Inverse Scattering of a Dielectric Sphere Partially Buried in a Ground Plane Using a Radial Basis Function Network
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- Nigel Barker
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1 5 C OURL VOL 9 O OVR I cg o Dlcc ph lly u Gou l Ug Rl uco wo C Loo Uy o ouh lb Dp o lccl gg obl lb 6688 U -l: h@uouhlu TRCT lyc oluo o h pobl o lcogc cg by lcc phcl c g o o plly bu pcly coucg gou pl ppo by plly uc ph oul ug h ho o g Th c l coc ol cly o h h c l c b lu ywh I pcul h cg co co c b clcul uco o h ph u py wll h uc ph c o y pc gl o cc Th oluo o h pobl l o ly h cg by copl hol bo plc cbg ough uc c whch h l bcgou c b ol by h gou pl whl h copl boy c b ul by ph o y o ph plly uc g o h gou pl I o o ol h cg pobl w ploy l b uco wo o h c l copl coc o h T T polo c h wo pu o pc h h oupu o h lccl u bul c l py o h ph Th wo bl o h h oo p o w whch o h lg ITRODUCTIO Th oluo o h pobl o lcogc cg by plly bu lcc ph pl l o ly h cg by copl h-ol bo plc cbg ough uc c whch h l bcgou c b ol by h gou pl h copl boy c b ul by ph o y o ph plly bu h gou pl Glly h pplco h co o h lcc chco o h g o b po cly o l Tho h lop o ccu lo ucl lgoh o h cg pobl l lycl ucl chqu o olg h cg pobl copuolly hy qu o cuc lo o gphcl o ho [-] I h p w y ul wo chqu h b u o olg cg pobl wh pc o ocog h wbc o cly olg h pobl [5-8] Th chqu pl ghow llow bl uco h copuol coquly p o ob y oluo Th g popy o ll ho pobl qug ly po cly o l Th pobl o ow lcogc cg by plly bu lcc ph pl ug uc ph ppoo h b ol by [] pc gu Thy ol h pobl bu o cy ou h oluo o h po h Th goou lyc oluo o h pobl oul ug h ho o g Th c w u uo pl lcogc w o by gl o cc Th ho o g ppl o plc h plly bu ph gou pl by wo olppg ph o qul o by wo ouchg ph o qul h ph g o h gou pl upply c pl lcogc w uch h h ol lcc l ll po wh h gou pl loc h ogl pobl Th c upply c l p o ppop phcl w uco To po h bouy coo o h uc o h ph h lol o ho o h phcl w uco u o p h coo y o h c l o o ph o h coo y o h oh ph lg o quo whch c b uclly o co h c l coc I h pp w po h oluo o h oo cg pobl by ployg h - co lol o coc uco by Xu whch qu l o Cu oul o o oco h pobl oc wh Cu oul poucg o lu o T c [] Th c l coc g by c ho ob o whch h c l c b lu ywh I pcul h cg co co c b clcul uco o h ph u py wll h bul c o y pc gl o cc C
2 Loo : I cg o Dlcc ph lly bu Gou l Ug Rl uco wo 6 ω Φ y y Φ ω y g Goy o h pobl ucl ul p o h ol cg co-co σ uco o c gl I o o ol h cg o plly uc lcc ph g o coucg pl pobl chqu b o ul wo ly p wh h wo o ol h ol lohp bw h chco o h ph h copl cg coc W ploy l b uco wo h co o pu ly wh ou o pu h ly ug Gu oly uco oupu ly wh h oupu Th ou o pu h pu ly h l gy lu o h copu c l copl coc o h T T polo c whl h oupu h lccl u bul c o h g ph wll l py Th pl o o h wo g how g Th wo h ug h ohogol l-qu lgoh [9] wh pc g o h lccl u λ o 5λ pc ub o lg pl 5 o ch oupu o o h u bul c l py o h ph o w h o h lg Th ul by pplyg h chqu o o coc o w g o lcc co Typcl ul p