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Vladimir P. Lukin V.E. Zuev Institute of Atmospheric Optics SB RAS,

OUTER SCALE OF TURBULENCE IN THE ANISOTROPIC BOUNDARY LAYER. Vladimir P. Lukin V.E. Zuev Institute of Atmospheric Optics SB RAS, Zuev Sq.,1, 634055, Tomsk, Russia, lukin@iao.ru.

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Vladimir P. Lukin V.E. Zuev Institute of Atmospheric Optics SB RAS,

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  1. OUTER SCALE OF TURBULENCE IN THE ANISOTROPIC BOUNDARY LAYER Vladimir P. Lukin V.E. Zuev Institute of Atmospheric Optics SB RAS, Zuev Sq.,1, 634055, Tomsk, Russia, lukin@iao.ru During a period of 40 years we have performed successively the investigations of the effect of low-frequency spectral range of atmospheric turbulence on the optical characteristics. The turbulence models as well as a outer scale of turbulence have been determined and its influence on the characteristics of telescopes and systems of laser beam formations has been investigated too. Centre for Advanced Instrumentation, Durham University, UK, Sept. 2014

  2. CONTENT • 1. INTRODUCTION. PHASE FLUCTUATIONS MEASUREMENTS • 2. DEVELOPMENT OF THE MODELS OF TURBULENCE SPECTRA • 3. OUTER SCALE OF TURBULENCE AND INSTABILITY PARAMETER • 4. INVESTIGATION OF ANISOTROPY OF THE ATMOSPHERIC TURBULENCE SPECTRUM IN LOW-FREQUENCY REGION • 5. INVESTIGATION OF THE ATMOSPHERIC TURBULENCE DYNAMICS OF THE BASIS OF ASTROCLIMATIC OBSERVATIONS • 6. HIGH-ALTITUDE OF ATMOSPHERIC TURBULENCE • 7. THE MODEL “AVERAGED” OVER THE ENTIRE COLOMN ATMOSPHERE • 8.OUTER SCALE OF ANISOTROPIC TURBULENCE • 9. CHARACTERISTICS OF GROUND-BASED OPTICAL TELESCOPE DUE TO ATMOSPHERIC TURBULENCE

  3. In the early 70’s the scientists in Italy (A.Consortini, M. Bertolotti, L. Ronchi), in USA (Ochs, Buser, S.Clifford) and in USSR (V.Pokasov, V.Lukin) almost simultaneously discovered the phenomenon of deviation from the power law and the effect of saturation for the structure phase function. This meant the existence of correlation for phase fluctuations and the need in applying the turbulence spectrum with a finite outer scale Lo. My main papers for subject are: V. Lukin, V. Pokasov, S. Khmelevtsov, “Investigation of temporal characteristics of optical waves phase propagating in ground-boundary layer”, Izv. VUZov. Radiofizika, 15, No.12, pp.1861-1866, 1972. V.Lukin, V.Pokasov, “Optical wave phase fluctuations”, Applied Optics, 1981, V.20, No.1, pp.121-135.

  4. CONTENT • 1. INTRODUCTION. PHASE FLUCTUATIONS MEASUREMENTS • 2. DEVELOPMENT OF THE MODELS OF TURBULENCE SPECTRA • 3. OUTER SCALE OF TURBULENCE AND INSTABILITY PARAMETER • 4. INVESTIGATION OF ANISOTROPY OF THE ATMOSPHERIC TURBULENCE SPECTRUM IN LOW-FREQUENCY REGION • 5. INVESTIGATION OF THE ATMOSPHERIC TURBULENCE DYNAMICS OF THE BASIS OF ASTROCLIMATIC OBSERVATIONS • 6. HIGH-ALTITUDE OF ATMOSPHERIC TURBULENCE • 7. THE MODEL “AVERAGED” OVER THE ENTIRE COLOMN ATMOSPHERE • 8.OUTER SCALE OF ANISOTROPIC TURBULENCE • 9. CHARACTERISTICS OF GROUND-BASED OPTICAL TELESCOPE DUE TO ATMOSPHERIC TURBULENCE

  5. 2. DEVELOPMENT OF THE MODELS OF TURBULENCE SPECTRA

  6. 2. DEVELOPMENT OF THE MODELS OF TURBULENCE SPECTRA (cont.)

