Abstract

We present an analysis of spatial and temporal spectra of the observations of scintillations in a laser beam (532 nm, 200mW power) traveling along a 144 km path at an altitude of 2–2.4 km above sea level, just above the atmospheric boundary layer, between the islands of La Palma and Tenerife. The observations were performed during nighttime on July 18 and 21, 2011, by means of a telescope with an aperture diameter of 1 m. Strong scintillations were observed. We compared the temporal and spatial spectra of the scintillations. For the temporal spectra, we performed the correction for the aliasing effect due to the low frame rate. The 2D spatial spectra of the scintillations in the observation plane were found to be close to isotropic. This allowed for transforming them into 1D spectra. We found a good agreement between the temporal and 1D spatial spectra. This corroborates the applicability of the Taylor hypothesis of frozen turbulence for finite-size laser beams and strong scintillations.

© 2014 Optical Society of America

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  1. G. R. Ochs, R. R. Bergmtan, and J. R. Snyder, “Laser-beam scintillation over horizontal paths from 5.5 to 145 kilometers,” J. Opt. Soc. Am. 59, 231–234 (1969).
    [CrossRef]
  2. N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142  km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
    [CrossRef]
  3. M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149  km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.
  4. A. S. Gurvich, M. E. Gorbunov, O. V. Fedorova, G. Kirchengast, V. Proschek, G. González Abad, and K. A. Tereszchuk, “Spatiotemporal structure of a laser beam over 144  km in a Canary Islands experiment,” Appl. Opt. 51, 7374–7383 (2012).
    [CrossRef]
  5. G. I. Taylor, “The spectrum of turbulence,” Proc. R. Soc. Lond. Ser. A 164, 476–490 (1938).
    [CrossRef]
  6. V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Keter, 1971).
  7. J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144  km open path in the Canary Islands,” Atmos. Meas. Tech. 5, 2309–2319 (2012).
  8. G. Kirchengast and S. Schweitzer, “Climate benchmark profiling of greenhouse gases and thermodynamic structure and wind from space,” Geophys. Res. Lett. 38, L13701 (2011).
    [CrossRef]
  9. A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence, Vol. 2 (Dover Publications, 2007).
  10. G. V. Azizyan, A. S. Gurvich, and M. Z. Kholmyanskiy, “Influence of transport velocity variation on the cross spectra of the temperature fluctuations,” Izv. Acad. Sci., USSR, Atmos. Oceanic Phys. 16, 154–159 (1980).
  11. A. S. Gurvich, “Influence of the temporal evolution of turbulent inhomogeneities on frequency spectra,” Izv. Acad. Sci., USSR, Atmos. Oceanic Phys. 16, 231–237 (1980).
  12. S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarskii, Elements of Random Fields, Vol. 3 of Principles of Statistical Radiophysics (Springer-Verlag, 1987).
  13. M. B. Priestley, Multivariate and Multidimensional Processes, Vol. 2 of Spectral Analysis and Time Series (Academic, 1981).
  14. A. M. Yaglom, Correlation Theory of Stationary and Related Random Functions (Springer-Verlag, 1987), Vols. 1 and 2.

2012

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144  km open path in the Canary Islands,” Atmos. Meas. Tech. 5, 2309–2319 (2012).

A. S. Gurvich, M. E. Gorbunov, O. V. Fedorova, G. Kirchengast, V. Proschek, G. González Abad, and K. A. Tereszchuk, “Spatiotemporal structure of a laser beam over 144  km in a Canary Islands experiment,” Appl. Opt. 51, 7374–7383 (2012).
[CrossRef]

2011

G. Kirchengast and S. Schweitzer, “Climate benchmark profiling of greenhouse gases and thermodynamic structure and wind from space,” Geophys. Res. Lett. 38, L13701 (2011).
[CrossRef]

2006

N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142  km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
[CrossRef]

1980

G. V. Azizyan, A. S. Gurvich, and M. Z. Kholmyanskiy, “Influence of transport velocity variation on the cross spectra of the temperature fluctuations,” Izv. Acad. Sci., USSR, Atmos. Oceanic Phys. 16, 154–159 (1980).

A. S. Gurvich, “Influence of the temporal evolution of turbulent inhomogeneities on frequency spectra,” Izv. Acad. Sci., USSR, Atmos. Oceanic Phys. 16, 231–237 (1980).

1969

1938

G. I. Taylor, “The spectrum of turbulence,” Proc. R. Soc. Lond. Ser. A 164, 476–490 (1938).
[CrossRef]

Azizyan, G. V.

G. V. Azizyan, A. S. Gurvich, and M. Z. Kholmyanskiy, “Influence of transport velocity variation on the cross spectra of the temperature fluctuations,” Izv. Acad. Sci., USSR, Atmos. Oceanic Phys. 16, 154–159 (1980).

Beale, C. A.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144  km open path in the Canary Islands,” Atmos. Meas. Tech. 5, 2309–2319 (2012).

Beresnev, L. A.

M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149  km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.

Bergmtan, R. R.

Bernath, P. F.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144  km open path in the Canary Islands,” Atmos. Meas. Tech. 5, 2309–2319 (2012).