whch how cll pco by h ul wo Th oulo o h oluo o h cg pobl g h ollowg co l oluo g co Dl o h popo ppoch o cg ug ul wo pl co ollow by h cpo o h wo g lgoh co 5 Th copu ulo ul g co 6 h cocluo w co 7 Ipu ly ORULTIO O T ROL Co lcc phcl c wh u l lcc co ε o b g o o plly uc by ph o h gou pl lyg h -y pl Th ph c O llu by pl lcogc w wh u lcc-l y who popgo co l h - pl gl wh h - cou-clocw h - pl how g Thu h c lcc gc l h h o y co wh co wh bg h w ub h u c pc o h ph whl ŷ ẑ h u co log h y pcly pplyg h g chqu wh pc o h gou pl wll uc h pobl o h o cg by h ph g u o h ogl c w wll g pgg ulouly upo h wo ph Ug p upcp o o h lcc l o u plu h gc l o h l g o h c w w h y co ly o l b uco g Rl b uco wo Oupu ly
3 wh co π π Th c pl w c b p wh c o h phcl coo y o h ph c O : co co!! co wh h oc Lg uco o h whl h phcl l uco o h pg h c w h o o phcl w po W b o cl phcl w o coc WC co phcl w uco VW h l u o h c w o h ph : 5 Th l u o h g o h c w o h ph : 6 7 Th l u o h c w o h g ph : 8 9 Th l u o h g o c w o g ph : wh h phcl co w uco o h o h phcl l uco g : co co [ ] [ ] R R R R co co co o o h whl ow c l coc o by gl o cc y b w h o: co!! co!! 5 co 6 co 7 co 8 co 9 co co co co Th c l o h lcc ph : 5 Th c l o h g ph : 6 7 Th l h lcc ph : 8 9 Th l h g ph : o h h l plc by ε h lcc ph pc lcc wh o gc lo To po h bouy coo h ougog c l o h g ph u b p o cog l o h l ph c hc w pply h phcl co lol o ho 7 C OURL VOL 9 O OVR
4 5 wh Xu lo o ho coc g h pp y y co co y y y y I ou c c h g ph lwy poo blow h l ph o h coucg gou qul o o Th bouy coo o h uc o h lcc ph g qu couy o h gl lcc gc l c wh h ouw u ol o h uc o h lcc ph g pcly o h bouy coo bo h lcc gc l o h uc o h ph g c b p : Tol Tol Tol Tol o h bouy coo w h: [ ] o h bouy coo w h: [ ] 5 o h bouy coo w h: [ ] 6 o h bouy coo w h: 7 pplyg h ohogoly pop o h phcl w uco yl h oluo o h c l coc υ 8 u 9 υ 5 u 5 8 Loo : I cg o Dlcc ph lly bu Gou l Ug Rl uco wo
5 9 C OURL VOL 9 O OVR wh υ u h lcc gc cg coc o gl lcc ph whch g by [ ] [ ] 5 υ [ h ] h [ ] [ ] [ ] u h [ ] [ h ] 5 wh π / λ / ε / ε h c o h lcc whch y b l o copl pg o whh h lcc lol o loy whl ε ε h p o h ph h uoug u pcly quo 8 o 5 bo c b w o [ ] υ υ [ ][ ] υ [ ][ ] 5 [ ] u u [ ][ ] u [ ][ ] 55 [ ] υ υ [ ][ ] υ [ ][ ] 56 [ ] u u[ ][ ] u[ ][ ] 57 quo 5 o 57 o copl l lgbc quo houl b ol ulouly o yl h uow cg coc Th bo y y b w h ollowg o I υ [ ] [ ] [ ] υ υ 58 υ [ ] u[ ] I υ [ u [ ] ] u [ I ] u [ I ] [ ] u [ ] υ [ ] u [ wh [ ] [ ] [ ] ] c oc wh h lo o coc [ ] [ ] [ ] [ ] colu c cog h cg coc Th bo quo c ow b ol cly by h ug C ul o by ulplco o h o h gol o h l o quo 58 I o h u b uc o ub o oluo o quo 58 yl h c coc quo o ou c o pq pq qul o o h bo y coul b ol o ch ply c h o couplg bw uhl o Oc h c l coc copu h ol c l c b ywh o h po: Tol 65 Tol 66 R-ILD ROXITIO how h pou co boh o h ul c l o copo ph ol pc ph-c coo y ollowg h oluo o bouy coo o ll pl cg coc h p o couc gl-l po o h ol c l o ggg o wo ph whol Th p po o gg ow copl wo-ph cg oluo O pcul h o c l I h l ppoo»» w h co co h [ h ] h [ h ] 7 Rg o coo coo c O how g h ol c l c lo b p VW wh y pl oo olg oly pl ph Th bcu h lo o VW bw plc coo y h obouly coc ypoc o l h o: co 7 co 7 co 7 co 7 ubug h bo quo o quo 6 ug boh quo ogh yl h ol c lcc l h o [ ] 75 Tol wh [ ] co co co co co 76 77
