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1 (Iager) Optical Propagatio KUELA Corporatio 0A5900 Copyright KUELA Corporatio 009. All Rights Reserved Derotator Absorptio [] SchrÖdiger Equatio Maxwell s Equatios Scatterig [Maxwell s Equatios] LOWRAN,MODRAN Atospheric urbulece or Optical urbulece) [ ] Navier-Stokes Equatio Maxwell s Equatios Radiatio) [] 4 (pp) 5 Coffee Break 6

2 Absorptio [] SchrÖdiger Equatio Maxwell s Equatios Scatterig [Maxwell s Equatios] LOWRAN,MODRAN Atospheric urbulece or Optical urbulece) [ ] Navier-Stokes Equatio Maxwell s Equatios Radiatio) 7 Absorptio [] SchrÖdiger EquatioMaxwell s Equatios N N O O Coffee Break(eV ev=h(=hc/c)=k c(u)(ev)=.4, c(u)(k)=4.4 O C O 0eV 0.u 0,000K ev.u,000k 0.eV u,00k 0.0eV0.0K 0.00eV.K 0.000eV.K Hz () () ()() H O H Hz 8 Coffee BreakCO u Eergy Level (c) N V ) N, V, J J(J+)J 0,000[c]= 9 Coffee Break N N O O O C O H O H XYZ)( XYZ)( 0 Coffee Break θr θr J (J + ) exp J( J + ) Coffee Break θ V exp V ( ) V = θ V exp( ) h ER J( J + ) 8π I h θ R = 8π I k ER [] I [] J h [] k [J/K] R[K] N O COK H j J=0, j =00K J =00K J N Jax8 CO Jax6 EV ( V + ) hν V hν V θv = k EV [J] V [/S] V h [JS] k [J/K] V N, O, V V= V N =00K V O =00K V

3 Coffee Break Coffee Break 4 Coffee Break COLaser0.6u K 9K 56K 95K 5404K 9K 960K 80K 5 N O HO CO )= 6 Coffee Break Vibratioal - Rotatioal Eergy level Absorptio Spectral Lies of NO 7.78 NOCO (k)(%) R Brach P Brach (), () ( () R Brach (JJ+) P Brach (JJ) RefItroductio to Molecular SpectroscopyG.M..Barrow,McGRAW-HILL 7 8 M

4 (k)(%) (k)(%) () () ) (), ( ) ( ), ( ) (), ( +) () ( ), ( ), ( ) (), () 9 M Eye Safe Laser 0 M Coffee Break Active Dipole Moet Dipole Moet Active + HO() HO() Dipole Moet HO() Absorptio [] SchrÖdiger Equatio Maxwell s Equatios Scatterig [Maxwell s Equatios] LOWRAN,MODRAN Atospheric urbulece or Optical urbulece) [ ] Navier-Stokes Equatio Maxwell s Equatios Radiatio) Scatterig [Maxwell s Equatios] Optical Scatterig otal Scatterig Cross SectioPhase Fuctio or Scatterig FuctioDifferetial Scatterig Cross Sectio RayleighMieOptical Labert s Law Extictio Coefficiet Visibility Koschieder s Law AerosolWater Scatterig Phase Fuctio 4 4

5 Optical Scatterig ad=a) 5 Mii Coffee Break rado otal Scatterig Cross SectioPhase Fuctio or Scatterig FuctioDifferetial Scatterig Cross Sectio (s) ( σs[ ] + σa[ ]) P [ W IN ] PS[ W] + PA[ W]; PS[ W] = IS( θ, ϕ)[ W ] dω sr 4π =S+A,[/sr] 4π, I S ( θϕ, )[ W ] P( θϕ, )[ sr] Sr P( θϕ, ) dω= P [ W] S I W P sr P W Sr S( θϕ, )[ ] = σs[ ] ( θϕ, )[ ] IN[ ] Coffee Break4 P( θϕ, ) dω= 4π 4π 6 RayleighMieOptical Coffee BreakMie Far Field Far Field W/^ Near FieldW/^ Mie 7 Far Field W/^ 8 Labert s Law Extictio Coefficiet SR, P [ W IN ] α = ( σ + σ ) N, α = σ N, α = σ N E S A S S A S r R[^] [ ] ( ) [. SR Φ W = S P σ + σ N par ] S dx P + σ P(0,0) P r dφ dφ = ( σs + σa) N dx Φ = ( σs + σa) N dx Φ l( Φ) = ( σ + σ ) N x Φ = Φ exp( ( σ + σ ) N x) R IN S A R IN S IN S A 0 S A Extictio CoefficietE Scatterig CoefficietSAbsorptio CoefficietA Φ = Φ 0 exp( α E x) w here α E[ ] = α S[ ] + α A[ ] [W] [/] 9 [^][par/^] Coffee BreakLabert s Law E E E Φ = Φ exp( α x) + Φ exp( α x) + Φ exp( α x) E E E Φ ( Φ + Φ + Φ )exp( α x ) 0 E 0 5