  7. 2. DEVELOPMENT OF THE MODELS OF TURBULENCE SPECTRA (cont.) • Atmospheric turbulence models with a finite outer scale, such as Greenwood-Tarazino’s, Von Karman’s, Russian model, have found wide usage. • In 1993 I showed that it is possible to pass from one model to the other: • V.P. Lukin, "Intercomparison of models of the atmospheric turbulence spectrum", Atmos. Oceanic Opt. 6, pp. 628–631, 1993. • V. Lukin, “Comparison of spectral model of atmospheric turbulence”, Proc.SPIE, 1994, V.2222, pp.527-535. • V.V. Voitsekhovich, J. Opt. Soc. Am. A12, pp.1346–1353, 1995. • V.V. Voitsekhovich and S. Cuevas, J. Opt. Soc. Am. 12, pp.2523–2531, 1995. , .

  8. CONTENT • 1. INTRODUCTION. PHASE FLUCTUATIONS MEASUREMENTS • 2. DEVELOPMENT OF THE MODELS OF TURBULENCE SPECTRA • 3. OUTER SCALE OF TURBULENCE AND INSTABILITY PARAMETER • 4. INVESTIGATION OF ANISOTROPY OF THE ATMOSPHERIC TURBULENCE SPECTRUM IN LOW-FREQUENCY REGION • 5. INVESTIGATION OF THE ATMOSPHERIC TURBULENCE DYNAMICS OF THE BASIS OF ASTROCLIMATIC OBSERVATIONS • 6. HIGH-ALTITUDE OF ATMOSPHERIC TURBULENCE • 7. THE MODEL “AVERAGED” OVER THE ENTIRE COLOMN ATMOSPHERE • 8.OUTER SCALE OF ANISOTROPIC TURBULENCE • 9. CHARACTERISTICS OF GROUND-BASED OPTICAL TELESCOPE DUE TO ATMOSPHERIC TURBULENCE

  9. 3. OUTER SCALE OF TURBULENCE AND INSTABILITY PARAMETER • Measurements of phase structure function in saturation region may to give information for outer scale: • In experiments we used a homodyne phasometer and obtained the nice tool for measurements of outer scale in near surface region of atmospheric. • In the experiments also were employed: measurers of the temperature and wind velocity at fixed altitudes, data were used for calculating the temperature structure parameter and instability parameter

  10. 3. OUTER SCALE OF TURBULENCE AND INSTABILITY PARAMETER (cont.) • In 1980 I found that the outer scale of turbulence Lo depends on the thermodynamic stability of the atmosphere. • In the surface layer of the atmosphere the outer scale of the turbulence can be comparable, on the one hand, with the hight over the underlayer surface and, on the other hand, the scale is dependent on characteristics of thermodynamic instability.

  11. CONTENT • 1. INTRODUCTION. PHASE FLUCTUATIONS MEASUREMENTS • 2. DEVELOPMENT OF THE MODELS OF TURBULENCE SPECTRA • 3. OUTER SCALE OF TURBULENCE AND INSTABILITY PARAMETER • 4. INVESTIGATION OF ANISOTROPY OF THE ATMOSPHERIC TURBULENCE SPECTRUM IN LOW-FREQUENCY REGION • 5. INVESTIGATION OF THE ATMOSPHERIC TURBULENCE DYNAMICS OF THE BASIS OF ASTROCLIMATIC OBSERVATIONS • 6. HIGH-ALTITUDE OF ATMOSPHERIC TURBULENCE • 7. THE MODEL “AVERAGED” OVER THE ENTIRE COLOMN ATMOSPHERE • 8.OUTER SCALE OF ANISOTROPIC TURBULENCE • 9. CHARACTERISTICS OF GROUND-BASED OPTICAL TELESCOPE DUE TO ATMOSPHERIC TURBULENCE

  12. 4. INVESTIGATION OF ANISOTROPY OF THE SPECTRUM OF ATMOSPHERIC TURBULENCE IN LOW-FREQUENCY REGION Together with the dependence of the outer scale of turbulence on variations of meteorological parameters of the atmosphere, there exists anisotropy of atmospheric turbulent spectra. The properties of inhomogeneities with dimensions exceeding several meters depend on direction. As a consequence, the characteristics of some parameters of optical waves appear to be direction dependent. Three dimensional turbulent atmospheric spectra for optical wave propagating application is converted into two-dimensional one. Actually we take into account two sizes of outer scale along two perpendicular direction: For example, the random two-directional displacements of an image formed along the horizontal atmospheric path on aperture with radius , which is formed by the optical radiation passed through layers, exhibit such properties:

  13. 4. INVESTIGATION OF ANISOTROPY OF THE SPECTRUM OF ATMOSPHERIC TURBULENCE IN LOW-FREQUENCY REGION (cont.) • In our papers • Lukin V.P., Investigation of anisotropy of the atmospheric turbulence in the low-frequency range, Proc. SPIE, Vol.2471, 1995. • Lukin V.P., Antoshkin L.V., Botugina N.N., Emaleev O.N., Lavrinova L.N., Investigation of turbulence spectrum in the ground atmospheric layer, Atmospheric and Ocean Optics, Vol.8, No.12, pp.993-996, 1995. • was been shown that for Hence, we may to calculate its ratios:

  14. 4. INVESTIGATION OF ANISOTROPY OF THE SPECTRUM OF ATMOSPHERIC TURBULENCE IN LOW-FREQUENCY REGION(cont.) • If the outer scale has equal horizontal and vertical dimensions ( ), then • and . In this case the isotropy takes place. • Alternatively, if , then we have an anisotropy. • Our new spectrum have two parameters in large-scale region: , The data of experiments give us to calculate two parameters too: . These two experimental parameters are not sensitive to experiment and path parameters ( ). Optical measurement were accompanied by corresponding meteorological measurements of temperature pressure and wind velocity

  15. 4. INVESTIGATION OF ANISOTROPY OF THE SPECTRUM OF ATMOSPHERIC TURBULENCE IN LOW-FREQUENCY REGION (cont.) • Meteorological data were used for calculating the following characteristics at the height of optical radiation propagation: - Obukhov’s parameter of stability, • outer scale of turbulence (Tatarski estimation from meteorological data). The so-called coefficient of anisotropyobtained in the experiment, varied in the interval from 0.82 to 2.87 with the mean value 1.85 that indirectly indicated that the optical inhomogeneities, which produce the phase fluctuations, were anisotropic in the large-scale region. The relationship is obvious between the coefficient of anisotropy value and the instability parameter. The measured values of anisotropy can be explained with the help of the spectrum as a model with two different projections of the outer scale of turbulence into the vertical and horizontal directions.

  16. CONTENT • 1. INTRODUCTION. PHASE FLUCTUATIONS MEASUREMENTS • 2. DEVELOPMENT OF THE MODELS OF TURBULENCE SPECTRA • 3. OUTER SCALE OF TURBULENCE AND INSTABILITY PARAMETER • 4. INVESTIGATION OF ANISOTROPY OF THE ATMOSPHERIC TURBULENCE SPECTRUM IN LOW-FREQUENCY REGION • 5. INVESTIGATION OF THE ATMOSPHERIC TURBULENCE DYNAMICS OF THE BASIS OF ASTROCLIMATIC OBSERVATIONS • 6. HIGH-ALTITUDE OF ATMOSPHERIC TURBULENCE • 7. THE MODEL “AVERAGED” OVER THE ENTIRE COLOMN ATMOSPHERE • 8.OUTER SCALE OF ANISOTROPIC TURBULENCE • 9. CHARACTERISTICS OF GROUND-BASED OPTICAL TELESCOPE DUE TO ATMOSPHERIC TURBULENCE

  17. 5. INVESTIGATION OF THE ATMOSPHERIC TURBULENCE DYNAMICS OF THE BASIS OF ASTROCLIMATIC OBSERVATIONS We applied the stars motion measurements in focal plane small telescope for near horizontal atmospheric paths. Several experiments with point source jitter for propagation along horizontal paths near ground ( h = 2.5 m) were made. Under the near surface conditions one can expect a strong anisotropy of the turbulence that leads to the anisotropy of the jittering process. As a result for horizontal propagation we have the strong anisotropy: Thus, the vertical size of large-scale turbulence smaller then horizontal one in (1.4 – 3) times and this level depend from parameter of stability of atmosphere

  18. 5. INVESTIGATION OF THE ATMOSPHERIC TURBULENCE DYNAMICS OF THE BASIS OF ASTROCLIMATIC OBSERVATIONS (cont.) Then we apply the stars motion measurements in focal plane small telescope for vertical and slant atmospheric paths we used. • For the stars, observed at small zenith angles the jitter is • practically isotropic – parameter • At the same time, observed at large zenith angles is order are • indicate of strong anisotropy too ( ). • Thus it implies that: • in the case of vertical propagation (along the zenith direction) the effective spectra of turbulence practically isotropic, • the anisotropy of the spectrum is maximum near ground surface (observed optical beams jitter along the horizontal propagation) and determined by the atmospheric instability.

  19. 5. INVESTIGATION OF THE ATMOSPHERIC TURBULENCE DYNAMICS OF THE BASIS OF ASTROCLIMATIC OBSERVATIONS (cont.) • In 1983 we have made the first approach for impact the effective outer scale for entire atmosphere. We have calculating the phase structure function with Russian model turbulence spectra for vertical wave propagation and presented the integral value (along the vertical path) as We used very known A.Gurvich’s model and the Coulman-Vernin vertical profile for outer scale: Here are is Fried’s radius for vertical path, is a fitting parameter to adjust the result of calculation with simple model.

