- ) 50 θ 7 0θ» ) 57

5 8 9 3 3 3 3 4 33 4 34 5 4 6 9 9 3-3 3 3 4 5 6 33 7 34 30 3η 3 3θ 35 4 4 38 38 4 40 3

43 4 44 44 4η 48 5 5 57 4

950- ) ) ) 970 [] ) [Ж Д3Ж ) [45] ) 5

[6] 80 [7] - - 3% 6»

- 7

[8 9] Д7] 8

) ё ) 9

) ) ) ) ) 3 4 θ η 7 8 ё - ) ) ) [] 0

) ) ) ) ) [0 ]

) 3 ) ) 4 000θ) 838 7 007η) 8 0004η) 09 h0 ) ) )

Υ=λ/D λ D [] 000 3 3 NGC74θ9 - - 3 [] 3 ) 3

C ξ 0 H0 k=π/λ λ DIMM Differential Image Motion Monitor) GSM Generalized Seeing Monitor) SCIDAR Scintillation Detection and Ranging) MASS Multi Aperture Scintillation Sensor) SLODAR SLOpe Detection And Ranging) [3] r0 C ξ [] 3»» Д3] τ = Vx τ0 τ0 33 4 r V r

) hξ [] ℎ 34 St 4 h = ℎ ℎ h St= 0 St St 08 Д] Д] 5

4 η 5 3 4 η θ 5 3) 4) ) η) )» Д4Ж Д5] τ 6

Д6Ж Д7Ж 00 000 τ τ Д8Ж Д9Ж τ 973 [0]» Д]»» φ τ = r t + + φ = r t + τ t+τ 5) [Ж - η 7

» 04 Д3Ж [4] Tip-tilt) ) 8

Ы ) ) 0 ДЖ Д8] 883 Re Re>Re Re<Re = / 9 6)

u L Vm L ё u L u L= -η /c Vm = 0η Re= 5 7*05) / L0 l0 L0 L0 z z ) L0>>z ΔU 0 Δ U 0 L /V L l0 ΔU 0 l0 L /V ε Д -3 Ж l<l0 εk 0

V ε = l0>> V К ε l0<<l<<l0 l0 [8] ) Д8] Ч и p p - Dn = [n ]»

Dn Cn = Cn ρ ρбв) Фn æ = æ = L æm = r æ +æ exp æ ) æm l L0 l0 r = Cn k L у = D/r D ДЖ ) τ0 ДηЖ r τ = Vx τ0 V x 3 z t E=E ik E = E + ik n x y E z

ρ z t E=E x y z k= ) λ π λ n x y = + ) К a0 zd = ka г L ё г г 3

3 904 Д6Ж GreatRefractor 97 Д7] 60 0 [7] Д8Ж 4

3 6-6 ДηЖ Д9] ) ni ni nj εk = iii / Iij i= k n ni i= j= ni nj = jij / Iij i= Ii = j=j Iij Ij = ni=i Iij Iij i j i= ni j= nj ni nj ε i= j= 5 7

7 λ/d d Д30Ж ) 3 θ4 8 8) Д8Ж 8 4 ) r0) 6

) 3) J 06 05 04 03 0 0 3 0 4 00 003 004 005 006 007 008 009 0r0 8 ) θ4 3 θ4 75 4 33 W r Дη 9Ж Zi r W r = = c Z r ci r = x y k Nbasis Zj xk yk ) Wxk yk ) = cj x x j= 7

W x y y = j= Nbasis εk Nlens Nbasis [ cj j= k= e [ c = εk = f xy) Ф xk yk x Z k k= Nlens Z Z x y y = c =f = k Zj xk yk ) εk ] min x Z x y y ] min Ф j Ф xk yk y k П 89) cj Nlens Nbasis Zj xk yk ) [ cj εk ] = x u k= j= Nlens Nbasis Zj xk yk ) [ cj k] = u y k= j= 5) Zi Zj = An Rm n r 8 е иm=