6 g ol bc co-co h pl o plly bu lcc ph h cg gl o ε g ol bc co-co h pl o plly bu lcc ph h cg gl o ε g 5 ol bc co-co h pl o plly bu lcc ph h cg gl o 5 ε co co co co 78 co co co 79 co co co co 8 co co co 8 O h c o o coly u by h bc co-co Th bc co-co l Tol π τ σ 8 wh h u co τ og h co o polo o h c h obo po Wh τ h h co Tol h ol bc co-co g by π σ 8 Th ol bc co-co h pl ob by ubug π pcly o q 8 o h bccg co-co wh π π h copog ol bc-cg co co π σ 8 Th ol bc co-co p h pl plo o h plly bu lcc ph u h cg gl bw º 9º copog o cc o wll o bul g 6 ol bc co-co h pl o plly bu lcc ph h cg gl o 5 ε Loo : I cg o Dlcc ph lly bu Gou l Ug Rl uco wo
7 C OURL VOL 9 O OVR g 7 ol bc co-co h pl o plly bu lcc ph h cg gl o 75 ε g 9 ol bc co-co h pl o plly bu lcc ph h cg gl o 5 ε g 8 ol bc co-co h pl o plly bu lcc ph h cg gl o 75 ε c gu how h ol cg co-co o ph o lccl u bul c l lcc co ε ε uho gu cop h ucl ul o h coucg ph g o h gou pl h p by couou-l cu wh h lcc ph wh l py ε ε p by h bo-l cu o-l cu pcly Th h cu h lo h bho cp o oc h occu 79 o 8 o o h o-coucg ph h pl I c lo b h h gu o h bccg co co o h lcc c low g o boh pl gu 5 6 how h ol bc co-co o h lccl u l lcc co bu wh bul c o 5 I pp h h lcc ph ow how uch gc oc bho 78 8 o gu 7 o how h ol bc co-co o plly bu ph o lccl u wh h l lcc co bu wh bul c o g ol bc co-co h pl o plly bu lcc ph h cg gl o 5 ε 7 5 pcly I c b h h bho o h cu h bco w lccl u o h ph c T URL TWORK ROC Rl b uco R g o cl ul wo h l 98 ow h oo ch uch ol p cogo chqu o pl pol uco clug ucol ppoo pl polo u ol Th cll ppoo cpbl h b u by bg [] oggo Go [] Du o h ol ppoo pop R wo bl o ol copl ppg whch pcpo ul wo c oly ol by o ulpl y ly I o o h l pyε h lccl u h bul c o h ph λ λ o h ph pcly w ploy h l b uco wo how chclly g Th wo co o h
8 Loo : I cg o Dlcc ph lly bu Gou l Ug Rl uco wo ly; pu ly h co o ou o pu h ly ug Gu oly uco oupu ly wh h oupu ch h u p gl l b uco wh oc c poo wh uch h u o o co o l ch oupu u po wgh uo o h h u ug h ω wgh Th ou o pu h pu ly h l gy lu o h copu c l copl coc o h T & T & polo c whl h oupu h lccl u bul c o h ph wll l py Th wo g o po ol ppg o h pu ly o h h ly whch h ollow by l ppg o h h ly o h oupu ly o h w choo uco y wh h ollowg o: 85 y ω bl p h pu co whl ol uco ow h l b uco h co o Gu uco / σ c ucl o Th ow po o b h c o h l b uco Th g o h wo clu h lco o h wh p σ h wghg uco ω uch h h c bw h wo oupu h oupu Th g o h wo wll b cu h co ollow by h oo o h g ul co 6 5 TWORK TRIIG I o o u Rl uco wo w o pcy h h u co uco h ub o pocg u co o olg g g lgoh o g h p o h wo g h h o R wo p h c h wh h wgh cll wo g Th wo cgo o g lgoh: up uup