2.,, Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 4
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,,. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 17
:,,,,,,,.,. SEM, AFM, SAM,,,, Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 18
:,,,,,,,, :,,, :,,, :,, Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 19
( ),.,... g o + e o = f(x, n) (1) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 20
, Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 21
Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 22
, span, dynamic range accuracy Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 23
N l = 1 N S 2 = 1 N 1 : N l i (2) i=1 N (l i l) 2 (3) i=1 systematic error accidental error Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 24
,, 2. y = f 1 (x 0 +Δx, Δe) f 2 (x 0 +Δx, Δe) (4) f 1 (x 0, 0) = f 2 (x 0, 0) (5) f 1 x = f 2 x=x0,e=0 x (6) x=x0,e=0 f 1 e = f 2 x=x0,e=0 e (7) x=x0,e=0 (8) y 2 f x Δx +2 2 f ΔxΔe (9) x e, Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 25
: : : Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 26
3.,, 1790 4000 1 1m :. 1872 :. 1960 86 2P 10 5d 5 1650763.73 : 1982 299792.458 1 :,. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 27
2 θ 2 dm L L = d (10) tan θ 2 Δd θ L +ΔL = d tan θ + Δd (11) tan θ θ Δθ θ. d L +ΔL = (12) tan(θ +Δθ) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 28
, Δt L = cδt (13) 2. 1mm (1mm) = cδt 2 Δt 6ps 6 10 12, Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 29
. f Λ Λ= c f (14) φ L L = 1 2 (N + φ )Λ (15) 2π L>Λ/2 Λ > 2L. L = φ Λ 4π (16) N = 1 2π (Λ Λ φ φ) (17) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 30
A cos 2πft K cos 2πf L t = 1 2 AK[cos 2π(f +f L)t+cos2π(f f L )t] (18) B cos(2πft + φ) K cos 2πf L t = 1 2 BK[cos(2π(f + f L)t + φ)+cos(2π(f f L )t + φ)] (19), f f L 1 2 AK cos 2π(f f 1 L)t 2 BK cos(2π(f f L)t + φ) (20) φ. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 31
:. λ, L 1, L 2 I = A + B cos 2π(L 1 L 2 ) (21) λ, 1/10 (50nm). Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 32
GPS:,. VLBI:...( ) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 33
, (km) ( ) (m) (nm, μm, mm) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 34
:,,,,,,.,,. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 35
. (a) 1. h 2. θ (b) 1. 2. θ δ a = h tan θ hθ (22) δ b =(L d)(1 cos θ) L d θ 2 (23) 2 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 36
N, N 1 N. : K N 1 + x. 0 <x< 1/N. M (M 1)/N = x + M(N 1)/N 2 (24). x = M/N 2. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 37
:,. :.. : p θ a = θ p (25) 2π.( ) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 38
,,., ( ),.,. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 39
:,. : x, θ θ = x (26) a L 2θ d =2θ L =2 x a L = 2L a x (27) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 40
4.,,,,.,,. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 41
,. r(θ) R = V E (28), Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 42
C = ɛs d (29) C (F), d (m), S (m 2 ), ɛ (F/m) Δd Δd C 1 = ɛs d +Δd, C 2 = ɛs d Δd (30), ΔV = V 1 V 2 = V d Δd (31). Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 43
( 1). ( ),,,. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 44
( 2) A B 1/4 B UP (1) (2) A (1) (2) (3) (4) (6) (3) DOWN (4) (5) (5) UP (7) (6) (7) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 45
0 1 X 2 X 3 XX 4...... X... 127 XXXXXXX 128 X 129 X........ X. 252 XXXXXX 253 XXXXXX X 254 XXXXXXX 255 XXXXXXXX Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 46