6 䋨䋵䋩ⷞ -䋱 䊶JIS Z-8(998)䇸ᾖ 䇹䈱..䇸ⷞ 䇹䈮䉋䉎ቯ 䋨䋵䋩ⷞ -䋲䋺䉮䊮䊃䊤䉴䊃䋨䌃䋩䈫䌍䌔䌆䈫䉮䉲䊠䊚䊷䉻䈱ᴺ ⷞ 䋨Visibility䋩䋺 㑆䇮 ᐔᣇะ䈱 䉕 ᥊䈫䈚䈢㤥䈝䉖䈣 䋨ᄢ䈐䈘䈏ⷞ 䋰䋮䋵ᐲએ 䇮 䋵ᐲએਅ䈱䉅䈱䋩䉕 䈪 䉎ᦨᄢ 㔌䇯 䇭䊶 ⷞ 䈫䉅 䈉䇭䊶 ภ䋺䌖䇭䊶න 䋺K 䇭 ᥊䋺 䋨ㅢᏱ 䋩 LB 䋺ᑪ 䈱ノᐲ LW 䋺 ᥊䈱ノᐲ 䈎䉌 䈢 ᑪ 䇮Ⴁ 䋨䋶䋩䉣䉝䊨䉹䊦䋨Aerosol䋩䈫 䋨Water䋩- 㸠䈖䉏䈏శㅘㆊᏪ䈱ㅘㆊ 䉕 䉄䉎ᦛ 䊶䉣䉝䊨䉹䊦䋺 ਛ䈮ṫ䈉ᓸዋ䈭 䈶ᶧ ሶ䉕 䈉䇯 䇭䇭䇭䇭䇭䇭䇭䇭䊶ᓸዋ ሶ䋺ᄢ䈐䈘䈫ಽᏓ䈲䋿䇭䊶 ሶ䋺䈬䉖䈭䈱䈏䈅䉎䈱䋿䇭䊶ᶧ ሶ䋺䈬䉖䈭䈱䈏䈅䉎䈱䋿 Ṽ䈎䉌䈱㘑䈮䉋䉎 䇮 䋨䋾䋱㱘䌭䋩 䈶Ἣጊ䈎䉌䈱 ൻ (SO)䋨䋼䋱㱘䌭䋩 ᶏ䈎䉌䈱㘑䇮 ᵃ 䈮䉋䉎Ⴎ ሶ 䋨NaCl䋩䋨䋾䋱㱘䌭䋩 䇮 ᴤ䇮 䈱Ά 䈮䉋䉎䉴䉴䇮ᾍ(C)䋨䋼䋱㱘䌭䋩 䈶 ൻ (SO)䈫 ൻ (NO,NO)䋨䋼䋱㱘䌭䋩 C = exp( α S L) C α S V = l(0.05) =.996 MF = ( LW + L B ) LW 䋩 䈱 䇭䇭䇭䇭䊶䌊䌉䌓ⷙ 䋺 శቇⷞ 㔌䋨Meteorological Optical Rage䋩 䇭䇭䇭䇭䊶ℂൻቇ 䋺ⷞ 䋨Visual Rage䋩= Ộᐲ䋨urbidity䋩 䊶MODRAN䋺Surface Meteorological Rage, Surface Visibility, Observer Visibility䇭 䉮䉲䊠䊚䊷䉻䈱ᴺ 䋨Koschieder s Law䋩 䊶ⷞ 䋨䌖䋩䈏ಽ䈎䉎䈫 䇭 ᢔ ଥᢙ䋨㱍䌳䋩䈏ಽ䈎䉎 τ X = exp( α X L) 䋺ㅘㆊ 䇭 ᥊䋺 䋨ㅢᏱ 䋩 ᵈ䋩䊶 䈪 䈜䉎䈱䈣䈎䉌䇮 䇭䇭䇭䇭䇭䇭ⷞ 䈲นⷞ 䈮䈧䈇䈩䈱䉂ቯ 䈘䉏䈩䈇䉎䇯 (ਛ 䇮 䈱ⷞ 䈲䈭䈇䋩 䇭䇭 䊶ቯ 䈎䉌䈚䈩䈎䈭䉍䈇䈇ട 䈭 㔌䇯 䇭䇭 䊶ㅢᏱ ലᢙሼ䋱 䈪චಽ䋨䋱䋰䇮䋲䋰䇮䋵䋰䇮䋱䋰䋰䌫䌭 䋩䇯 䋺ᑪ 䈱ノᐲ LW 䋺 ᥊䈱ノᐲ 䌌 ᑪ 䇮Ⴁ ᵈ䋩 䈲㕍 䇭䇭䈪䉅 ᐔ 䇭䇭ᣇะ䈲 LB ઙ䋨䋱䋩ᄢ 䈱⓹㸢ๆ 䈲ዊ 䇭䇭䇭䋨䋲䋩೨ᣇᢔ 䈏ᡰ㈩ LB C= LW LB LW + LB = l(0.0) =.9 LW C = 䉮䊮䊃䊤䉴䊃 䇭䇭䋵䋦 䇭䇭䋲䋦 LB ലᢙሼ䉕 䈋䉏䈳 䋳䈫䋴䈪䌏䌋 LW LB = C exp( α S L) L +L W B 䊶ㅘㆊ 䉕ๆ 䈮䉋䉎䈫 䈋䉏䈳䉮䊮䊃䊤䉴䊃䈮ᄌൻ䈭䈇䋨䌃䋽䌃㵭䋩䇯 䇭䈚䈎䈚䇮ᄢ 䈱⓹䈲ᱴ䈬೨ᣇᢔ 䈏ਥ䈫 䈋䉏䈳䉮䊮䊃䊤䉴䊃䈲ૐਅ䈜䉎 ᵈ䋩ㄭ䈒䈪 䈩䉅ᑪ 䈱 䈲 䇭䇭 䈦㤥䈪䈭䈒䈩䈲䈭䉌䈭䈇 䋨䋶䋩䉣䉝䊨䉹䊦䋨Aerosol䋩䈫 䋨Water䋩- 䊶䉣䉝䊨䉹䊦 ሶ 䇭䇭䇭䇭䋨䋱䋩 ὼ 䋺 䊶 䇮Ⴎᓸ ሶ䋨NaCl䋩䇮䉴䉴䋨C䋩䋻 ᨋἫἴ 䈮䉋䉎 䋨䋲䋩Ꮏ ᵴ 䋺䊶䉴䉴䋨C䋩 䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭 䊶 䋺HNO(NO㸢NO+HO㸢HNO) 䇭䇭䇭䇭䇭 䊶 䋺HSO4䋨SO+HO㸢HSO4䋩 䇭䇭䇭䇭䇭䇭ᵈ䋩 䈲 䈩 䈫䈱 ᕈ䋨ๆ 䇮ṁ 䋩䈏㜞䈇 Coffee Break 䇭䋨ᄐ䈪䉅౻䈪䉅 ὼ 䇮Ꮏ ᵴ 䈲ᄌൻ䈚䈭䈇䈱䈮 䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䈭䈟ᄐ䈫౻䈪䈲ᄐ䈱ᣇ䈏ⷞ 䈏ᖡ䈇䈱䈪䈚䉊䈉䈎䋿䋩 䇭䇭䇭䇭䇭䊶 䈭䉎䈱䈲 䈫Ḩᐲ䈣䈔䇯䇭 ᵈ䋩䊶 ಽሶ䈲䉣䉝䊨䉹䊦䈮 䉌䈭䈇䇯 䇭䇭 䊶㔎䈲 䉌䈭䈇䋨ṫ䉒䈭䈇䈎䉌䋩䇯 䇭䇭 䊶 Ⴒ䈲 䉌䈭䈇䋨ṫ䉒䈭䈇䈎䉌䋩䇯 䇭䇭 䊶䉅䉇䇮㔵䈲 䉎䇯 Ref䋩NASA,Earth Observatory 䋩 ಽሶ䉕 䈫 䇭䇭䇭䇭 䈢 䈱 ଔ 䈱 䇭䇭䇭䇭 ᓘ䋨䌤䋩㻍䋰䋮䋳䌮䌭 Coffee Break(MODRAN䈮䈍䈔䉎䉣䉝䊨䉹䊦䈫 䈫HO Cotiuu䋩 MODRAN 䊶䉣䉝䊨䉹䊦 ሶ䈱ᄢ䈐䈘䈏 䇮Ḩᐲ䈪ᄌൻ䈜䉎䈫 䈋䈭䈔䉏䈳䈭䉌䈭䈇䇯 䇭䋨ᄐ䈱ᣇ䈏ᄢ䈐䈒䈭䉎㸢䉣䉝䊨䉹䊦 ሶ䈏 ಽ䉕ๆ 䈚䈩ᄢ䈐䈒䈭䉎䈱䋿䋩 4 Coffee Break䋨 ㅪ 䋺 ಽሶ䈱䉪䊤䉴䉺䋩 ዊ䇭㸠䇭ㅘㆊ 䇭㸢䇭ᄢ 䋱䇭 䇭䋨䋱䋩HO Bad ype䇭㸢䊋䊮䊄 ๆ Ꮺ 䇭䋨䋲䋩HO Cotiuu䇭 䇭䇭䇭䇭䇭䇭㸢 ㅪ 䈎 ㅪ Ꮺ䈎䋿 䋲䇭Aerosol & Hydro 䇭䇭䉣䉝䊨䉹䊦䈫 䈮䉋䉎ᢔ ๆ 䋺ਛ ᄖ 䋺 ᄖ ዊ䇭䇭㸠䇭䇭ๆ 䇭䇭㸢䇭䇭ᄢ 䊋䊮䊄ๆ Ꮺ ᄢ 䈱⓹䈮䈍䈇䈩䈲䋺 䇭䇭䊶㜞Ḩᐲ䈪䈲 ᄖㅘㆊ 䈏ᖡ䈒䈭䉎䇯 䇭䇭䇭䈖䉏䈲 ㅪ 䈱 ᚑ䈮䉋䉎ๆ 䇭䇭䇭䈮䉋䉍 ㅪ ๆ Ꮺ䈏 䈛䈢䈢䉄䇯 䇭䇭䊶ਛ 䈲 ㅪ 䈱 䈲ዋ䈭䈒Ḩᐲ䈮ᒝ䈇䇯 ㅪ ๆ Ꮺ 䋱 ᵈ䋩 ㅪ Ꮺ䈲ᢔ 䈪䈭䈒ๆ 䇯 䇭䇭ᢔ 䈪䈅䉏䈳䊧䊷䊥ᢔ 㗔 5 䇭䇭䈭䈱䈪 䈲 䋼ਛ 䈱䈲䈝 Ref) 6 6

