ou A impddance de su ace e de cibles inhomogenes", wo kshop on RCS o ganized by Dassaul -A ia ion, Socid d Mo hesim and he Uni e si e de P o ence. (5) E.F. Kno , J.F. Shae e , M.T. Tuley, "Rada C oss sec ion: I s P edic ion, Measu emen and Reduc ion", A ech House, Inc., Dedham, MA, 1985. (6) A. Michaeli, "Elimina ion o In ini ies in Equi alen Edge Cu en s, Pa I: F inge Cu en Componen s", IEEE T ans. on An ennas and P opag., Vol. AP-34, No.7, July 1986 Meoszmemen by 5. Mb o. Can adin Space Agency Figu e 3 Resul s o GRECO code (solid, dashed o dosed hick line) o he h ee kinds o edge di ac ion coe icien s compa ed wi h compac - ange measu emen s (solid hin line). 387 -0 I eX 2 ACS zz 25 x2 25 20 15 10 -10k -15 -20_ 0 0 20 40 60 go 100 170 140 160 80 PO + R + PTD USun se IOC M zne