wth Modfed Suface-nomal Vectos fo RCS calculaton of Scattees wth Edges and Wedges N. Omak N. Omak, T.Shjo, and M. Ando Dep. of Electcal and Electonc Engneeng, Tokyo Insttute of Technology, Japan 1
Outlne. Backgound. wth modfed nomal vecto (Modfed ). Objectve v. Smplfed suface-nomal vectos fo RCS Accuacy check fo edge (sample: 2D-stp) fo wedge (sample: cone eflecto) Analytcal explanaton of the accuacy ffo 3-D D objects compason wth expements and PTD (sample: Cubes) Concluson Hghe accuacy ( ) ) than 2
Backgound Physcal Optcs () easy algothm no sngulaty eo nea edges H : ncdent wave nˆ : unt nomal vecto 3
The Empcal Idea to Intoduce the Modfed Suface-nomal Vectos Scattee Infnte plane E d dffacton eo 1 2πk ρ jkρ j 4 ( D D ) e = Ε π Souce Incdent feld : H Nomal vecto : ˆn Modfed nomal vecto : nˆ Obseve Fcttous plane s E = J S J exp ( jk ) o o = 2nˆ H ds Modfed J = 2nˆ + 2 ˆ H n H ( H = H 2 nˆ ( H n ˆ )) 4
Outlne. Backgound. wth modfed nomal vecto (Modfed ). Objectve v. Smplfed suface-nomal vectos fo RCS Accuacy check fo edge (sample: 2D-stp) fo wedge (sample: cone eflecto) Analytcal explanaton of the accuacy ffo 3-D D objects compason wth expements and PTD (sample: Cubes) Concluson Hghe accuacy ( ) ) than 5
Defntons of the Modfed Suface-nomal Vectos Reflecton component Reflecton egon Souce Shadow component Reflecton egon Souce n n k n n Obseve kd φ d φ Obseve kd φ d φ nˆ = kˆ ˆ d k kˆ kˆ d Scattee nˆ = k k d d k k m m -n Scattee km Shadow egon Shadow egon Image Lne cuent Obseve Lne cuent Statonay phase pont Stp 60deg Statonay phase pont Stp -60 deg Mo Modfed J = 2nˆ + 2 ˆ H n H ( 2 H = H nˆ ( H n ˆ )) Obseve 6
Pocedue to ntoduce the modfed suface-nomal vectos n the Reflecton component Shadow component Equvalent cuents I J M = nˆ H = E nˆ = 2n ˆ H + J M = = nˆ H E nˆ Dffacton coeffcents Dffacton coeffcents GTD Equvalent cuents φ + φ φ φ d d sn sn 2 + 2 φ + φ φ φ d d cos cos 2 2 1 1 + φ + φ φ φ d d cos cos 2 2 ( H ˆ ) M J = nˆ + ˆ 2 ˆ H n H n n 2 Modfed φ + φ d sn 2 φ + φ d cos 2 1 φ + φ cos d 2 J = ˆ n H M = ˆ E n + + + φ φ d sn 2 φ φ d cos 2 Modfed nomal vecto 1 φ φ d cos 2 J = ˆ n H M = ˆ E n 7
Eo coecton of Fne ageement at all angles Refeence fom Shjo et al.[2]) 8
Outlne. Backgound. wth modfed nomal vecto (Modfed ). Objectve v. Smplfed suface-nomal vectos fo RCS Accuacy check fo edge (sample: 2D-stp) fo wedge (sample: cone eflecto) Analytcal explanaton of the accuacy ffo 3-D D objects compason wth expements and PTD (sample: Cubes) Concluson Hghe accuacy ( ) ) than 9
Smplfcaton of the Modfed Sufacenomal Vectos n RCS Reflecton component Shadow component nˆ = kˆ ˆ d k kˆ kˆ d nˆ = kd k m k k d m Modfed J = 2nˆ + 2 ˆ H n H ( 2 H = H nˆ ( H n ˆ )) Ognal suface-nomal vectos J = 2nˆ H 10