7 Coffee Break NaCl, (C), HNO, HSO4 Absorptio [] SchrÖdiger Equatio Maxwell s Equatios Scatterig [Maxwell s Equatios] LOWRAN,MODRAN + Aerosol & Hydro Coffee BreakCoffee Break Lie Spectral 7 Atospheric urbulece or Optical urbulece) [ ] Navier-Stokes Equatio Maxwell s Equatios Radiatio) 8 Phase Diagra of Water Saturated Water Vapor Pressure Water Vapor Pressure Relative Huidity Absolute Saturated Huidity Absolute Huidity Dew Poit eperature Precipitable Water Abiet eperature Abiet Pressure Psw Pw Rh sw w d lw a Pa Pascal Pascal % g/^ g/^ or K /k or K Pascal Pressure(Pa) a Liquid PSW[ Pa] = F( ) exp.80 d[ K] ( d[ K]) [ K] = G( P) d l( PSW[ Pa]) PSW [ Pa] = F( ) exp d [ K] d [ K] = G( P) l( P [ Pa]) SW 9 Ref) 40 Phase Diagra of Water 0 C 60Pa PSW[ Pa] = F ( ) exp.80 d[ K] ( d[ K]) dpsw where 7K PSw d [ K] = G( P) d l( PSW[ Pa]) whe re P 0 C 60Pa 0 d SW 60Pa PSW [ Pa] = F( ) exp whered 7K d [ K] d [ K] = G( P) wherepsw 60Pa l( P [ Pa]) SW 4 Coffee BreakLOWRAN Phase Diagra of Water LOWRAN SW g A A A ρ [ ] = exp( ) 7 wherea = o 7 + d [ C] LOWRAN PSW [ Pa] = exp.87 d [ K] ( d [ K] ) LOWRAN 4 7

