Modeling and Simulation of Visible Light Scattering Properties of Spatial Object Using STK

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1 /2013/33(2) Chin. J. Space Sci. ρ»ο""fl Li Yanjie, Jin Guang, Zhong Xing. Modeling and simulation of visible light scattering properties of spatial object using STK. Chin. J. Space Sci., 2013, 33(2): _Ξ STK PjbsHicYtu x fq±tω *,( 1,2 ) ' (*K<K 9KGK*lo4r PN/a 9K ) 2(*K<K XK fl( ) Λ Ψ1slFJD4fi i5 UA M.o:S2ff?, W^ln STK islh4cωyßl19 l Yu<. HiT+ffi1ο'RS (BRDF).[ Yu<, ον^cωyßnvi>ffif+1ka; 32yß xwψ?btu»a.[l WyßxWu<, Λ(u<&?nvbο, `^CΩyßΛslD4fi &ygi l19l Y<D; ψyfl974ω (STK) o:ies yßfl9 D4fl9) ibfis2, W^ln STK i]nρ#iyß9l Yu<, ΛMu<&?>U» Uον, "qhffi1 Yu<&? fi. ψmflr, BRDF u<gbiχff fl$ hffi1u<5flffi RΛfiψψ-, 5#Yyßfln*`i> ka, M, q STK i ψy~i, AΩ>5Π FffiqigyßA D4< t&fil19l. XdM CΩyß, sld4, T+ffi1ο'RS, l19l, Satellite Tool Kit (STK) fiyuk V 556 Modeling and Simulation of Visible Light Scattering Properties of Spatial Object Using STK LI Yanjie 1,2 JIN Guang 1 ZHONG Xing 1 1(Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun ) 2(University of Chinese Academy of Sciences, Beijing ) Abstract For supplying the space-based optical observation system designer with referenced data, equivalent magnitude model of spatial object is established using STK. First, the visible light scatting characteristics of spatial object surface cell is analyzed by using BRDF five-parameter model. Second, combined with the characteristics of object shape and material property, the configuration model of space target is built, and formulation of equivalent magnitude computing model of space object is carried out by analyzing every single surface cell. Last, Satellite Tool Kit (STK) was used to provide relationship among sun, space object and observation satellite to simplify the solving of KΛ,yON/ΨΦ c(z:4 (2011AA ) Mcx-, McDz- liyanjiehao@yahoo.cn

2 ff#ν : $ STK fflρ»flffiß ffiχψ!μfi% & 189 the formulation, and then, a new magnitude computing model based on STK is established. It was verified with one example and some analyses. The result displays that the new model is much more precise than the diffuse one. Besides, the results show that the best observing time and the corresponding magnitude can be easily solved with STK. Key words Space target, Space-based observation, BRDF, Equivalent magnitude, STK 0 co 1996 kjφ0hbψ) KPfi8 (Midcourse Space Experiment, MSX) /U ]=flei *fl (Space-Based Visible, SBV), rkbψxο 3 L-9Bfi( [1]. % mpkbψxο I, rkb Ψxο I%Npοfid C3ff% pοwffik" &, 3lffWjG. rkbψxο=fle*0j@ %>»tt L-, =ΦrkEIg3ff BΨxοχ>TΨ$)_j@%, W± [0 DΨfim9χhfl0d. ffl$φ", ZΞIfflZ r kg3bψxο%>]νμt, WΞ νxο fimiφo'hgfl0fim (J$m) [2 3] j]no /fim [4], fflω9χfiχfi8fimfl0e~xh7 `@. ffi! [5-8] BΨxοfim=flE*0j@% >]8%L-, b% BRDF )χppxοh=fle *0BΨν&,!D]xοh=flE*0 ~pxο AS fimj@ C3ß~ C35NflΨhAff, il0d3phkm BRDF zxfi8e*0 ~ h»t Ω, %~=;flgbψxο C3%xF hk08k. ffib% BRDF -Zt;)χpPBΨxο muh=fle*0j@, z;210yhxοwvχ χx STK 0DhdRsC3fi 8 xο pcοff)h=;ff%,»v]==;ß "hbψxοk08kzxt;. 1 ff@ H-3mCρß BΨxοfim)_j@ ff%, Sh BRDF -Z BRDF -Zt;fiVCΦ [9] kr 2 cos α f r (θ i,θ r,φ r )=k b 1+(kr 2 1) cos α exp[b(1 cos γ) a ] G(θ i,θ r,ϕ r ) cos θ i cos θ r + k d cos θ i. (1) C), θ i,θ r,φ r νχφxοmu/h%0rwß C 3rwßT% ffß; k b,k d,k r,a,bφp)_la hzy-z; k b Φ,fl0ffR; k d Φgfl0ffR; α Φ±C.ΠmΩ#pxοmuΩ# *h ß, γ Φ ±C.Πm pcοff)h%0ß. fi8fimt h=fle*0 ~ [6] I S (θ i,θ r,φ r )= f r (θ i,θ r,φ r )E(0 )cosθ i cos θ r ds. (2) Ψ), E(0 ) Φ# nm }hdre 0 %0 xοfi8mu;hffi0ω~, wnνwffi6 hdr E ffiω~qr '# h#8%>pν, =ßfΨ χφ W m 2 ;ds ΦT mp. 2 ffn2:n}[ mxοfimhjw..mu, Ψ%0ßTC3 ß =~%z, al, E xο%>wv»t, 21= 7T)_ wvt;%>> Tmuaν, zxj. mu C3 */h=fle*0 ~, νj.muh *0 ~%Ξ, Y%;Cv=ßfC3%xFhk0 8k. 2.1 rg`^eo "VBΨxο =:ΦHοp y2p 8 p y8pkfi[wv=phvξ. ffi,h MAT- LAB h V-Realm ' xο%>wv»t (fl~ 1), fi81pkw.ß ptw.y2p>;, fi8ß py26dym0=dr~fi.»vxο pc οff Oxyz BΦνμhk9Cοff. wsφfi8x οh'6, Oz wncοws, Nxοfi8h'6!* p6; Ox wncοws, ffmidπm}jffim Oz, py*7ffl!* % *; Oy JffimIdΠ m,!*idßw~h& *.

