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DIMM
. , .
4 2010 .

1

DIMM . : , , , . , DIMM. , . : 1. ( ). 2. ( ). 3. . . 4. . . MASS/DIMM 2007 2009 MASS DIMM. , , , , . DIMM . 5 .

1

2

[1] [2]. . , F (fx , fy ) 2 J = Cn h : F (fx , fy ) = F (f ) = 0.0229r
-5/3 -11/3 f 0

= 0.0229 · 0.423

2

2

Jf

-11/3

,

(1 )

2 2 , fx fy , r0 f = (fx + fy )1/2 . J , . , . , , . (g-tilt) [2], (z-tilt) [3]. [4]. , D, [2]: g Fa (fx , fy ) =

2

2

(2 (fx cos + fy sin ))

2

2J1 ( Df ) Df

2

F (fx , fy ),

(2 )

x , . x . Fd (fx , fy ) , DIMM, Fa , , B - x: Fd (fx , fy ) = [2 sin( B (fx cos( - ) + fy sin( - )))]2 Fa (fx , fy ) (3 )

= 0, ( ), = /2 . . 1 . x, . , . |f | = 0 . , (1) (2) .

2

:
+

=
-

2 d

Fd (fx , fy ) dfx dfy ,

(4 )

, (3) , , DIMM J . 4 [5]. , (2) , . z-tilt, [4], :
z Fa (fx , fy ) =

2

2

(2 (fx cos + fy sin ))

2

8J2 ( Df ) ( Df )2

2

F (fx , fy )

(5 )

g z-tilt Fa (fx , fy ) . g-tilt , .

3

ґ

ґ , ґ , , .

. 1: a) b) . DIMM u. 0.5. 3

, w. "" [7], .. , D/w. [2]: Fd ( ) = Fd ( 2 w
0

dfy Fd ( , fy ) w

(6 )

, x . , , ґ . 4 ) . 2.

90° 10
-12

60°

10

-12

60° 30°

90°

30° 10 w()/2, m
-13

10 w()/2, m

-13

10

-14

10

-14

10

-15

0°

10

-15

0°

0.01

0.1 1 /w, 1/m

10

0.01

0.1 1 /w, 1/m

10

. 2: . D = 0.09 , B = 0.2 r0 = 0.1 . , , . . -1 . w/D , . 4

DIMM 0 4/3. 1 - 3 . , "" . 8

4

DIMM

, DIMM, , .. D2 z . . MASS/DIMM, , (8 24 ) . , DIMM JDI M M - JM AS S , [5, 6, 8]; , [5], [4, 9]. . , ( MASS [10, 11]), 2 2 Cn (z ) :

2 =
0

2 Cn (z )W (z ) dz ,

(7 )

, z , (1) cos2 ( z f 2 ), , , [4]: F (f , z ) = 0.009687 2
2 2 Cn (z )z f -11/3

cos2 ( z f 2 ),

(8 )

, , [7]: F (f ) = 0.009687 2
2 0 2 Cn (z )f -11/3

cos2 ( z f 2 ) dz .

(9 )

, (, ) z 2 z . 2 (fx , fy ). , D, B . 5

, d, :
+ 2 dz Cn (z ) в 0.009687 -

2 =
0

dfx dfy (fx , fy )f

-11/3

cos2 ( z f 2 ).

(1 0 )

1.0

2.0

0.9

1.9
2

/ (0)

2

0.7

2

0.8

l /

2

t

1.8

1.7

0.6 0 5 10 15 20 25

1.6 0 5 10 15 20 25

H, km

H, km

. 3: : W (h)/W (0) g-tilt. . : = 500 ,

DIMM , . = 750

DIMM W (z ), , MASS, . Wl (z ) Wt (z ) .
+

Wl,t (z ) = 0.009687
-

dfx dfy l,t (fx , fy )f

-11/3

cos2 ( z f 2 ).