8 Moograph =0,00Pa Rh[%] = PW[ Pa] PSW[ Pa] 00 Coffee BreakMoograph /^ /k g PW [ Pa] W = l g W = ρw a[ K] k ρ [ ].65 [ ] [ ] Pa P = exp K [ ] = A P = PSW = D P = PW P = exp.80 K [ ] ( K [ ]) = P= P, = P= P A SW D W 4 44 a Rh[%] PSW [ Pa] = F( a[ K]) PW [ Pa] = PSW [ Pa] 00 PW [ Pa] ρw[ g ] =.65 lw[ ] = ρw[ g ] [ K] k [ K] = G( P [ Pa]) d W a ad PW [ Pa] PSW [ Pa] = F( a [ K]), PW [ Pa] = F( d [ K]) Rh [%] = 00 P [ Pa] P [ Pa] ρ [ g ] =.65 l [ ] = ρ [ g ] W W W W a[ K] k F() G(P)P F ( ) exp.80 ( ) GP K [ ] ( K [ ]) l( PPa [ ]) SW (Assa Hygroeter) Psychroeter Moisture Chart for Assa Hygroeter a[] [] [%] 46 Coffee Break:Moisture Chart for Assa Hygroeter a[][][%] 47 Coffee BreakSprug a[][]aw[%] where W[] Rh[%] Sprug 0 0 P ( W + 7)[ Pa] (0.5/ 755)[ C] [ C] 0,00[ Pa] = P ( a + 7)[ Pa] 0 0 P( a + 7 )[ Pa] (0.5 / 755)[ C] [ C] 0,00[ Pa] = P ( a + 7)[ Pa] Rh > P ( )[ Pa] exp.80 K [ ] ( K [ ]) 48 8