Rm n n m r = p= p m Zj = An Rm n r r cos mц е иm m Zj = An Rm n r r sin mц е иm n p! [p! m n n+m p! An = n + p!] rn m p nm) η n m [3] n m 0 0 0 r МШЬ ) x - r ЬТЧ ) y 3 θrьтч ) 4 0 3r) 5-6 rмшь ) 6 3 3 r3 ЬТЧ3 ) 7 3 3r3-Ы) ЬТЧ ) 8-3 3r3-Ы) МШЬ ) 9-3 3 r3 МШЬ3 ) 0 4 4 0 r4 ЬТЧ4 ) 4 0 4r43r) ЬТЧ ) 0 4 5 6r4-6r+) 3-4 0 4r4-3r) МШЬ ) 4-4 4 0 r4 МШЬ4 ) 5 5 5 3 r5 ЬТЧη ) 9 η- ηё 5 m n

A C = B AT A AT A C = AT B AT A C = AT A C = AT A AT B AT B AT A C B 34 0 r0 vx 0» 003 м) 0 03r0 / v x [] vx 03r0» 004 м 006 м) r0» 007 м 0 м) [7] 30» 00 м 9

9 3 4 η / a 0 00 0θ3 I 05 ) 9) 8x8 θx6 9) 93) 94) η η 9η) Ы0 0a0 8x8 θxθ 8x8 θ4 pxl θxθ 8x8 0» 4 3 pxl θx6 4 W λ) W λ) N 0 64 7 90 53 36 379 44 505 - N 0 64 7 90 53 36 379 44 505 - -4-4 0 N W λ) 8x8 3 θx6 0 ηxη 8x8 θxθ 3

09484 6436 8x8 6x6 33 03549 3 3409 9569 4 35304 303644 5 7947 337434 6 095774 30 7 0988 7879 8x8 θx6 η η 8 8 θ θ θ4 θ4 3 3 35 [3] m= p = [ + )] z q r =x +y r r z k= /λ 3 λ m 4

m 8 m=) m=4) m=8) W e w e4 = exp = exp = exp = exp + + + + r0=005 33 )

4 Wλ) N 0 64 7 90 53 36 379 44 505 - -4 4 3 4 5 W λ) N 0 64 7 90 53 36 379 44 505 - -4 3 4 5 N W λ) 8x8 θ θ -0) 3 0) 4 0) η 0) 0-0 8 8 6x6 8x8 θx6 3 3 8x8 6x6 0555946 0575780 0585446 0579886 34 09856 09056 0588409 057758

3 8 8 θ θ 36»» 3 ) r0 3 W λ) θxθ N 3 8x8 r0= 00η 3 8x8 r0=00 3 8x8 35 θxθ θxθ r0=0

4 θ θ 8 8 3 r 4 k s D r0 3 5 ks D 6xθ 5 r0 3»» 5 36

5 ) θ θ 8 8 5 37

4 [33Ж 4» 0) S Nlens t Vx = S/ t S= D Ne Nscr f t = N T=/f /f ε ) Nlens [5 9] 38 )

Rlm = i= Nlens N i=lens εil εl ) εim εm ) N [ i=lens εil N εm ) ] εl ) i=lens εim j= Nlens εl и ε m и ε l=j+nl Nlens l=j+nm Nlens Nl Nm=0 N- / ε [34] Cε Cε T N T R lm 3 [35] Vx = h nfinal ncorr / Ncorr t 39

h nfinal Nfinal ncorr Ncorr nfinal Ncorr t 4 [5 7 9]» 0) ε 4 ) +»»» 8 8 θ θ 3 ) η η) pxl 00 θ θ 3 3) pxl 8 8 θ4 θ4) pxl I=05 / 0=005 λ=0θ3 8 8 / S=0θ4*8=000η =000η t= 0005/ θ θ 40 /

S=03*θ=000η 8 8 4 r0=00η» pxl» Vx / 4 8 6 3 64 004 008 06 03 064 0065 05 05 05 008 004096 00048 0004 0005 43 6 7) R lm 05 N 0 3 63 94 5 56 87 8 49 80 3 34 373-05 - 6 Rlm N 6 θ θ 8x8 Rlm θ θ 8 8 Nscr Vx = 0065 / 4