(1 1 )

e (11) [2] :

W

g ,z l,t

(z ) = 0.009687 в 8

3 0

df I

g ,z

(f ) 1 - 2 cos2 ( )J0 (2 f B ) + 2 cos(2 )

J1 (2 f B ) . (1 2 ) 2 f B

, g-tilt (2) z-tilt (5), I g,z (f ), : I g (f ) = f
-2/3

2J1 ( f D) f D 6

2

cos2 ( z f 2 ),

(1 3 )

I z (f ) = f

-2/3

8J2 ( f D) ( f D)2

2

cos2 ( z f 2 ).

(1 4 ) = /2, -

, = 0, :

W

g ,z l

(z ) = 2.403
0

df I

g ,z

(f ) 1 - 2J0 (2 f B ) + 2 df I
g ,z

J1 (2 f B ) 2 f B

(1 5 ) (1 6 )

W

g ,z t

(z ) = 2.403
0

(f ) 1 - 2

J1 (2 f B ) 2 f B

Wl,t (z ) , , atmos MASS. , , , , . , MASS [12], , . , ( 0.5) . . 3 , . , 2 rF = z , . , . 3 = 750 = 500 1.5 . Wl (z ) Wt (z ), (. 1). , 2 l2 /t , . 3 . , . , , : JDI M M - JM AS S . 2 l2 /t , . 4. 1.58 1.73 . . 4, , JDI M M - JM AS S 16 J16 . , "" . , 16 , , MASS. [4], DIMM , z-tilt. DIMM (14). , Wlgt (0) ,

7

1.0

6в10 4в10 2в10

-13

0.8

-13

-13

P( l/ t)

0.6

-1/3

2

JGL,m

0 -2в10
-13

2

0.4

-4в10 0.2

-13

-6в10

-13

0.0 1.0 1.2 1.4 1.6
2

-8в10 1.8
2 t

-13

2.0

2.2

2.4

-14

-13.5

-13
16

-12.5

l /

log J

2 . 4: : l2 /t "" ( ) "" () JDI M M - JM AS S . : 16 . 25 75% . , 0.3 A MASS

Wlzt (0) DIMM 12% 17%. , Wlzt (0) [5] 3 5% . , , DIMM, MASS, , . . , DIMM 5 , . 10 , 10 .

5

DIMM

, D2 z . [13], , , , [12] . DIMM () . z : () = ~ ~ (f , ) (f , ) cos ( z f 2 )df , 8 (1 7 )

10 10 8 8
-1/3

6

m

-1/3

g,z l,t

W

4

W

z l,t

m

6

4

2

2

0 0

5

10

15

20

0 0

5

10

15

20

h, km

h, km

. 5: : DIMM ( D = 0.09, Wlzt (0), Wlgt (0), , , , [5]. : DIMM: DIMMA IAC: D = 0.05, B = 0.20, - B = 0.05. ,

B = 0.196 ). , miniDIMM: D = 0.05,

~ ~ DIMM (f , ), (f , ) , f . : = ()A()d, (1 8 )

A() . , 0, 2 = 2 : 2 = (1 )(2 ) A(1 )A(2 )d1 d
2

(1 9 )

(1 )(2 ) (17): (1 )(2 ) =
2 2 ~ ~ ~ ~ (f1 , 1 ) (f2 , 2 ) (f1 , 1 ) (f2 , 2 ) cos ( 1 z f1 ) cos ( 2 z f2 )df1 df2

(2 0 ) (10) [12]: 4 2 ~ ~ (f1 , 1 ) (f2 , 2 ) = F (f1 ) (|f1 - f2 |) = Fl (f1 ) (|f1 - f2 |), 1 2 (2 1 )

9

, 42~ ~ d (f1 , f2 ) = 1 2 (f1 , 1 ) (f2 , 2 ), (20) : (1 )(2 ) = Fl (f )d (f ) cos ( 1 z f 2 ) cos ( 2 z f 2 )df (2 2 )

. (19),
2

SA (f , z ) =

A(1 )A(2 ) cos ( 1 z f 2 ) cos ( 2 z f 2 )d1 d2 =

A() cos ( z f 2 )d .