9 Pa Coffee BreakSprug Rh[%] = P ( W + 7) (0.5 / 755) 0,00 P ( a + 7) Coffee Break w[][]rh[%] [][][] Rh[%]= ( ) W W W 49 w 50 Mirror ype Dew Poit Meter Coffee Break LED PSW[ Pa] = F ( ) exp.80 d[ K] ( d[ K]) a=0=9kpsw=9pa d=.=75.kpw=70pa 70/9=0% Hair Hygroeter) 5 % 5 Coffee Break Coffee Break Methaol) = Methyl Alcohol Ethaol) = Ethyl Alcohol CH4O CH6O a= =94KPsw= 488Pa d= 4.4=77.4K Pw= 86Pa 86/488=4% =65% () 5. () 6. Ref) 54 9

10 Coffee Break Coffee Break =0,00Pa Iage L G-HO G-HO L L G- G-O G-HO 00K 00K568Pa 568Pa G- G-O G-HO L-HO 00K 568Pa L 568Pa 568Pa 568Pa 568Pa =0,00Pa Coffee Break a[ K] W[ K] F ( ) (0.5/ 755) ( ) 0,00 [%] W a W Rh = F ( a) R P [ ] ( ) [ ] h SW Pa = F a PW Pa = PSW [ Pa] d [ K] = G( PW [ Pa]) 00 P [ ] [ g ].65 W Pa ρw = lw[ ] = ρw[ g ] k a a [ K] Rh[%] PSW Rh [ Pa] = F( a ) PW [ Pa] = PSW 00 [ Pa] d [ K] = G( PW [ Pa]) ρ [ g P [ Pa] ] =.65 l [ ] = ρ [ g ] W a k W W W a [ K] d [ K] PW [ Pa] PSW [ Pa] = F( a ), PW [ Pa] = F( d ) Rh [%] = 00 P [ Pa] P [ Pa] ρ [ g ] =.65 l [ ] = ρ [ g ] W a k W W W F ( ) exp.80 GP ( ) K K PPa SW [ ] ( [ ]) l( [ ]) Absorptio [] SchrÖdiger Equatio Maxwell s Equatios Scatterig [Maxwell s Equatios] LOWRAN,MODRAN Atospheric urbulece or Optical urbulece) [ ] Navier-Stokes Equatio Maxwell s Equatios Radiatio) 58 LOWRAN, Coffee Break:FORRAN CodeLOWRAN5 LOWRAN(Low Resolutio rasittace Code) MODRAN(Moderate Resolutio rasittace Code) HIRAN(High Resolutio rasittace Code) (FASCODE, DISOR, ICRCCM, LBLRM, etc) LOWRANAir Force Cabridge Research Laboratory LOWRANLORAN(988) MODRAN,HIRAN LOWRANFORRANOPEN