8 8 θ θ 7 Rlm [7] Rlm 05 0 3 5 37 49 6 73 85 97 09 33 45 57 69 8 93 N -05-7 3 Rlm N r0 =00 r0 =00η 3 r0 =0 Rlm»»»»»»» Rl m x Дn] n Rx) Rx) 8 4

Rx) 05 N 0 3 63 94 5 56 87 8 49 80 3 34 373-05 - Rx) 05 N 0-05 3 63 94 5 56 87 8 49 80 3 34 373 - R x) 05 N 0 3 63 94 5 56 87 8 49 80 3 34 373-05 - Rx) 05 N 0 3 63 94 5 56 87 8 49 80 3 34 373-05 - 8 ) 4 ЩбХ Vб=00θη / ) ) 8 ЩбХ Vб=0η / ) ) θ ЩбХ Vб=0η / ) ) 3 ЩбХ Vб=05 / ) 8 8 8 θ θ 8 8 Rlm θ 6 η 43

5 x pxl Vx / 4 0064 8 08 6 056 3 05 64 04 5 3% 44 ) 9 9 ) ) ) ) ) 0 44

0 ) ) ) ) ) Rx) 05 N 0 6 3 46 6 76 9 06 36 5 66 8 96-05 3 - Rx) 05 N 0 6 3 46 6 76 9 06 36 5 66 8 96-05 3 - Rx) N 4 pxl -0) -05) 3 0) 0) 0η) 3) 3) 45 8 8

Rx) Rx) 4 pxl Rx) 05 N 9 7 5 33 4 49 57 65 73 8 89 97 05 3 9 37 45 53 6 69 77 85 93 0-05 - Rx) 05 N -05 9 7 5 33 4 49 57 65 73 8 89 97 05 3 9 37 45 53 6 69 77 85 93 0 - R x) 4 pxl 8 8 Rx) θ 6 64 pxl 3 pxl 6 pxl 8 pxl 4 pxl 8 8 8 8 7 6 4 40 7 00 4 40 7 36 3 56 04 00 40 7 36 46 48 88 00 56 04 64 0

6 4 pxl 8 8 pxl θ4 6 pxl 3 3 pxl 6 64 pxl 8 Rx) 3 3 R ) 47

7 7 x pxl Vx / 4 0064 7 8 08 6 056 3 05 64 04 3% 45 [36] [37] 0θ3 / a 0 005 I 05 ) 8x8 48

Д-00 00Ж 000 0065 / 4 ) ) ) η η N ) ) ) [-00 00] ) Д-0 0] 49

5»» θ [-00 00] [-0 0] R lm 05 N 0 3 4 5 6 7 8 9 0 3 4 5 6 7 8 9-05 - 6 [-00 00] Д-0 0] 0064 / 3% 6 [-00 00] [-0 0] N Rlm 3c 3 50

8 8 θ θ 3% 0 3 SCOPUS [35 3847] [4850]» θ04 606 η-9-003» 5

// 04 84 θ C 599 640 // 009 4η 8898 3 // 4 008 η 9/3 5964 Kazuhiro S Kazuhiro K Shuichi M and et al Extended depth of focus adaptive optics spectral domain optical coherence tomography // Biomedical optics express Oct 0 V 3 0 P 353370 4383 5 0083408/8 6 0θ 986 3 9 8088 999 4 9 8 00 // 7 / G0J 9/00 97θ 73 98η 33θ Д 0 Ж URL http//wwwlaserportalru/content_8 300η0η) Fundamentals of Atmospheric and Adaptive Optics [ http//wwwaeosulgacbe/upload/aopdf ] URL 300505) 000 Д http//acoifmoru/upload/publications/book_basic_optics_000pdf Ж URL 0006) 3 0 8 5