R wo u ly up pplco I up pplco w po wh o pl cll g o whch h copog wo oupu ow I h c h wo p ou uch h hy co uco: 86 { y } wh h ol ub o co o h g h g lu o h oupu co y p h oupu co oc wh pl o h g I Gu b uco u o h co uco o c po ochc g c ly ob h up quo: ω y { y } ω σ σ { y } ω σ wh h lg 89 I uup g h oupu g o lbl o h g g O o h ppoch gg b uco o ch o h pl Th oluo po o b p o oy qu h ub o p Oh ppoch choo oly o u ow h h u wgh clcul h oupu wgh ω by olg y o quo who oluo g h g Th o qu h ppoch copuolly p coul cu ucl pobl c uo wh h gul o R wo g h gh ub o p cucl Th ol yg o h opl ub o h u c h ly o h c o g w h u o og g u po o cw lo ow lco wo wy o pug gowg R wo I bcw lo wo couc wh ll h bc uco h c pool ch p h u h l c h o l o h wo g h pocu cou ul o ol lco co op cg h po h coply o h ol u uc o p h ulyg uco coply I ow lco o g l wo coguo c pool o b uco; ypclly Gu c h g po ch p h h b uco u whch c h o o uch u-quo o o h c pool o h wo Though ow lco ol opo chqu h h g o o hg o h ub o h u c cbl ol lco c copuol ccy Th poco o h c wh h u h b g by T 9 T wh h colu o h g Φ copog o h o cly cu h
9 C OURL VOL 9 O OVR u Th uco h u-qu-o u o h o o h u g by y 9 T Th u whch uc h u-qu-o o h cho c Goclly h wll b h u who copog b co o cloly lg o h ppcul o ŷ o h cu - ol pc Though h u-qu-o uc o h u h ol lco co wll ch u bo cg g Th h po wh h poc opp ow lco lly lgoh bu c b p up uh ug chqu cll ohogol l qu [9] Th G- ch ohogolo poc [5] whch u h ch w colu o h g o h gowg ub ohogol o ll pou colu Th pl h quo o h chg uqu-o ul o c lgoh y c b co o h pouc o wh ohogol colu whch upp gul I pcul h g p R c b co o ~ U 9 wh ~ ~ ~ ~ p [ h h L h ] R h ohogol colu ~ T ~ h h U R upp gul Wh cog whh o h b uco ~ copog o -h colu o h ull g ~ h poco o h pc ly p by h colu o h cu g l Oly poco ppcul o h pc ly T ~ ~ h ~ 9 ~ h T ~ h h c cobu o uh uco h g o h uco T ~ y 9 ~ ~ T Copuo o h chg u-qu-o low cop o h uol o g quo 9 Th h b o h c ccy o ohogol l qu ll oh cy o h colu o h ull g ohogol o h pc p by h colu o h gowg g o up h upp gul ~ lc h w ohogol ull g ~ ~ T ~ ~ ~ 95 ~ T ~ h upp gul up o ~ T ~ ~ T U 96 U T O ~ Illy U Th ohogol opl wgh co ~ T ~ w~ T y 97 h uohogl opl wgh quo h l by w U w~ 98 6 TWORK IULTIO RULT Th g g o h popo Rl uco wo w c ou ug TL cp h Rl uco wo wh o cho lg w o h o h lg g o lu h wo Th lg qu 5 c pl lu o ch o h h oupu Tho 5 pl qu h lg Th g o h lccl u o h g ph o λ o 5λ Th g o h bul c o o hl bu h coucg gou o g o h uc o h coucg gou whl h g o h l py ε o o 9 ch o h pl hol o pu g oupu Th o pu : : Rl lu o c l coc o T polo c: l l : Rl lu o c l coc o T polo c: l l : Igy lu o c l coc o T polo c: g g : Igy lu o c l coc o T polo c: g g wh Th hgh h o o h hgh h ccucy o h oupu h lg o h ppg uco c bco y coly o lu hl h coc o o up o h o w uc o g o ph wh lcc u λ o 5λ lly h u o oly o o h c l coc l wll ul poo poc Th ul plo g o 8 gu how h R wo bul c o h ph wh lcc u