3 190 Chin. J. Space Sci. ρ»ο""fl 2013, 33(2) 1 yßxwu< Fig. 1 Object geometry model 2.2 VΦRaw [y2pe*0νμφtiuqxοffi0 ~ zx Ω. =[νy2p:φw.3l n ulhl 2, Ψ) n ffmfflνw, n L2p)»V;Cο ff Ox 0 y 0 z z 0 0pwWL2mΩ# *.X, $ ~ 2 `E. ;Cοff=[:ΦHνxοh pcο ff Oxyz ΠYTF5fah, F50νkfi8hwV >;6y. F5Cοffhy_Φ R x (θ) = 0 cos(θ) sin(θ), 0 sin(θ) cos(θ) cos(θ) 0 sin(θ) R y (θ) = 0 1 0, sin(θ) 0 cos(θ) cos(θ) sin(θ) 0 R z (θ) = sin(θ) cos(θ) Z N o TdR%0 *?Z N s Ox j y j z j )μφ n o = R x ( α j )R y ( π 2 n S = R x ( α j )R y ( π 2 ) N o, ) N s. =[ßD r j.2m)dr%0rwß θ i TD0 rwß θ r [s% ffß φ r. ] θ i,θ r 7 (0,π/2) ffl };, 'm+~ C3a, 'm C3 */h E*0 ~Φ I sj (θ i,θ r,φ r )=f r (θ i,θ r,φ r )E(0 )cosθ i cos θ r S sj. (3) fl±'m C3 */he*0 ~=!Φ 0. BΦLrdR~h6%, kmdr%0 *]fi 8}>;Ψ)μ, dr~fi V!xοfi8 pcο ff y 0=;F5 (fl~ h* EmΩ# *pre%0?zb+ff>@. ß, Π Ψ), R k (θ) fie! k 0ß*F5 θ ß. χx~ 1 = fi, ~ 2 ) n L2hCοff Ox 0 y 0 z 0 =:ΦH! y 0ß*F5 90 fah. m~ 2 )k92mhr j.%a2m, =ν k92mω# z 0 0! x 0 0&*F5 α j ß$a' r j.2mhω# z j F, 4L;'m/hCοff Φ Ox j y j z j, F50νΦ R x ( α j ), R α j =2πj/n. kmbψxοas% mdr xοtc3ff flψh5niuz., =[^e. ±g3 *? 2 n M3? Fig. 2 Prism of n edges