Outlne. Backgound. wth modfed nomal vecto (Modfed ). Objectve v. Smplfed suface-nomal vectos fo RCS Accuacy check fo edge (sample: 2D-stp) fo wedge (sample: cone eflecto) Analytcal explanaton of the accuacy fo 3-D objects compason wth expements and PTD (sample: Cubes) Concluson Hghe accuacy ( ) ) than 11
Samples Applcaton of the Modfed to RCS (monostatc( monostatc) TARGETS 12
Smplfcaton of the Modfed Sufacenomal Vectos n RCS Reflecton component Shadow component nˆ = kˆ ˆ d k kˆ kˆ d nˆ = kd k m k k d m Modfed J = 2nˆ + 2 ˆ H n H ( 2 H = H nˆ ( H n ˆ )) Ognal suface-nomal vectos J = 2nˆ H 13
Accuacy Check fo a 2D stp (E polazaton) 30 RCS(dBlm) 20 10 0-10 MoM GTD Modfed -20 0 15 30 45 60 75 90 Angleθ (deg) 14
RCS(dBlm) Accuacy Check fo a 2D stp (H polazaton) 30 20 10 0-10 MoM GTD GTD (1st ode) Modfed -20 0 15 30 45 60 75 90 Angleθ (deg) 15
Samples Applcaton of the Modfed to RCS (monostatc( monostatc) TARGETS 16
Modfed Suface-nomal Vectos fo a Cone Reflecto n RCS Reflecton component Shadow component nˆ = kˆ ˆ d k kˆ kˆ d nˆ = kd k m k k d m Modfed J = 2n ˆ + 2 ˆ H n H ( H = H 2 nˆ ( H n ˆ )) Ognal suface-nomal vectos J = 2nˆ H 17
Accuacy Check fo a Cone Reflecto (E polazaton) RCS(dBlm) 30 20 10 0-10 edge2 GTD Modfed edge1-20 0 15 30 45 60 75 90 Angleθ (deg) φ 18
Accuacy Check fo a Cone Reflecto (E polazaton) RCS(dBlm) 30 20 10 0-10 edge2 edge1 GTD Modfed -20 0 15 30 45 60 75 90 Angleθ (deg) φ 19
Accuacy Check fo a Cone Reflecto (E polazaton) RCS(dBlm) 30 20 10 0-10 edge2 edge1 GTD Modfed -20 0 15 30 45 60 75 90 Angleθ (deg) φ 20
Accuacy Check fo a Cone Reflecto (H polazaton) RCS(dBlm) 30 20 10 0-10 edge2 GTD Modfed edge1-20 0 15 30 45 60 75 90 Angleφ (deg) 21
Accuacy Check fo a Cone Reflecto (H polazaton) RCS(dBlm) 30 20 10 0-10 edge2 GTD Modfed edge1-20 0 15 30 45 60 75 90 Angleφ (deg) 22
Accuacy Check fo a Cone Reflecto (H polazaton) RCS(dBlm) 30 20 10 0-10 edge2 edge1 GTD Modfed -20 0 15 30 45 60 75 90 Angleφ (deg) 23
GTD dffacton coeffcent s h = D D D Dffacton coeffcent fo wedge wedge D s h π sn n 1 1 = n π ( φd φ) π ( φd + φ) cos cos cos cos n n n n Dffacton coeffcent fo edge edge D s h = 1 1 1 2 φ cos d φ φ cos d + φ 2 2 24
Smplfcaton of the Modfed Sufacenomal Vectos n RCS Reflecton component Shadow component nˆ = kˆ ˆ d k kˆ kˆ d nˆ = kd k m k k d m Modfed J = 2nˆ + 2 ˆ H n H ( 2 H = H nˆ ( H n ˆ )) Ognal suface-nomal vectos J = 2nˆ H 25
Modfed Suface-nomal Vectos fo a Cone Reflecto n RCS Reflecton component Shadow component nˆ = kˆ ˆ d k kˆ kˆ d nˆ = kd k m k k d m Modfed J = 2n ˆ + 2 ˆ H n H ( H = H 2 nˆ ( H n ˆ )) Ognal suface-nomal vectos J = 2nˆ H 26
Defnton of n Vectos fo Shadow Component Patten1 Patten2 27
Accuacy Check fo a Cone Reflecto (E polazaton) 5 edge2 GTD (wedge) (edge1+edge2) Modfed edge1 30 20 edge2 GTD Modfed edge1 0 RCS(dBlm) 10 0-10 -5 0 15 30 45 60 75 90 Angle Angleθ φ (deg) Dffacton coeffcent -20 0 15 30 45 60 75 90 Angle Angleθ φ (deg) RCS analyss 28