,. v(m/s). x p x A y p y B. A T A, B T B. x v x T A y v y T B T x = p x /v x, T y = p y /v y (32) v =(p x /T x p y /T y ) T. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 47
( 1) L 2, 2 x v., f(x)(, ).. A(x =0) B(x = L).. f A (t) =f(0 vt), f B (t) =f(l vt) (33) f(x). φ ff (x) = lim X 1 2X X X f(χ)f(χ + x)dχ (34) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 48
( 2) f A (t) f B (t). φ AB (t) = lim T 1 2T T T f A (τ)f B (τ + t)dτ (35) f A (t) =f(0 vt) f B (t) =f(l vt). φ AB (t) = lim T 1 2T T T f( vτ))f(l v(τ + t))dτ = φ ff (L vt) (36) φ ff (x) x =0. φ ff (L vt) t 0 v = L/t 0. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 49
seismic pick up ( ). m k, c.. x a. m d2 x dt 2 + cdx dt m + kx = ma (37) d 2 x dt 2 + c dx m dt + k x = a (38) m Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 50
seismic pick up ( ). d 2 x dt 2 + c dx m dt + k x =0 (39) m (39) Ce γt (39).. γ 2 + c m γ + k m γ. γ = 1 2 ( c m ± c 2 =0 (40) m 2 4k m ) (41) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 51
seismic pick up ( ) (39) C 1 exp( 1 2 ( c m + c 2 m 2 4k m )t)+c 2 exp( 1 2 ( c m c 2 m 2 4k m )t). (42) ω n = k/m, ζ = c/2 mk C 1 exp( ζω n t+ ωn(ζ 2 2 1)t)+C 2 exp( ζω n t ωn(ζ 2 2 1)t) (43). ζ 2 < 1. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 52
seismic pick up ( 4) g(t). d 2 (g(t) a(t)) dt 2 +2ζω n d(g(t) a(t)) dt + ω 2 n(g(t) a(t)) = a(t) (44) t<=0 g(t) =0,. s 2 G(s)A(s)+2ζω n sg(s)a(s)+ω 2 ng(s)a(s) = A(s) (45) G(s) g(t). d 2 g(t) dt 2 s 2 G(s), dg(t) dt sg(s), g(t) a(t) G(s)A(s). Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 53
seismic pick up ( ) G(s) G(s) = 1 s 2 +2ζω n s + ω 2 n (46) s = jω ω. 1 G(jw)= (jw) 2 +2ζω n (jw)+ωn 2 (47) G(jw), arctan(im(g(jw))/re(g(jw))). G(jw) = x(t) a(t) = (1/ω 2 n) (1 (ω/ωn ) 2 ) 2 +(2ζω/ω n ) 2 (48) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 54
-.,. R = ρl/a(a, ρ ) ΔR R = Δρ ρ + Δl l ΔA A (49) K =( ΔR R )( l Δl )=1+(Δρ ρ )( l Δl ) (ΔA A )( l Δl ) (50) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 55
( 1) R 2 : R 1 = R 3 : R 4, R Δe = E( 3 +ΔR 3 R 2 +ΔR 2 ) R 3 +ΔR 3 + R 4 +ΔR 4 R 1 +ΔR 1 + R 2 +ΔR 2 = E (R 3 +ΔR 3 )(R 1 +ΔR 1 ) (R 2 +ΔR 2 )(R 4 +ΔR 4 ) (R 1 +ΔR 1 + R 2 +ΔR 2 )(R 3 +ΔR 3 + R 4 +ΔR 4 ) 1 (R 2+ΔR 2 )(R 4 +ΔR 4 ) (R 1 +ΔR 1 )(R 3 +ΔR 3 ) = E = E (1 + R 2+ΔR 2 R 1 +ΔR 1 )(1 + R 4+ΔR 4 R 3 +ΔR 3 ) 1 R 2+ΔR 2 R 1 +ΔR 1 R 4 +ΔR 4 R 3 +ΔR 3 (1 + R 2+ΔR 2 R 1 +ΔR )(1 + R 4+ΔR 4 1 R 3 +ΔR ) = E 3 (1+ΔR 4 /R 4 ) (1+ΔR 1 /R 1 )(1+ΔR 3 /R 3 ) 1 (1+ΔR 2/R 2 ) (1 + R 2+ΔR 2 R 1 +ΔR 1 )(1 + R 4+ΔR 4 R 3 +ΔR 3 ) (51) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 56
( 2) Δe E 1 (1 + α)(1 + 1/α) (ΔR 1 R 1 ΔR 2 R 2 + ΔR 3 R 3 ΔR 4 R 4 ) R 1 =R 2 =R 3 =R 4, ΔR 1 =ΔR 2 =ΔR 4 =0 (52) Δe = 1 4 (ΔR 3 R 3 )E (53) Δe = 1 4 K(Δl )E (54) l Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 57
..., α Δe E (1 + α) 2(((ΔR 3 ) R T ( ΔR 4 ) 3 R T +( ΔR 3 ) ɛ ) (55) 4 R 3 α Δe E (1 + α) 2(ΔR 3 ) ɛ (56) R 3. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 58
,. ΔR A = ΔR C = ΔR R A R C R (57) ΔR B = ΔR D = ν ΔR (58) R B R D R ν. Δe E 1 4 (ΔR R + νδr R + ΔR R + νδr R )=1 Kɛ(1 + ν)e (59) 2 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 59
/, 90 4. θ = 32L πd 4 G T (60) L, d, G P = 2πn 60 T (61) n. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 60
5. ( ) ( ) ( ) ( ) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 61
6. p, v p 0 = p + 1 2 ρv2 (62). p, 1 2 ρv2 p 0, 2(p v = 0 p) ρ. (63). Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 62
i 2 R w (T w T )(a + bv n dt w )=C w dt i R w. (64) R w i, i. dt w dt =0 C w,.. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 63