11 MODRAN IputHorizotal Path, Altitude=0K, No Clouds or Rai Horizotal Pass Legth=5k,at,0,.50. Card [Model Atosphere()] Atteuatio Mode to use MODRAN Model Atosphere Meteorological Data Iput ype of Atospheric Path Horizotal Path Mode of Executio rasittace use AM Layer Cards Modtra Iput Model Atosphere() VIS X RH Y X =K, Y = (Aerosol & Hydro) Card [Aerosol()] Aerosol Model Used Rural-VIS=K or Rural-VIS=5K Surface Rage for Boudary Layer K Card C Paraeter Boudary Altitude of #of 0 Pressure at or b eperature or K HO ( or ) Card [Geoetry ad Spectral Bad()] Iitial Altitude 0K Path Legth Iitial Frequecy Fial Frequecy Modtra Iput Plot Cards Ru Model Plot Database 0.5 =40,000(/c) 0. =,(/c) 0.4 =5,000 (/c) 0.5 =0,000 (/c) 0.8 =,500 (/c) =0,000 (/c).5=6,666 (/c) =5,000 (/c).5 =4,000(/c) =, (/c) 4=,500 (/c) 5=,000 (/c) 8=,50 (/c) 0=,000 (/c) =8 (/c) 5=667 (/c) 6 0=500 (/c) 6 Horizotal Pass Legth=5k,at, Horizotal Pass Legth=5k,at,0,0 VIS X RH Y X =K, Y = (Aerosol & Hydro) Aerosol & Hydro HO Cotiuu Eye Safe CO Eye Safe 6 64 Horizotal Pass Legth=5k,at,0,0 VIS X RH Y X =K, Y = Aerosol & Hydro) (HO Cotiuu) Aerosol & Hydro) Aerosol & Hydro) (HO Cotiuu) 65 66

12 Coffee Break: τ 0.55 Rk [ ] λµ [ ] V[ k] F( V) a = exp.9 ( ) 0.55 F( V) Rk [ ] τ = exp.9 ( ) λµ [ ] V[ k] Koschieder s Law WhereF( V ) 0.7 : V.7k V : V.7k = RANSMISSIONa Visibilityk k Visibility,,5,0,0,50,00k Visibility00k 67 RANGEVISIBILIY 68 :4u τ 0.55 Rk [ ] λµ [ ] V[ k] F( V) a = exp.9 ( ) Visibility00k 0.55 F( V) Rk [ ] :0u τ a = exp.9 ( ) λµ [ ] V[ k] Visibility00k RANSMISSIONa Visibilityk Visibility,,5, 0,0,50,00k RANSMISSIONa Visibilityk Visibility,,5, 0,0,50,00k RANGEVISIBILIY 69 u RANGEVISIBILIY 70 0u Absorptio [] SchrÖdiger Equatio Maxwell s Equatios Scatterig [Maxwell s Equatios] LOWRAN,MODRAN Atospheric urbulece or Optical urbulece) [ ] Navier-Stokes Equatio Maxwell s Equatios Radiatio) 7 Atospheric urbulece or Optical urbulece ) [ ] Navier-Stokes Equatio Maxwell s Equatios :Static Pheoea Road Mirage Mirage Statioary Pheoea Atospheric urbulece Optical urbulece rad Adaptive Optics 7

13 ρ = β Whereβ 0 ρ S 4 S P 7 PPa [ ] = β 8 0 PS [ K] 7 d β d ρ β dp d d = = β ρ P dp/p 74 :Static Pheoea 0 0 d d 0 δ = dα d ta( α ) β d ta( α ) Whereta( α ) R D radat =00K,d=00K, 0=84: d 75 rad (at =00K,d=5K,0=89) 76 Coffee Break R D 0 L0 0 d d L δ = dα ta( α ) β ta( α ) Whereta( α ) D β L K 7 µ rad D 0. 4 C = 0 = 0.K Wherer = 0 77 cc si( θ ) C c 0c Where = d d β d θcc β ccrad rad. 78