  20. 5. INVESTIGATION OF THE ATMOSPHERIC TURBULENCE DYNAMICS OF THE BASIS OF ASTROCLIMATIC OBSERVATIONS (cont.) We made a measurements of star angular displacements variance for different aperture sizes. Aperture average function of star image jitter data on TT-600 (Zelenchuk, 1982) presented on Figure. Experimental dots are out of theory curves calculated for Kolmogorov model of turbulence with infinite outer scale. These calculations of effective size of outer scale based on these measurements gave =1.6 m.

  21. 5. INVESTIGATION OF THE ATMOSPHERIC TURBULENCE DYNAMICS OF THE BASIS OF ASTROCLIMATIC OBSERVATIONS (cont.) • Under similar approximation the phase structure function presented as: • and for have two regions: . For NTT (3.6m, La Silla) data it gave us two parameters for entire atmosphere = (0.6-0.8) m, =17 cm (for 0.5 mkm).

  22. 5. INVESTIGATION OF THE ATMOSPHERIC TURBULENCE DYNAMICS OF THE BASIS OF ASTROCLIMATIC OBSERVATIONS (cont.) Using similar formulas we may calculate the temporal structure function of phase difference: Then for , , but for . . We used the data of R.Angel measurements on MMT (Arizona, 6.5 m, Mt. Graham) and obtained the next estimation:

  23. 5. INVESTIGATION OF THE ATMOSPHERIC TURBULENCE DYNAMICS OF THE BASIS OF ASTROCLIMATIC OBSERVATIONS (cont.)

  24. CONTENT • 1. INTRODUCTION. PHASE FLUCTUATIONS MEASUREMENTS • 2. DEVELOPMENT OF THE MODELS OF TURBULENCE SPECTRA • 3. OUTER SCALE OF TURBULENCE AND INSTABILITY PARAMETER • 4. INVESTIGATION OF ANISOTROPY OF THE ATMOSPHERIC TURBULENCE SPECTRUM IN LOW-FREQUENCY REGION • 5. INVESTIGATION OF THE ATMOSPHERIC TURBULENCE DYNAMICS OF THE BASIS OF ASTROCLIMATIC OBSERVATIONS • 6. HIGH-ALTITUDE OF ATMOSPHERIC TURBULENCE • 7. THE MODEL “AVERAGED” OVER THE ENTIRE COLOMN ATMOSPHERE • 8.OUTER SCALE OF ANISOTROPIC TURBULENCE • 9. CHARACTERISTICS OF GROUND-BASED OPTICAL TELESCOPE DUE TO ATMOSPHERIC TURBULENCE

  25. 6. HIGH-ALTITUDE OF ATMOSPHERIC TURBULENCE • To describe the optical radiation propagation at vertical and slant optical paths it is necessary to introduce into account vertical distribution of parameters of atmospheric turbulence. Undoubtedly, the outer scale of the turbulence undergoes significant variations both in the surface layer and at the large altitudes. • At present, there are exist a lot of models of height profiles L0(h). Some models chosen for the study are presented below: (A) (B) (C)

  26. 6. HIGH-ALTITUDE OF ATMOSPHERIC TURBULENCE (cont.) (D) (E) The model (A) is recommended for small heights, (B) is proposed by D.L. Fried, and (C) is a generalization of (A) and (B). The models (D) and (E) are obtained by generalizing results of measurements performed in the USA, France, and Chile. Model E is known Coulman-Vernin profile. Models (D) and (E) obtained from data of astronomical measurements, hence, its is not good for altitude below altitude of site summits.

  27. 6. HIGH-ALTITUDE OF ATMOSPHERIC TURBULENCE (cont.) A modified Coulman-Vernin profile of the outer scale of turbulence according to-situ sounding made during the PARSCA campaign (PARanal Seeing Campaign) in March 1992. According the PARSCA data (see Figure), the average outer scale of turbulence presents a maximum at ground level twice larger than maximum of the model: here is the altitude of the mountain summit. At Paranal = 2636 m.

  28. 6. HIGH-ALTITUDE OF ATMOSPHERIC TURBULENCE (cont.)IAO SB RAS experimental data of CT2 (left) and outer scale Lo (right) from acoustical sounding. These data gave us the values of outer scale for small altitudes above the ground.