( ) 2 2θ. 2, 2λ n / sin θ. λ n. v y f = v/(2λ n / sin θ).,. θ θ v Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 64
( ).. (, ). p 1 + 1 2 ρv2 1 = p 2 + 1 2 ρv2 2 (65) (, ) S 1,S 2 Q = S 1 v 1 = S 2 v 2, S Q = 2 2(p 1 p 2 ) 1 (S2 /S 1 ) 2 (66) ρ Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 65
..,. E v =( D/2 0 E = BD v 2πrv(r)dr)/(πr 2 ) (67) Q = v πd 2 /4=E (πd)/(4b) v B Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 66
.,. f = S v (68) d. S 0.2.,., Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 67
,,,.,. ( ). Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 68
:., : :,,, :,,,,. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 69
,.. ΔI/I =(F 2 /a)dc(ρ/ρ 0 ) dρ (69) dρ Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 70
. ΔD = C(ρ ρ 0 )D (70),. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 71
7..,,,. 1993,ISO. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 72
(accuracy) precesion( ) dispersion( ) type A uncertainty( certainty( standard un- ) ) trueness( ) bias( ) Type B uncertainty( ) combined standard uncertainty( ) exonded uncertainty ( ) A. B. Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 73
( 1). x 1, x 2, y 0. y 0 = x 1 + x 2 (71) n e 1n, e 2n n e 0n = e 1n + e 2n (72). N 1 N e 2 N 1 0n = 1 N e 2 N 1 1n + 1 N N 1 n=1 n=1 n=1 e 1n e 2n + 1 N 1 N n=1 e 2 2n (73) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 74
( 2) x 1 x 2 N e 1n e 2n =0 (74). n=1 N 1 N e 2 N 1 0n = 1 N e 2 N 1 1n + 1 N 1 n=1 n=1 N n=1 e 2 2n (75) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 75
( 3) y 0, x 1, x 2 S 0, S 1, S 2. S 2 0 = S2 1 + S2 2 (76) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 76
( 4) y 0 = a 1 x 1 + a 2 x 2 + + a m x m (77) S y0 = a 2 1 S2 a1 + a2 2 S2 a2 + + a2 ms 2 am (78) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 77
( 5) y 0, x. y = Ax (79). y = Ax + n (80) Σ nn,,,, Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 78
... Σ nn = = lim N = lim N lim N 1 N 1 1 N 1 1 N n n n T n (81) N 1 n=1 n 1n N n 2n. ( n 1 n 2 n M ) (82) n=1 n Mn Nn=1 n 1n n 1n Nn=1 n 1n n Mn..... Nn=1 (83) n Mn n 1n Nn=1 n Mn n Mn Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 79
. lim N = lim N =Σ nn 1 N 1 N (y n Ax n )(y n Ax n ) T (84) n=1 1 N 1 N n n n T n (85) n=1 (86) a m, (m =1, 2,...,M) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 80
A x ˆx. ˆx = A 1 y = A 1 (Ax + n) (87) ˆx. lim N = lim N 1 N 1 N (ˆx n x n )(ˆx n x n ) T (88) n=1 1 N 1 = A 1 ( lim N N (A 1 n n )(A 1 n n ) T (89) n=1 1 N 1 N n n n T n )(A 1 ) T = A 1 S nn (A 1 ) T (90) n=1 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 81
2 N : l i, i =1, 2,..., N N (l i X) (91) l=1 ˆX ˆX, (BLUE=Best Linear Unbiased Estimate).. X = 1 N N l i (92) l=1 Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 82
2 ( ),. y, x, e x. y = f(x, e) (93),. f(x, e) ax 2 + bx + c + e (94),. r i = y i (ax 2 i + bx i + c + e i ) (95) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 83
2 ( 2), e i r i r i = y i (ax 2 i + bx i + c) (96) N N Q = ri 2 = N yi 2 2 y i (ax 2 i + bx i + c)+ i=0 i=0 i=0 â, ˆb, ĉ N (ax 2 i + bx i + c) 2 i=0 (97) 2 Q Q a =0, Q b =0, Q =0 (98) c Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 84
2 ( 3) Q a = 2 N i=0 y i x 2 i + N a ( (a 2 x 4 i + b2 x 2 i + c2 +2abx 3 i +2bcx i +2cax 2 i )) = 2 i=0 N y i x 2 N i +2 (ax 4 i + bx3 i + cx2 i ) (99) i=0 Q b = 2 N i=0 Q c = 2 N i=0 y i x i +2 y i +2 i=0 N (ax 3 i + bx2 i + cx i) (100) i=0 N (ax 2 i + bx2 i i=0 + c) (101) Mon, 2006, 401, SAGA, JAPAN Dept. of Mechanical Engineering, Saga Univ., JAPAN 85