Accuacy Check fo a Cone Reflecto (E polazaton) 5 edge2 GTD (wedge) (edge1+edge2) Modfed edge1 30 20 edge2 edge1 GTD Modfed 0 RCS(dBlm) 10 0-10 -5 0 15 30 45 60 75 90 Angle Angleθ φ (deg) Dffacton coeffcent -20 0 15 30 45 60 75 90 Angle Angleθ φ (deg) RCS analyss 29
Accuacy Check fo a Cone Reflecto 5 edge2 edge1 GTD (wedge) (edge1+edge2) Modfed 30 20 edge2 edge1 GTD Modfed 0 RCS(dBlm) 10 0-10 -5 0 15 30 45 60 75 90 Angle Angleθ φ (deg) Dffacton coeffcent -20 0 15 30 45 60 75 90 Angle Angleθ φ (deg) RCS analyss 30
Accuacy Check fo a Cone Reflecto (H polazaton) 5 edge2 GTD (wedge) (edge1+edge2) Modfed edge1 30 20 edge2 GTD Modfed edge1 Lnea 0 RCS(dBlm) 10 0-10 -5 0 15 30 45 60 75 90 Angleφ (deg) Dffacton coeffcent -20 0 15 30 45 60 75 90 Angleφ (deg) RCS analyss 31
Accuacy Check fo a Cone Reflecto (H polazaton) 5 edge2 edge1 GTD (wedge) (edge1+edge2) Modfed 30 20 edge2 GTD Modfed edge1 Lnea 0 RCS(dBlm) 10 0-10 -5 0 15 30 45 60 75 90 Angleφ (deg) Dffacton coeffcent -20 0 15 30 45 60 75 90 Angleφ (deg) RCS analyss 32
Accuacy Check fo a Cone Reflecto (H polazaton) 5 edge2 edge1 GTD (wedge) (edge1+edge2) Modfed 30 20 edge2 edge1 GTD Modfed Lnea 0 RCS(dBlm) 10 0-10 -5 0 15 30 45 60 75 90 Angleφ (deg) Dffacton coeffcent -20 0 15 30 45 60 75 90 Angleφ (deg) RCS analyss 33
Samples Applcaton of the Modfed to RCS (monostatc( monostatc) TARGETS 34
RCS Compason wth PTD 10 cm Cube @ 10GHz (E // x ncdence) 35
RCS Compason wth Expements 6 nch Cube @ 10GHz (E // x ncdence) Exp. data fom Natsuhaa et al.[4]) 36
RCS Compason wth Expements 6 nch Cube @ 10GHz (H // x ncdence) Exp. data fom Natsuhaa et al.[4]) 37
Outlne. Backgound. wth modfed nomal vecto (Modfed ). Objectve v. Smplfed suface-nomal vectos fo RCS Accuacy check fo E wave ncdence fo edge (sample: 2D-stp) fo wedge (sample: cone eflecto) Analytcal explanaton of the accuacy ffo 3-D D objects compason wth expements and PTD (sample: Cubes) Concluson Hghe accuacy () than 38
Concluson Applcaton of the Modfed to RCS (monostatc( monostatc) Smplfed suface-nomal vectos fo RCS Hghe accuacy () than Analytcal explanaton to wedge Futue wok Accuacy check to cuved suface 39
Refeences [1] J. Goto, Intepetaton of hgh fequency dffacton based upon, bachelo thess, Tokyo Insttute of Technology, Tokyo, chap.3 (2003-3). [2] Y. Z. Umul, Modfed theoy of physcal optcs, OPTICS EXPRESS, vol.12, no.20, Oct. 2004 Page(s) 4959-4972 [3] T. Shjo, L. Rodguez, M. Ando, Accuacy demonstaton of physcal optcs wth modfed suface-nomal vectos Antennas and Popagaton Socety Intenatonal Symposum 2006, IEEE, 9-14 July 2006 Page(s):1873 1876 [4] K. Natsuhaa, T. Muasak, and M. Ando Equvalent Edge Cuents fo Abtay Angle Wedges Usng Paths of Most Rapd Phase Vaaton, IEICE Tans. Electon., Vol. E75-C, No.9 Sep. 1992 [5] Robet G. Kouyoumjan, seno membe, IEEE, and Pabphaka H. Pathak, A Unfom Geometcal Theoy of Dffacton fo an Edge n a Pefectly Conductng Suface, Poceedngs of IEEE, Vol. 62, No. 11 Novembe 1974 40