10 Loo : I cg o Dlcc ph lly bu Gou l Ug Rl uco wo g bolu o % o l o ph u % g R wo bul c ε 5 g bolu o 59 g l pcg o 95% g R wo lcc u 5 ε 5 g bolu o 67 % o l o ph u 67% g R wo bul c ε l py ε ε pcly Wh bul c h ph hl bu h coucg gou wh bul c h ph ouchg g o h coucg gou o h ul plo g g h bul c ou o b y ccu h pcg o o h bul c l o h ph u l h % gu how h R wo lcc u o h ph wh bul c 5 l py ε pcly Th wo g poo pco ε ul wh h lccl u o h ph blow clo o o wh h ph ppg Whl gu 5 o 8 how h R wo co o h ph wh lccl u bul c g bolu o g l pcg o 7% g R wo lcc u 5 ε 5 5 pcly pc h ph p y clo o h g lu 7 COCLUIO Th p o h pp cb c oluo o h pobl o cg by plly uc lcc ph g o gou pl Th bc co-co ul w ob o ou lccl bul ph o h uc ph l py o h ph c h u c pc o h ph uco o h l lcc co o h l o h ph ε I obou h h p oluo houl o h o coucg ph plly bu gou pl ε
11 5 C OURL VOL 9 O OVR g bolu o 8 g l pcg o 8% g 5 R wo co g bolu o 6 g l pcg o 6% g 7 R wo co 5 g bolu o 8 g l pcg o 8% g 6 R wo co 5 uho h oluo houl o wll ow oluo o h pcl c wh [] Copg o lycl ucl chqu h popo ho o ug ul wo cg pl ghow g c o o qu o cuc lo o gphcl o ho o h p o h ph o h copu ulo ul h popo ho h po c pcg h o-l lo bw h c l coc pu h ph p oupu Th wo h uccully h bul c u l py o h lcc ph plly bu coucg gou g h cg coc o h c bo byo h poc o h popo R wo popool o h ub o lg pl g bolu o 7 g l pcg o 8% g 8 R wo co T ho by cg h ub o lg pl b pco o h wo wll b ch CKOWLDGT Th uho wh o cowlg h cl c o h ol cc ouo RRC [] -K lcogc cg by lcc ph plly bu pl C oul o hyc ol 8 pp [] C u Dc cg by ph o bl o co oul o hcl hyc ol o pp
12 Loo : I cg o Dlcc ph lly bu Gou l Ug Rl uco wo 6 [] yl D Wb L ol cg I oul o ppl hc 59 pp [] I T Ro T V Youl & TDTbou I cg ug h -l ho ol opo Tchqu I T O cow Thoy Tchqu ol 7 o pp [5] -K ul-wo ppoch o h -cg pobl o ccul coucg cylcl c cow Opcl Tch L ol o 6 pp [6] Co Ro cg ppoch b o ul wo chqu o h co o lcc cyl bu loy hl-pc og lcogc Rch o 6 pp 69-9 [7] Co Gb lcogc co o lcc cyl by ul wo ppoch I T o Gocc Ro g ol [8] X Gog Y Wg ul wo ppoch o h cow cg pobl wh g-pg gulo Ro cc ol 6 o 5 pp 85-8 [9] Ch C Cow G Ohogol l qu lg o l b uco wo I T O ul wo ol o pp [] Y L Xu lcogc cg by ggg o ph: l ppl Opc ol 6 pp [] W bg Ul ppoo ug l b uco wo ul Copuo ol pp [] T oggo Go 99 wo o ppoo lg oc I ol 78 o 9 pp 8-97 [] o lcogc Thoy cgw- ll w Yo 9 [] h R Ro Ry opcl cg by wo ph ch l Ubg ol pp 5-97 [5] R o C R oho ly Cbg Uy Cbg UK 985 DIX Xu co lo o ho coc: pq pq pq pq p p pq p co pq p p p pq pq pq pq b p wh p p p p pq p co pq pq p p pq p p p p p b p h Gu coc g by!! p! p p!! p! p p wh h ybol h o-cll Wg - ybol Th g p h uo h lu - - Chy-w Loo c h g h g boh lccl gg o h Uy o ouh lb Culy h hd u h Dp o lccl gg Uy o pp ch o g cg chl Gu o cgll Uy ol wh g Dg 96 g Dg 96 o h Uy o Tooo wh hd g 966 ll lccl gg o h Uy o ob 965 wh h bc oo o lccl gg o h Lbooy w Vg oo h Uy o Clo D Cl lo ply oo o lccl gg h Uy o ouh lb p p o h Iol cow ow Iu llow o I I publh cl 5 p
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