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くにもとほがり
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1 MRR Physical Basis( 1.8.4) METEK MRR 1 MRR 1.1 MRR 24GHz FM-CW(frequency module continuous wave) 30 r+ r f+ f 1.2 1

2 4 MRR 24GHz mW 1 rf- (waveguide) (horn) 60cm ( monostatic radar) (continuous wave) ( ) 1.4 FM-CM ( ) ( ) ( ) 2 f0 B/2 f0 B/2 th = 2h/c h ( ) c th, T 2 2

3 1.4.2 s () t S sin( ϕ () t ) = ( ) S ϕ () t ( t)dt S ω s B ω () t = π t s ω 2 0 T T 2 t T

4 B 2 s() t = S sin ω t 2π t T t h = 2h c (th ) ϕ e () t = ϕ ( t t ) e t) = E sin s h ω B 2 2 t ω t 2 ( + ) 0 h π t tht t T ( 2 0 h (mixing) s(t) e(t) 2 s(t) e(t) 2 s(t) e(t) B f0 2f0 ϕe ( t) ϕs ( t) B 2 1 B 1 B 2 1 B 2 ϕm( t) = ω0t ω0th 2π t + 2π tht 2π th ω0t + 2π t ( ) 2 T 2 T 2 T 2 T f ( ) m = ( 1/ 2π ) ϕ ( t) / t th fm = B T f=1/t ( ) th f T δ t h = δ f ( ) B ( ) f 1/T th h h=(1/2)c th δh 1 = 2 c B ( ) m 4

5 1.4.3 FFT 1/T FFT ( ) 3 (Beat signal) ( 1 FT) ( )r 3 10 (0 r 9) MRR

6 / /T 1/nT 2 FT ( ) N=1/T f = / 4 f N f 2 / 2 0 N (1 /h) 2000m -3 (=2 /l) (500m 50m ) 10 4 m FM CW 6

7 (Incoherent Averaging) (random) (spectral power) (stochastic) incident (power) (expectation, ) (ensemble) n 1 1/ MRR SP(?) % (n=25 n=5 1/ n=0.8) SP single power spectra (n=150 1/ n=0.08) 8% 0.34dB 1/T 1/nT ( ) 2FT N=1/T ( ) ( ) ( % ) ( ) 8% 0.34dB S/N( ) 7

8 4 2 1 p( f ) df = C( r) η ( f ) r h f 8

9 h r C(r) MRR η( f ) df f 2 2 nd FT η( f ) df C(r) p ( f ) df PC MMR2-control MMR ver1.3 C(r) 32 ( r ) MRR2-control 2 2 nd FT F 64 ( 3 8 ) (0 63) F dbη F η = 10 F /10 η( f, ) = η / f f = f, f = Hz MRR2 2 η(ν ) Gu& intzer(1949) Atlas(1973) ( 5 ) -1 ν ( )[m/s] = 9.65m/s -10.3m/s exp(-0.6mm [mm]) δv( h) for mm v ρ δv( h) = [ h h ] ν ν f ν η ( ) = η( f, ) 2.7 v 9

10 1 [ m ] f = v ν / [m/s/mm] = 6.18 exp(-0.6 [mm]) δv (h) ( (2.5) ) η( )[m -1 mm -1 ] = η( f, -1 ) exp(-0.6mm [mm] ) 2.8 ) σ η ) N ) ( ( ( N( η( ) ) = 2.9 σ ( ) 2.8 (2.9) σ () 2 m 2 m1 + K 2 5 π 1 6 σ R ( ) = 2.10 λ m K MRR σ () 6 MRR =(6V/ ) 1/3 V MRR2 N MRR ver1.3 ν = /s (2.8) 0.246mm 5.03mm 0.78 / (h) 8.97m/s 7 10

11 11

12 ) ( ) ( ) MRR min(h) max(h) (summation) (h=0) min(h)=4 max(h)= max( h) g( f ) df (3.1.1) g min( h) g f ) ( g = g( f, ) f (3.1.2) 12

13 f = 30.5Hz f 1 g( v ) = g (3.1.3) ν f f 1 1 = (3.1.4) v f [m/s] f 1 v g( ) = g (3.1.5) ν f f v 1 v 1 [ mm ] = 3.15 (9.65 v( h) v[ m / s]) f δ (3.1.6) (3.1.5) g g (2.9) N ) η η ) ( ( GHz 0.2dB/km 10g/m3 nac(not attenuation corrected) (recursive) r = 1 N(, r) N(, r) nac exp h κ ( N(, i)) (3.2.1) i= 1 (3.2.1) ( h κ( N(,1))) N(,2) = N(,2) nac exp (3.2.2) N(,1) N(,1)nac = max( h) κ = N( ) σ ( ) (3.2.3) = min( h) e e() e 13

14 (account for) 3.3 Z e 4 λ = 5 π 1 K 2 0 η( f )df (3.3.1) Z e 4 λ = 5 π 1 K 2 0 ( ) dν η ν (3.3.1) ( ) Ze 6 Z 0 6 ( ) d = N (3.3.2) (2.9) (3.1.1) (3.3.2) 14

15 (3.3.2) 3.4 w π LWC = ρ w N ( ) d[ g / m ] (3.4.1) 3.5 rr() v() ( / ) N() 3 RR π = N( ) 3 ν ( )d 6 (3.5.1) W λ = 2 η 0 ( f ) fdf η( f )df 0 (3.6.1) R()=N() R() (2 10) R η R ( f ) = N( ) σ R ( ) ( f / ν )( ν )( ) R (3.6.1)

16 4 4.1 MRR (23 6) 9% 4.2 ( (2.5): ) ( 10m ) (2.5) (2.5) (2.8) Richter(1993) 100m log(Rcorr/Runcorr) 1dB 10,000 12dB 16

17 4.3 C C 10% C ( ) 30K 10% ( ) 4.4 (0 ) MRR 17

18 ( ) 5 MRR yymmddhhmmss : 2 H ( ) db ( ) FFT F η N04-N49 ( ) ( ) FFT (2.5) = v( ) / δv( ) ln h Z (3.3.2) RR (3.4.1) (mm/h) (3.5.1) (g/m 3 ) W (3.6.1) 1 18

19 19

20 6 20

(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x

(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x Compton Scattering Beaming exp [i k x ωt] k λ k π/λ ω πν k ω/c k x ωt ω k α c, k k x ωt η αβ k α x β diag + ++ x β ct, x O O x O O v k α k α β, γ k γ k βk, k γ k + βk k γ k k, k γ k + βk 3 k k 4 k 3 k