14 : (Road Mirage) radk=k D= COH R=0 d R δ β ta( α0) Whereta( α0) D radat =00K,d=00K, 0=84: ( :(Road Mirage) Mirage d θcc β =00K,d=5Krad radk= d δ β ta( α0) =00K,d=5K,0=890.6rad radk= 8 8 Mirage Statioary Pheoea Atospheric urbulece Kologorov urbulece Model Optical urbulece

15 Atospheric urbulece r ur ( + rt, ) R ( + rt, ) R ( + rt, ) R ur ( + rt, ) R+ r ( R+ r, t) R+ r R ( + rt, ) R+ r 85 Ref:Wave Propagatio i a urbulet Mediu by atarski 86 urbulece Uiversal Equilibriu Rage Iertial (Sub)Rage Dissipatio Rage Outer Scale(L0) (=Exteral Scale or Large Scale) Ier Scale(l0) (=Iteral Scale or Sall Scale) = Noralized Mea urbulece Kietic Eergy Spectru per Uit Mass per Uit Wave Legth L0 R l 0 Kologorov Spectru 4 e L.F.Richardso(88-95) 87 Vo Kara Spectru L O l O atarskii Spectru 88 RefChapaAIAA-J,979,Vol.7-,P9 l [ ] u[ ] ρ[ kg sec ] [ ] [ ] [ ] sec l u η N R sec e = = Whereν[ ] = η[ N sec sec ] ν[ ] sec [ kg ρ ] N sec kg kg P[ Pa] atair sec 87 [ K] ηair [ ], ρ[ ] ν AIR [ ] sec at, 00K Outer Scale 0[ ] [ ] 6 Re = sec [ ] sec Paρ kg at K 5.0 0,.8[ ], Kologorov urbulece Model ()Icopressible Mediu ()Locally Hoogeeous ()Locally Isotropic (4)Locally Statioary (5)Locally Ergodic Du () r Wherel0 < r < L0 (Velocity Structure Fuctio) = { ur ( rt, ) urt (, )} dv Vol + = Vol ie ie { ur ( + rt, ) urt (, )} dt= D u = Cu r 5 = u urbulece Kietic Eergy Spectru per Uit Mass per Uit Wave Legth Ek ( ) D( r) exp( irkdr ) Ek ( ) k u = E( k) dk 0 Mea urbulece Kietic Eergy per Uit Mass Kologorov Siilarity heory of urbulece 90 Scale Siilarity heory of Kologorov u (Velocity Structure Costat) 5

16 Kologolov r^(/) D D Ier Scalel0 y = r = C r = C r r() Outer ScaleL0 y = r r() r 5 k 5 : r k : 9 urbulece Noralized urbulece Kietic Eergy Spectru per Uit Mass per Uit Wave Legth Vo Kara Spectru L O Uiversal Equilibriu Rage Iertial (Sub)Rage l O Dissipatio Rage L R l 0 0 Kologorov Spectru atarskii Spectru 9 RefChapaAIAA-J,979,Vol.7-,P9 4 e Kologorov urbulece Model ()Icopressible Mediu ()Locally Hoogeeous ()Locally Isotropic (4)Locally Statioary (5)Locally Ergodic Wherel0 r L0 { ( R+ r, t) ( R, t) } dv= { ( R+ r, t) ( R, t) } dt = D = C r Vol Vol ie ie (eperature Structure Fuctio) { R ( rt, ) Rt (, )} dv Vol + = Vol ie ie { R ( + rt, ) Rt (, )} dt= D = C r (Refractive-Idex Structure Fuctio) β = = PPa [ ] 7 (eperature Structure Costat) C [ ] C [ K ] C [ ] (8 0 ) C [ K ] [ K] 0^- 9 (Refractive-Idex Structure Costat) Kologorov Siilarity heory of urbulece Scale Siilarity heory of Kologorov [(r,t)] [(r,t)] [(0,t)] r r uv/ uv ie { rt (, ) (0, t) } dt= Dr ( ) ie ( ) r C r = (0) ( ) = ie { r (, t) (0, t) } dt= D r ( ) ie ( ) = (0) ( r ) = C r C β C = 94 C^ 0^- 0^- C^ 0^- D 50^-7 0^-7 D D 0^-6 0^-7 D [] 0. 0^-6 70^ Scitilloeter 0^-4 0^-5 0^-6 0^-7 0^- 0^- 0^-4 0^-5 50^ ^ ^ ^ ^ ^ ^ ^ c 0^ ^ ^ ^ ] β = β =, β 0 4 C C r D D = C r, D = C r D = (0) ( r) D = (0) ( r) ( ) ( ) [^-(/)] [K^ ^-(/) ] [] uv/ uv 95 C [ c ].5 C [ ] SUN Rise Noo SUN Set Ref)J.E.Perso:JOSA,975,Vol.65,No.8,P