4 ff#ν : $ STK fflρ»flffiß ffiχψ!μfi% & 191 ffiemfflω Ω0a, al, dr~fi #l*em %xfhffiω~l=!. ΠdR~fi hcοffp dr%0ß~=;%a. =k STK n9hre%0 *?ZzXfaμf0νΛNΠfadR~fi E*0 ~hzx Ω. /> h/mπ/p C%>E*0 ~z X, ±%xfh=ffiω~zx;cφ E(θ i,θ r,φ r )= m s n I sj (θ i,θ r,φ r ) j L 2. (4) Ψ), m Φ>.R, L ΦC3fi8pxοfi8Ψh 5N. 2.3 Q v Qaw hk0i8kifierph ~. k08ky_ ΦY.EwZ%7 100 fflh8p, Ψ ~%7 5. 8k. ffidrφ-;8, k0i8kφ 26.74, Ψ =fle# }hω~φ E o, mhω~φ E m hbψ xοhk0i8k Q Φ Q = lg(E m /E o ). (5) 21C (5) =νxοfi8 C3%xFhffiΩ~5 dφk08k. 3 μ ρß 3.1 rggwkl]~xznkl 4 y ~ 1 `Et ;)dr~fi has Φ 20 mm 6000 mm 2350 mm, :*drhwmv ldr~t@, vfi 1 )h)_ 3, ffimfflω Ω 0a, E*0 ~ffl=!. 1p)hß p> A SΦ 2250 mm 2250 mm 2250 mm, y2p> Φ π 700 mm 700 mm 2000 mm, fflfimhψ $)_νχφfi 1 )h)_ 1 T 2. I 1 Jn BRDF Lmp OLmff Table 1 Parameters value of BRDF five-parameter model fl9fln*` k b k r b a k d *` *` *` ±4BΨxοhId2RΦ: a = km, e =0.0011, i = , Ω = , ω = , M = Ψ), a ΦId8Φ0, e Φ 6d, i ΦId»ß, Ω Φ:οsC+, ω Φ'6s!ß, M ΦΠ'sß. Gffi MSX fi8h}>idbφc3πc}> Id, ΨId2R$fl: a = km, e =0.0008, i = , Ω = , ω = , M = SΨaw STK )4%%ehId-RT Qu, S h STK wv?z63,»vxο!*drtc3 ff h?z, ShΨ)h Report 63, 9;BΨx οheω;ψtg3fl=g3;ψ (g3fl% p οfi^), fflοrvφbψxο=c3;. ffiψ ) :36:00 UT 07:10:00 UT ΦT%>z Xνμ, fdl;ψ_ }dr%0?z N s TC3?Z N o ];Ψhμd. ν/-r_% MATLAB Πcv=faxοfi8 C3%xFhC3ffiΩ ~Tk08k]C3;ΨhμdAff. νxο:bgfl0p, gfl0pmuh=fle* 0 ~Φ I(θ i,θ r )=σe(0 )cosθ i cos θ r ds/π. (6) Ψ), σ Φgfl0ffR, ffixοh8 p> y2 p> TdR~Π hgfl0ffrνχφ 0.8, 0.4, νc (6) Y%C (4) TC (5), xοhwv» t > smuaν Cοff5f Ω%μ. ztχ X STK n9h%ar1, Y% MATLAB Πc, v=faxοfi8gfl0t;hc3ffiω~tk0 8k];ΨhμdAff. 3.3 SΨg[ΠU ~ 3 0D]]%0rwßΦ 10, 30, 45, 70, % ffßφ 0 ;, }h -Zt;fDhxοfi m)_ BRDF χ]c3ßμd G. k~ 3 =fi, w3jyhc3ß~, (,)_7Q,)fl0, Ψ ), 8 p> h,)ffχ@+, dr~fi h,) ffχ@o. p)_ 7j@lA.