(2 3 ) : 2 = Fl (f ) d (f ) SA (f , z )df (2 4 ) SA (f , z ) [12] : 2 ~ SA (f , z ) = [A(z f 2 /2)] . (2 5 ) , - , . , , . (24) , cos2 ( z f 2 ) SA (z f 2 /2). , . (13) (14). . 6 . W(z) DIMM . 6 . , . , , DIMM .

6

, DIMM 0.01 , , [2] [14] . . DIMM (interlacing) (., , [4]). , , 5 10 .

10

1.0 1.0 0.8 0.9 0.6
A

W(z)/W(0)
0

S

0.8

0.4

0.7 0.2 0.6 0.0 1в10
6

2в10
2

6

3в10
-1

6

4в10

6

0

5

10

15

20

25

zf /2, m

z, km

. 6: : EC650 A0 V ( ) K0 III (). : DIMM: ( A0 V), . , . , . dimm . . , . [2] x (, x ) , w :
2 1 (w ) = -

dfx dfy Fd (fx , fy ) sinc2 (fx w ),

(2 6 )

sinc2 (fx w ) , . , DIMM . , 2 p (p ) 2 (w , p ) :
2 2 (w , p ) = -

dfx dfy Fd (fx , fy ) sinc2 (fx w ) cos2 ( fx wp ),

(2 7 )

11

1.0

1.0

0.9

0.9

2

0.8
0

0.8

/

2

0.7

0.7

0.6

0.6

0.5 1.0 0.8 0.6

0

10

20

30

40

0.5 1.0 0.8 0.6 0.4 0.2 0.0 -0.2

0

10

20

30

40

1

0.4 0.2 0.0 -0.2

0

10

20

30

40

0

10

20

30

40

w, m/s

w, m/s

. 7: : 2 (w) . : 1 . : . : . , , - 45 . ( ), 16 ( ). 4 5

sinc2 (fx w ) cos2 ( fx wp ) . 1 : 1 =
2 22 (w , p ) -1 2 1 (w )

(2 8 )

12

1.00 0.95

1.00 0.95

()/ (0)

0.85 0.80 0.75 0.70 1.0 0.8 0.6

()/ (0)

0.90

0.90 0.85 0.80 0.75 0.70

2

2

0.4
1

0.2

0.0

2

2

1.0

0.8

0.6

0.4
1

0.2

0.0

. 8: 1 .

, . . 7. , 2.5

. 7 2 (w )/ 2 (0) 1 , DIMM : = 4 p = 5 . , , 40 /, 50 70% , . , . 2 . 1 . , : , - . , . , 2 (w ) 2 (w ) 1 , . 8, , 45 . .

13

7

[2, 14] 2 Cn (h) w(h). . , . 8 . , , , 2 1 . ~ , h, 2 (h), 2 (h)1 (h). ~ ~ , , ( ), : 2 = ~ 2 (h) dh, ~ 2 1 = ~ 2 (h)1 (h) dh ~ (2 9 )

( ) 2 2 = 2 (h) dh = 2 (h) · f (1 (h)) dh, ~ (3 0 )

f (1 (h)) , . a0 + a1 1 , (3 0 ) : 2 = 2 (h)(a0 + a1 1 (h)) dh = a0 ~ 2 (h) dh + a1 ~ 2 (h)1 (h) dh = a0 2 + a1 2 1 . (31) ~ ~ ~

, , , , . , . , . 8 2 (1 )/ 2 , ~ : 2 / 2 (1 ). ~ , , 1 , 2007 2009 . . 9, , , . 0.85 . 1 , 0.03. 1 . , , - , . , . 8 , 50% 2% ( 1% ). 90% 14

()
0.0 1.0 0.1 0.2 1.00 0.95 0.8 0.90

F(1), F(),

0.6

1
0.4 0.2 0.0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.85 0.80 0.75 0.70 0.65

0

1

2

3

4

5

6

7

8

1

w, m/s

. 9: : 1 ( ). , . 1 1 ( ). : 1 ( ) (). 25 75% . - 45 . 5%. , 1 , 2 = 2 (1 + 0.15(1 - 1 )) . ~ (3 2 ) 1 < 0.5 8% . DIMM , 4 . 2009 2.5 . -. . 8, , . , .