  29. CONTENT • 1. INTRODUCTION. PHASE FLUCTUATIONS MEASUREMENTS • 2. DEVELOPMENT OF THE MODELS OF TURBULENCE SPECTRA • 3. OUTER SCALE OF TURBULENCE AND INSTABILITY PARAMETER • 4. INVESTIGATION OF ANISOTROPY OF THE ATMOSPHERIC TURBULENCE SPECTRUM IN LOW-FREQUENCY REGION • 5. INVESTIGATION OF THE ATMOSPHERIC TURBULENCE DYNAMICS OF THE BASIS OF ASTROCLIMATIC OBSERVATIONS • 6. HIGH-ALTITUDE OF ATMOSPHERIC TURBULENCE • 7. THE MODEL “AVERAGED” OVER THE ENTIRE COLOMN ATMOSPHERE • 8. OUTER SCALE OF ANISOTROPIC TURBULENCE • 9. CHARACTERISTICS OF GROUND-BASED OPTICAL TELESCOPE DUE TO ATMOSPHERIC TURBULENCE

  30. 7. THE MODEL “AVERAGED” OVER THE ENTIRE COLOMN ATMOSPHERE • The possibility to introduce an efficient outer scale as an integral characteristic of turbulence is of great interest as it can permit one to change the height profile for the outer scale. • One of the reasons to introduce this parameter is that the applicability of the models of height profiles of atmospheric turbulence is restricted due to their dependence on geographical location. It will also permit one to simplify mathematical calculations connected with the account for influence of the atmospheric turbulence on the phase of optical wave. • A.Gurvich’s model

  31. 7. THE MODEL “AVERAGED” OVER THE ENTIRE COLOMN ATMOSPHERE (cont.) • We propose methods for determining the effective outer scale, namely, by the discrepancy between structure functions of phase fluctuations on the saturation level. • To determine the effective outer scale by this model, minimization of the integral square discrepancy of structure functions of phase fluctuations . This Figure presented several variants of introducing we used.

  32. 7. THE MODEL “AVERAGED” OVER THE ENTIRE COLOMN ATMOSPHERE (cont.) • Analysis of the value obtained by different methods for the same height profile demonstrates that its growth i.e., • [0...10 m] < [0...Arg(90%)]  •   [0...]) • is caused by the necessity to compensate for increasing influence of the portions at large argument values with the increase of • (i.e., for intervals • [0...10 m] < [0...Arg(90%)]  • < [0...]). • Studying the dependence of the value • on the model of • one can say that lower value • of for the “best” vision conditions is caused by essential distinctions in the behavior of . The “best” profile rapidly falls off with the growth of height, and the probability of appearance of large-scale fluctuations diminishes.

  33. 7. THE MODEL “AVERAGED” OVER THE ENTIRE COLOMN ATMOSPHERE (cont.) • Figure presented the structure function for the profile (C) and the family of structure functions calculated for fixed values of • . • The structure function for the profile  – C and for the corresponding effective outer scale -for model (C). • V. Lukin, B. Fortes, E. Nosov, “Effective “outer scale of turbulence” for imaging through the atmosphere”, Proc. SPIE, Vol.2319, pp.98-106, 1997.

  34. 7. THE MODEL “AVERAGED” OVER THE ENTIRE COLOMN ATMOSPHERE (cont.) • Dr. Borgino alike us suggested to use the effective outer scale for the atmosphere as a whole as a given in formula: • For the outer scale of turbulence, several models of its vertical profile in the atmosphere were proposed. • Based on them I calculated the effective outer scale for the atmosphere as a whole for Gurvich model of structure parameter. • This scale turned out to be about 10-20 meters for the best observatories of the world.

  35. 7. THE MODEL “AVERAGED” OVER THE ENTIRE COLOMN ATMOSPHERE (cont.) • Effect of underlying terrain on jitter of astronomic images • As can be seen from formula the effective outer scale of turbulence depends on the receiver’s height above the surface . • However, this height is often taken zero. • Estimates show that the relative error introduced by substitution of zero • ( = 0) for the real receiver’s height is • on the order of . • This error becomes significant for large ground-based telescopes, in which the center of the entrance mirror is typically located at the heights of some tens of meters from the underlying surface. • For example, for the 25m receiver’s height • = 25 m the error is 20%. = 3 (a), 6 (b), 12 (c), 24 (d), and 48 m (e).

  36. 7. THE MODEL “AVERAGED” OVER THE ENTIRE COLOMN ATMOSPHERE (cont.) • 1. One can introduce the effective outer scale of turbulence as an integral parameter describing the character of atmospheric turbulence along the whole propagation path. • 2. Introduction of the effective outer scale can considerably simplify mathematical calculations connected with the account for the influence of atmospheric turbulence on the phase of optical wave propagated along vertical atmospheric paths. • 3. The description accuracy studied demonstrate that the error caused by the change of the height profile of the outer scale for a constant value, i.e., the effective outer scale, considerably varies depending both on the model of a parameter profile and the method of determination. • 4. The error in determination of the Strehl parameter does not exceed 16% in the situation when the effective outer scale is larger than the diameter of a telescope.