17 C^ Ref)R.S.Lawrece,etalJ.O.S.A.,Vol.60,No.6,970,p86 968/9/8 0^-0^- C ( -/) C^ [^-/] 0^- 0^- 0^-4 0^-5 0^ C 4 (0 0 ) h[ ] Ref)D.L.Walters et alj.o.s.a.,vol.7,98,p ^ Altitude () Ref)DARPA:High Precisio Day/Night Laser Desigator 98 Optical urbulece P[ W ] Gauss r r () = r () + r () l( P( r)) = l( P( r)) + l( P( r)) (0) = (0) + (0) l( P(0)) = l( P(0)) + l( P(0)) Gauss 99 ω P = P exp ( i( ωt kz) ) = exp l( P) + i( ωt z) C ω ( ) ω = exp l( P) + i( ωt ) + Dl( P) i ( D ) z C C ω C ω v=, = k = k v C Logarith-of -Aplitude Fluctuatio Phase-Fluctuatio C^ 00 Optical urbulece MFLog Exposure Iage Blur MFShort Exposure Iage Blur (Iage Motio or Iage Dacig or Iage Waderig) Outer Scale Phase-& Log-Aplitude Fluctuatio) Seeig Scitillatiowiklig (Bea Spreadig or Bea Broadeig or Speckle) Bea Dacig or Spot Dacig or Bea Waderig or Bea Motio (Bea Bedig) 0 Optical urbulece Log Exposure Iage Blur 5 MF( r) exp C [ ] λµ [ ] r[ lp / rad ] R[ k] 0.9WhereC = 0, λ = 0.5, r = 0, R = WhereC = 0, λ = 0.5, r =, R = WhereC = 0, λ = 0.5, r =, R = WhereC = 0, λ = 0.5, r = 0, R = 5 WhereC = 0, λ = 0.5, r =, R = Ref)D.L.Fried;J.O.S.A.,Vol.56,No.0,p7(966) 0 7

18 Optical urbulece MF Iage Motio or Iage Dacig δ [ rad] 4 C [ ] D[ ] R[ ] MF Aexp 5 6.6µ radwherec = 0, D = 0., R = µ rad WhereC = 0, D = 0., R = µ radwherec = 0, D = 0., R = µ radwherec = 0, D = 0., R = 5 0 k Ref980,Vol.,No.,P096 Ref)Atospheric Propagatio of RadiatioEdited by F.G.Sith,SPIE,Vol,Chaper,p Coffee BreakOuter Scale Ier Scalel0 Outer ScaleL0 rad Ier scale Outer scale C^) Outer ScaleL0 Ier Scalel0 Outer Scale 05 LOWRAN,MODRAN 06 Absorptio Spectru of Liquid Water

19 Friedr0 5 λr MF( r) LE = exp{ 0.5 D( λr) } = exp.44 r ρ r0 π D( ρ) =.9 ρ C R A ρ = 6.88 λ π A=.9 C R λ 5 π r0 =.68 C R λ P θ ( )[ ] ( cos ( )) π π ( θ) ω θ ϕ ( cos ( θ)) siθ 4π 0 0 ω θ θ ϕ θ θ θ 4π 4π 4π sr = + 6π P d = d d + = 6π d = si d d, si( ) = si 4si dω = 4π 4 cos θdω = π 6 + θ dω = π ( cos ) θ 09 0 (Assa Hygroeter) Psychroeter PSW[ Pa] = F ( ) exp.80 d[ K] ( d[ K]) a= 0=9KPsw= 440Pa d= 6.4=79.4K Pw= 96Pa 96/440=9% =4% =.574% GOOD 9

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