5 192 Chin. J. Space Sci. ρ»ο""fl 2013, 33(2) ~ 4(a) ΦShgfl0zXt;T ffi BRDF x ο8kzxt;fdhxο C3%xFhC3ffi Ω~]C3;ΨhμdAfffi#, ~ 4(b) ΦSh Y,t;fDhC3%xFhk08kp;ΨhA ff. k~ 4 =fi, C3; }, Y,t;fDhμd G%V, Uq ffi BRDF 8kzXt;Hßχh; min, BRDF t;fdhffiω~dχffχ, fi #ffgfl0t;fifl, "XxοfimΨ$)_Q, )fl0 *0j@% hf=; C3h 8 16 min, xο %xfhffiω~w]φ 0, k08kfflνw, v%~c3axο, Uq ψl;xοfi8 drω 0, g3fl% pοfi^, #ile*0% C 3 Fig. 3 3 )-*` BRDF ψ^&1ue1sxρiνeμh BRDF of three different samples varying with the incident and received zenith angle Fig. 4 4 yßοqχff q<ωibfi (a) tl19lq<ωibfi (b) Target satellite irradiance variation with time (a) and the equivalent magnitude variation with time (b)

6 ff#ν : $ STK fflρ»flffiß ffiχψ!μfi% & 193 ff. al, wn ffih»t Ω=hfxο@ g 3; [s%ehk08k. L, eh STK =[EW=χ"^;Ak08 khzx, ffflψb»t Ω4Ξ»Efl. 4!f b% BRDF -Zt;)χpP]fi8fimm uh=fle*0j@, 210yhxοwVχ>AS wn xοfim Π=7T)_%>muaν, jw.mu%>ν μ vξ,»v]km BRDF -Zt;hrkC 3)xοfi8k08kzXt;. [xοfidt;φ T, GΠ%Afi8hId-Z, Y% STK, νμ ]xοfi8 C3%xFhffiΩ~Tk08k. wn νχlpgfl0pt;%> ff, Φχ BRDF t; hfi#ffφfifl, Q ffχχ,, Uq ffit;p fim)_h=~@'4ξ%". L, p STK χx, =[4»phf"^Idxο"^;AC3ff %xfhk0i8k, I djdkn9r1ρ>. Khz} [1] Zhou Yiyu, Li Jun, An Wei. Information processing technology in optical space-based space surveillance [J]. Opto- Elec. Eng., 2008, 35(4): In Chinese (/Xs, Q8, ΞD. tmgkdffzρφj7ρhpyoßο [J]. Gu8=, 2008, 35(4):43-48) [2] Harvey J B, Vemold C L. Transfer function characterization of scattering surfaces revisited [J]. Proc. SPIE, 2004, 3141: [3] Zeng Dexian, Du Xiaoping. Analysis and simulation of characteristics of space objects for space-borne optical sensor [J]. Chin. J. Space Sci., 2008, 28(6): In Chinese ( effi, }/±. DffzρΞtmGKi5*jlBßο r» [J].Dff<KKfi, 2008, 28(6): ) [4] Liu Jianbin, Wu Jian. Light scattering of spatial target [J]. J. Astron., 2006, 27(4): In Chinese (cμψ,. DffzρjG,2N/ [J]. sskfi, 2006, 27(4): ) [5] Wu Zhensen, Dou Yuhong. Visible light scattering and infrared radiation of spatial object [J]. Acta Opt. Sin., 2003, 23(10): In Chinese ( μ., Ft. Dffzρj?fflG,2r Λψ2 [J]. GKKfi, 2003, 23(10): ) [6] Cao Yunhua, Wu Zhensen, Zhang Hanlu, et al. Research on light scatting of spatial targets based on spectral BRDF of target samples [J]. Acta Phot. Sin., 2008, 37(11): In Chinese (1 `, μ., ΨPE, m. mop0uλ GΦ BRDF jdffzρ?fflg,2n/ [J]. G<Kfi, 2008, 37(11): ) [7] Wu Ying, Yang Ling. A method of modeling spatial objects visible light scattering characteristic [J]. J. Harbin Univ. Sci. Tech., 2009, 14(2): In Chinese ( d, Q b. Dffzρj?fflG,2lBμvr»N/ [J]. O±!P 8XKKfi, 2009, 14(2):82-85) [8] Zhang Wei, Wang Hongyuan, Wang Zhile, Sun Chengming. Modeling method for visible scattering properties of space target [J]. Acta Phot. Sin , 37(12): In Chinese (ΨΩ, Ξ[z, Π(K, _<s. Dffzρ? fflg,2lbμv ffn/ [J]. G<Kfi, 2008, 37(12): ) [9] Wu Zhensen, Xie Donghui, Xie Pinhua. Modeling reflectance function from rough surface and algorithms [J]. Acta Opt. Sin., 2002, 22(8): In Chinese ( μ., 5 g, 5Ξ`. P0ffioqG,2} μvuffzff [J]. GKKfi, 2002, 22(8): )

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