  37. CONTENT • 1. INTRODUCTION. PHASE FLUCTUATIONS MEASUREMENTS • 2. DEVELOPMENT OF THE MODELS OF TURBULENCE SPECTRA • 3. OUTER SCALE OF TURBULENCE AND INSTABILITY PARAMETER • 4. INVESTIGATION OF ANISOTROPY OF THE ATMOSPHERIC TURBULENCE SPECTRUM IN LOW-FREQUENCY REGION • 5. INVESTIGATION OF THE ATMOSPHERIC TURBULENCE DYNAMICS OF THE BASIS OF ASTROCLIMATIC OBSERVATIONS • 6. HIGH-ALTITUDE OF ATMOSPHERIC TURBULENCE • 7. THE MODEL “AVERAGED” OVER THE ENTIRE COLOMN ATMOSPHERE • 8. OUTER SCALE OF ANISOTROPIC TURBULENCE • 9. CHARACTERISTICS OF GROUND-BASED OPTICAL TELESCOPE DUE TO ATMOSPHERIC TURBULENCE

  38. 8. Outer scale of anisotropic turbulence • V.I. Tatarski determines the vertical outer scale from the condition of equality of mean squares of random difference of temperatures and its systematic difference . • This condition gives • 1.17, • In our paper we generalized this expression for the case anisotropic turbulence: • where is the height, is the function of similarity ( • and are the Monin-Obukhov number and scale), is the temperature scale, • and are the energy and temperature functions of anisotropy. • V.V.Nosov, O.N.Emaleev, V.P. Lukin, E.N.Nosov, Results of measurements of surface turbulence of the atmospheric air in the mountains of the Baikal Astrophysical Observatory. //X International symposium “Atmospheric and Ocean Optics. Atmospheric Physics”. Papers abstracts, Tomsk, 2003. 3.0.

  39. 8. Outer scale of anisotropic turbulence (cont.) • From measurements of meteorological characteristics (in the mountain of the Baikal Astrophysical Observatory) on the surface values were reconstructed of outer scale of anisotropic turbulence – in the wide range of local temperature stratifications (from stable to super-strong instable). • A comparison of experimental and theoretical results of outer scales measurements L0T in mountain region for anisotropic turbulence: • 1 – experiment (data from spectra on 5/3 dependence), • 2 – experiment (data from spectra in saturation regime), • 3 – experiment (data on Tatarski determination), • 4 – semiempirical theory for anisotropical layer, • 5 – semiempirical theory for isotropical layer. Bolbasova L.A., Lukin V.P., Nosov V.V. Comparison of Kolmogorov’s and coherent turbulence // Applied Optics. 2014. Vol.53. Iss.10. p.B231-B236.

  40. CONTENT • 1. INTRODUCTION PHASE FLUCTUATIONS MEASUREMENTS • 2. DEVELOPMENT OF THE MODELS OF TURBULENCE SPECTRA • 3. OUTER SCALE OF TURBULENCE AND INSTABILITY PARAMETER • 4. INVESTIGATION OF ANISOTROPY OF THE SPECTRUM OF ATMOSPHERIC TURBULENCE IN LOW-FREQUENCY REGION • 5. INVESTIGATION OF THE ATMOSPHERIC TURBULENCE DYNAMICS OF THE BASIS OF ASTROCLIMATIC OBSERVATIONS • 6. HIGH-ALTITUDE OF ATMOSPHERIC TURBULENCE • 7. THE MODEL “AVERAGED” OVER THE ENTIRE COLOMN ATMOSPHERE • 8.OUTER SCALE OF ANISOTROPIC TURBULENCE • 9. CHARACTERISTICS OF GROUND-BASED OPTICAL TELESCOPE DUE TO ATMOSPHERIC TURBULENCE

  41. 9. CHARACTERISTICS OF GROUND-BASED OPTICAL TELESCOPE DUE TO ATMOSPHERIC TURBULENCE • In 1986 I completed working at the monograph, • V.P.Lukin, Аtmosfernaja adaptivnaja optika, Nauka, Novosibirsk, 1986. • V.Lukin, Atmospheric Adaptive Optics, SPIE Press, 1996. • which developed the theory of adaptive correction of laser beams and images in the atmosphere as a turbulent, absorbing, and refractive medium. • The following subjects were studied in this monograph for the first time: • A) capabilities of a two-color adaptive system (1979), • V.Lukin, “Efficiency of some correction systems”, Optics Letters, 4, No.1, pp.15-17, 1979. • B) possibilities of applying an artificial reference source(1979-1983) for image correction; later on such sources were called laser guide stars, • V.P. Lukin, “Correction of random angular displacements for optical beams”, Quantum Electronics, 1980, т.7, №6. с.1270-1279. • V.Lukin, V.Matuchin, “An adaptive image correction”, Kvantovaja Electronika, 1983, 10, No.12, pp.2465-2473. • C) dynamic characteristics of adaptive optical systems (1986), where the ideas of “predicting” fluctuations for adaptive system operation were used for the first time • V.Lukin, V.Zuev, “Dynamic characteristics of optical systems”, Applied Optics, 1987, 27, No.1, pp.139-147.