8

DIMM : Tb Tb /p ( ) ^^ (l , t ) (l2 , t ) . Ta N = Ta /Tb ^ ^2 15

1:
25% Ptot Plow - Ptrend Pt t o . Pl w o Pl w /Pt t o o l/t Pl /P l/t Pl /Pt
t

50% 75% 0.578 0.048 0.002 0.570 0.043 0.175 1.567 1.148 0.926 0.076 0.008 0.917 0.067 0.130 1.690 1.664

25% 50% 75% 0.248 0.026 0.001 0.243 0.023 0.056 0.372 0.042 0.002 0.365 0.037 0.104 0.588 0.067 0.007 0.580 0.060 0.186

0.380 0.031 0.001 0.373 0.027 0.043 1.442 0.779

, Ta = 60 Tb = 2 . , . (26), Tb . , ^^ (l , t ) , ( l , t ). : 1) , (, 0.99) 2) (l2 , t ) ^ ^2 . , Phigh 2 ( l2 , t ), Plow = ( (l - l )2 , (t - t )2 ), Ta , DIMM. Ptot = Phigh + Pl
ow

=

2

+ ( ( - )

2

,

(3 3 )

l t . i i-
2 ^ i = i + (i - )2 .

(3 4 )

, , . 1. Ptrend , . , , ( Pt t Pl w ) o o 10%, 1.5 2%. ( l , t ) , ( , ) 0.034 0.022, . 1. , , . 16

, ( 1 ) . . 10, , . , , Pl w o .

0.3

med l all med t all

0.8

l, observed t, observed l, calculated t,calculated

0.6 0.2
low tot low

0.2

P

P
0.4 0.1 0.2

P
0.1 0.0 0

0.0

0

1

2

3

4

5

6

0.0 7

/Ptot

1

2

w, m/s

3 4 w, m/s

5

6

7

. 10: : . , . Plow Ptot . : . 25% 75% . , . , , . , , , . , , . , . . 10, , . , (6) . ґ , . , 34 Plow /Ptot , . 1 / . , , 17

. , , DIMM, , .

0.4 0.08 0.3 0.06
low

/Ptot P
low

P

0.2

0.04

0.02

0.1

0.00 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0

0

1

2

3

4

5

P

tot

w, m/s

. 11: : Plow Ptot . , . : ( ) (). , . Plow Ptot , . 11 , Ptot 0.5, , , , , . , , , . , , , . , , DIMM, , 20 30% ( 50% ). DIMM , (33), 18

(34). , Ptot .

9

MASS

[1] Fried D.L., JOSA, 55, p. 1427, 1965 [2] Martin H.M., PASP, V. 99, p. 1360, 1987 [3] Fried D.L., Radio Science, 10, p. 71, 1975 [4] Tokovinin A., PASP, 114, 1156, 2002 [5] Sarazin M. Roddier F., Astron. Astrophys., 227, p.294, 1990 [6] Thomas-Osip J., Prieto G., Johns M., Phillips M.,Proceedings of the SPIE, V. 7012, pp. 70121U-70121U-12, 2008 [7] .. . .: , 1967 [8] Tokovinin A., Baumont S., Vasquez J., MNRAS, V. 340, Issue 1, pp. 52-58, 2003 [9] Tokovinin A., Kornilov V., MNRAS, 381, 1179, 2007 [10] Tokovinin A., Kornilov V., in ASP Conference Proceedings, V. 266. Edited by J. Vernin, Z. Benkhaldoun, and C. Munoz-Tunon, p.104, 2002 ~ ~ґ [11] Kornilov V., Tokovinin A., Voziakova O., Zaitsev A., Shatsky N., Potanin S., Sarazin M., Proc. SPIE, V. 4839, p. 837, 2003 [12] Tokovinin A., JOSA(A), 2003, 20, 686, 2003 [13] Berdja A., Borgnino J., Irbah A., Journal of Optics A: Pure and Applied Optics, V. 8, Issue 3, p. 244, 2006 [14] Soules D.B., Drexler J.J., Draayer B.F., et al, PASP, 108, 817, 1996

19