4 0040η 006 53 c 5 // 0 4 979984 6 // 04 7 0 9η93 7-008 η 8 // 00 3 07035 9 - // 00 3 04047 0 Vernin J Roddier F Experimental determination of two-dimensional spatiotemporal power spectra of stellar light scintillation Evidence for a multilayer structure of the air turbulence in the upper troposphere // J Opt Soc Am 973 V 63 P 7073 990 Matthias Schock Earl J Spillar Measuring wind speeds and turbulence with a wave-front sensor // Opt Lett Feb 998 V 3 3 P 505 3 Roopashree M B Akondi V Raghavendra B P Wind speed measurement from Shack Hartmann Wavefront Sensor data An experimental review of cross-correlation peak detection// ACEEE Nov 0 V 6 НШТ 0 IJRTET0θ09η 4 Wang C Hu LWang Y and et al Time delay compensation method for tiptilt control in adaptive optics system // Appl Opt Apr 05 V 54 P 33833388 5 Tokovinin A Measurement of seeing and the atmospheric time constant by differential scintillations // Appl Opt 00 V4 P 957964 6 Hartmann J Objetivuntersuchungen // Z Instrum 904 P 3397 7 Shack RB and Platt BC Production and use of a lenticular Hartmann screen// JOSA 97 V 6 P 65666 53

8 // 009 4η 8898 9 30 // 009 7 933 ё // 0 48 445 3 Ж [ URL http//wwwopticsru/rus_general_allhtm?http//wwwopticsru/zernikehtm 80θ) 3 Korolenko P Optics of Coherent Radiation Moscow Publishing House of the Moscow University 989 96 p 33 // 985 8 θ30 34 // 008 7η80 35 // 03 ηθ 8/3 79 36 Д 3) Ж URL http//wwwstormoffru/articles_565_84html 8036) Д 37 Ж URL http//wwwssauru/files/education/metod_/%d0%a%d0%b5%d%80%d0%b3%d0%b 5%D0%B5%D0%B%0%D0%9%D0%9%0%D0%A4%D0%B8%D0%BB%D%8C %D%8%D%80%D0%B0%D%86%D0%B8%D%8F%0%D%88%D%83%D0%BC %D0%BE%D0%Bpdf 38 5036) Goleneva NV Lavrinov VV Lavrinova LN Numerical research of measurements of ShackHartmann wavefront sensor according to the parameters of its optical parts and the intensity of turbulent distortions // Proceedings of SPIE 05 V9680 CID 9680 F P 968048 54

39 Goleneva NV Lavrinov VV Lavrinova LN Analysis of correlation properties of ShackHartmann sensor measurements depending on the characteristics of the intensity distribution in the laser beam // Proceedings of SPIE 05 V 9680 CID 9680 J P 968033 40 // 05 58 8/ η86 4 Goleneva NV Lavrinov VV Lavrinova LN and et al The numerical research of the dependence of the correlation property of the measurement of the ShackHartmann wavefront sensor on the lenslet array size and the turbulent distortions intensity // 4 05 58 0/3 47 // 05 η θ θ3 69 43 Goleneva NV Lavrinov VV Kopylov EA and et al Investigations of parameters of image quality for adaptive optical systems of BSVT // Proc SPIE 905 V9680 doi 07/05600 O [9680 O- O-5] 44 Goleneva NV Antoshkin LV Lavrinov VV and et al Adaptive correction of turbulent distortion by MEMS flexible mirror // Proc SPIE 905 V9680 doi 07/05768 W [9680 W- W-] 45 Antoshkin LV Goleneva NV Lavrinova LN and et al Method of alculating the ross-wind Speed at the entrance aperture of an adaptive system based on ShackHartmann wavefront sensor measurements // Optoelectronics Instrumentation and Data Processing 05 V 5 θ P 6 46 Goleneva NV Lavrinov VV Lavrinova LN Numerical simulation of correlation method calculating the transverse component of the wind speed on basis of the measurements on the ShackHartman sensor // Proc SPIE 504 V99 doi 07/07500 P 9997 47 Antoshkin LV Goleneva NV Lavrinova LN and et al Analysis of efficiency of the correlation algorithm calculating the speed of the cross wind transfer of the turbulence // Proc SPIE 504 V 99 doi 07/075003 P9998 0θθ4θ0 48 / 55

0θθ87» 8 0θ 0θ 8 0ηθ804 49 / 0ηθη049 0» 0η 9 05 04θθ9η 50 / 04θ47θ3» 08 56 04 04

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