  42. 8. CHARACTERISTICS OF GROUND-BASED OPTICAL TELESCOPE DUE TO ATMOSPHERIC TURBULENCE (cont.) In the period of 1991-1995, we developed a Fourdimensional numerical dynamic model incliding the outer scale of turbulence of atmosphericadaptive systems: V.Lukin, B.Fortes, “Modeling of the image observed through a turbulent atmosphere”, Proc. SPIE, 1992, V.1688, pp.477-488. V.Lukin, B.Fortes, F.Kanev, P.Konyaev, “Four dimensional computer dynamic model of Atmospheric optical systems”, Proc.SPIE, 1994, V.2222, pp.522-526. E.A. Vitrichenko, V.P. Lukin, L.A. Pushnoi, V.A.Tartakovski, The problem of optical testing, Nauka, Novosibirsk, 1990, 350 p. V.Lukin, B. Fortes, Adaptive beaming and Imaging in the Turbulent Atmosphere, SPIE Press, PM109, 2002, 201 p.

  43. 9. CHARACTERISTICS OF GROUND-BASED OPTICAL TELESCOPE DUE TO ATMOSPHERIC TURBULENCE (cont.) In 1994 we completed a design project of an adaptive system for the 10-meter combined Russian telescope AST-10. V.Lukin, “Computer modeling of adaptive optics for telescope design”, ESO Workshop Proc. No.54, 1995, pp.373-378. V.P. Lukin, B.V. Fortes, “Partial phase correction of turbulent distortions in telescope AST-10”, Applied Optics, 1998, т.37, №21, pp.4561-4568. Characteristics of long-base stellar interferometers were calculated (1997) with allowance for the interferometer base orientation, wind velocity distribution, and the outer scale of turbulence. V.P. Lukin, B.V. Fortes, Ground-based spatial interferometers and atmospheric turbulence, Pure and Applied Optics, V.5, No.1, pp.1-11, 1996.

  44. 9. CHARACTERISTICS OF GROUND-BASED OPTICAL TELESCOPE DUE TO ATMOSPHERIC TURBULENCE (cont.) • Using an analytical algorithm for atmospheric correction the performance of the Euro50 telescope is analyzed. • The atmospheric model employed here is the ORM (Observatorio del Roque de los Muchachos) 7 layer model with an outer scale distribution. • Direct estimations of the effective outer scale of turbulence by formula Borgino based on the seven layers models of Cn2 and some assumptions for the vertical distribution L0 give value about 20…40 m, including the turbulence of the ground boundary layer. • The values of effective outer scale found that at apertures of modern telescopes of several meters the influence of the finite L0 on the energy balance between tip-tilt and higher order modes must be properly taken into account. • V. Lukin, A. Goncharov, M. Owner-Petersen, T. Andersen, *Institute of Atmospheric Optics RAS, Tomsk, Russia, Lund Observatory, Lund, Sweden • The effective outer scale estimation for Euro50 site. Proc. SPIE, Vol.5026, pp.112-118, 2002. • Lukin V.P., Nosov V.V. and Torgaev A.V. Features of optical image jitter in a random medium with a finite outer scale // Applied Optics. 2014. Vol. 53. Iss.10. p.B196-B204. • Lukin V.P. Adaptive optics in the formation of optical beams and images // Physics -Uspekhi 57 (6) 556 - 592 (2014). DOI: 10.3367/UFNe.0184.201406b.0599

  45. Papers, relevant with this topics • 1. Bouricius G.M.B., Clifford S.F. Experimental study of atmospheric ally induced phase fluctuations in an optical signal // Journ. Opt. Soc. Am. 1970. 60(11), 1484-1489. • 2. Consortini A., Ronchi L. and Moroder E. Role of the outer scale of turbulence in atmospheric degradation of optical images // J. Opt. Soc. Am. 63, 1246-1248 (1973). • 3. Takato N., Yamaguchi I. Spatial correlation of Zernike phase-expansion coefficients for atmospheric turbulence with finite outer scale // J. Opt. Soc. Am. A 12. 5, 958-963 (1995). • 4. Winker D. M. Effect of a finite outer scale on the Zernike decomposition of atmospheric optical Turbulence // J. Opt. Soc. Am. A 8, 10, 1568-1573 (1991). • 5. Dewan Edmond M., Grossbard Neil The inertial range “outer scale” and optical turbulence// Environ Fluid Mech (2007) 7:383–396. • 6. Voitsekhovich V. and Cuevas S. Adaptive optics and outer scale of turbulence // J.Opt.Soc.Am. A12. pp.2523-2531. 1995. • 7. Tokovinin A., Ziad A., Martin F., Avila R., Borgnino J., Conan R., Sarazin M. Wave-front outer scale monitoring at La Silla // Proc.SPIE. Vol.3353. pp.1155-1162. 1998. • 8. Reinhard G. W. and Collins S. A. Outer-Scale Effects in Turbulence-Degraded Light-Beam Spectra // JOSA, Vol. 62, Issue 12, pp. 1526-1528 (1972)9. Borgnino J. Estimation of the spatial coherence outer scale relevant to long baseline interferometry // Applied Optics 29 13 (1990) 1863-1865.

  46. 10. Borgnino J., Martin F., Ziad A. Effect of a finite spatial-coherence outer scale on the covariances of angle-of-arrival fluctuations // Optics Communications 91 (1992) 267-279. • 11. Buscher D.F., Armstrong J.T. et al. Interferometric seeing measurements on Mt. Wilson: power spectra and outer scales // Applied Optics 34 6 (1995) 1081-1096. • 12. Coulman C.E., Vernin J., Coqueugniot Y. and Caccia J.L. Outer scale of turbulence appropriate to modeling refractive-index structure profiles // App. Opt. Vol.27, no 1, January 88. • 13. Coulman C.E., Vernin J. The significance of anisotropy and the outer scale of turbulence for optical and radio "seeing" // App. Opt. 30, no 1, 1 Jan. 1991. • 14. Dalaudier F., Sidi C. Evidence and Interpretation of a Spectral Gap in the Turbulent Atmospheric Temperature Spectra // J. of the Atm. Sci. 1987. 44, 20, 15. • 15. Dalaudier F., Sidi C., Crochet M., Vernin J. Direct Evidence of "sheets" in the Atmospheric Temperature Field // J. of the Atm. Sci. Vol. 51, 2, 15 Jan. 1994. • 16. Kyrazis D.T., Wissler J.B. et al. Measurement of optical turbulence in the upper troposphere and lower stratosphere // SPIE proc. 2120, January 1994, 43-55. • 17. Ziad A., Borgnino J., Martin F., Agabi A. Experimental estimation of the spatial-coherence outer scale from a wavefront statistical analysis //Astron. Astrophys. 282, 1021-1033 (1994).

  47. 18. Wu Z.-S., Wei H.-Y., Yang R.-K., and Guo L.-X. Study on scintillation considering inner-and outer-scales for laser beam propagation on the slant path through the atmosphere // Progress In Electromagnetics Research, PIER 80, 277–293, 2008. • 19. Ziad Aziz, Schock Matthias, Chanan Gary A., Troy Mitchell, Dekany Richard, Lane Benjamin F., Borgnino Julien, and Martin Francois Comparison of measurements of the outer scale of turbulence by three different techniques // Applied Optics. 2004. 43(11). 2316-2324. • 20. Kornilov V. Angular correlation of the stellar scintillation on largetelescopes//Not. R. Astron. Soc. 000, 1–10 (2012) Printed 13 June 2012. • 21. Z.-S. Wu, H.-Y. Wei, R.-K. Yang, and L.-X. Guo STUDY ON SCINTILLATION CONSIDERING INNER- AND OUTER-SCALES FOR LASER BEAM PROPAGATION ON THE SLANT PATH THROUGH THE ATMOSPHERIC TURBULENCE // Progress In Electromagnetics Research, PIER 80, 277–293, 2008 • 22. Aziz Ziad, Matthias Scho ¨ ck, Gary A. Chanan, Mitchell Troy, Richard Dekany,Benjamin F. Lane, Julien Borgnino, and Francois MartinComparison of measurements of the outer scaleof turbulence by three different techniques //APPLIED OPTICS Vol. 43, No. 11 10 April 2004 • 23. V.A. Kulikov , M.S. Andreeva, A.V. Koryabin, V.I. Shmalhausen Method of estimation of turbulence characteristic scales • 24. Binson J., Mahalov A., Nicolaenko B., Kwan L.T., Variability of turbulence and its outer scales in a model tropopause jet • 25. Dewan E., Grossband N., The inertial range “outer scale” and optical turbulence // Environ Fluid Mech. (2007) 7: 383-396.

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