Brooke, J. S. A.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144  km open path in the Canary Islands,” Atmos. Meas. Tech. 5, 2309–2319 (2012).

Carhart, G. W.

M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149  km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.

Fedorova, O. V.

Gerbig, C.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144  km open path in the Canary Islands,” Atmos. Meas. Tech. 5, 2309–2319 (2012).

Giggenbach, D.

N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142  km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
[CrossRef]

González Abad, G.

A. S. Gurvich, M. E. Gorbunov, O. V. Fedorova, G. Kirchengast, V. Proschek, G. González Abad, and K. A. Tereszchuk, “Spatiotemporal structure of a laser beam over 144  km in a Canary Islands experiment,” Appl. Opt. 51, 7374–7383 (2012).
[CrossRef]

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144  km open path in the Canary Islands,” Atmos. Meas. Tech. 5, 2309–2319 (2012).

Gorbunov, M. E.

Gurvich, A. S.

A. S. Gurvich, M. E. Gorbunov, O. V. Fedorova, G. Kirchengast, V. Proschek, G. González Abad, and K. A. Tereszchuk, “Spatiotemporal structure of a laser beam over 144  km in a Canary Islands experiment,” Appl. Opt. 51, 7374–7383 (2012).
[CrossRef]

G. V. Azizyan, A. S. Gurvich, and M. Z. Kholmyanskiy, “Influence of transport velocity variation on the cross spectra of the temperature fluctuations,” Izv. Acad. Sci., USSR, Atmos. Oceanic Phys. 16, 154–159 (1980).

A. S. Gurvich, “Influence of the temporal evolution of turbulent inhomogeneities on frequency spectra,” Izv. Acad. Sci., USSR, Atmos. Oceanic Phys. 16, 231–237 (1980).

Hargreaves, R. J.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144  km open path in the Canary Islands,” Atmos. Meas. Tech. 5, 2309–2319 (2012).

Harrison, J. J.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144  km open path in the Canary Islands,” Atmos. Meas. Tech. 5, 2309–2319 (2012).

Henniger, H.

N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142  km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
[CrossRef]

Horwath, J.

N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142  km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
[CrossRef]

Kasyutich, V. L.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144  km open path in the Canary Islands,” Atmos. Meas. Tech. 5, 2309–2319 (2012).

Kholmyanskiy, M. Z.

G. V. Azizyan, A. S. Gurvich, and M. Z. Kholmyanskiy, “Influence of transport velocity variation on the cross spectra of the temperature fluctuations,” Izv. Acad. Sci., USSR, Atmos. Oceanic Phys. 16, 154–159 (1980).

Kirchengast, G.

A. S. Gurvich, M. E. Gorbunov, O. V. Fedorova, G. Kirchengast, V. Proschek, G. González Abad, and K. A. Tereszchuk, “Spatiotemporal structure of a laser beam over 144  km in a Canary Islands experiment,” Appl. Opt. 51, 7374–7383 (2012).
[CrossRef]

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144  km open path in the Canary Islands,” Atmos. Meas. Tech. 5, 2309–2319 (2012).

G. Kirchengast and S. Schweitzer, “Climate benchmark profiling of greenhouse gases and thermodynamic structure and wind from space,” Geophys. Res. Lett. 38, L13701 (2011).
[CrossRef]

Knapek, M.

N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142  km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
[CrossRef]

Kolle, O.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144  km open path in the Canary Islands,” Atmos. Meas. Tech. 5, 2309–2319 (2012).

Kravtsov, Y. A.

S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarskii, Elements of Random Fields, Vol. 3 of Principles of Statistical Radiophysics (Springer-Verlag, 1987).

Lachinova, S. L.

M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149  km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.

Liu, J.

M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149  km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.

Loescher, A.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144  km open path in the Canary Islands,” Atmos. Meas. Tech. 5, 2309–2319 (2012).

Martin, P. A.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144  km open path in the Canary Islands,” Atmos. Meas. Tech. 5, 2309–2319 (2012).

Monin, A. S.

A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence, Vol. 2 (Dover Publications, 2007).

Ochs, G. R.

Perlot, N.

N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142  km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
[CrossRef]

Priestley, M. B.

M. B. Priestley, Multivariate and Multidimensional Processes, Vol. 2 of Spectral Analysis and Time Series (Academic, 1981).

Proschek, V.

A. S. Gurvich, M. E. Gorbunov, O. V. Fedorova, G. Kirchengast, V. Proschek, G. González Abad, and K. A. Tereszchuk, “Spatiotemporal structure of a laser beam over 144  km in a Canary Islands experiment,” Appl. Opt. 51, 7374–7383 (2012).
[CrossRef]

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144  km open path in the Canary Islands,” Atmos. Meas. Tech. 5, 2309–2319 (2012).

Rao Gudimetla, V. S.

M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149  km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.

Rehder, K.

M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149  km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.

Riker, J. F.

M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149  km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.

Rytov, S. M.

S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarskii, Elements of Random Fields, Vol. 3 of Principles of Statistical Radiophysics (Springer-Verlag, 1987).

Schweitzer, S.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144  km open path in the Canary Islands,” Atmos. Meas. Tech. 5, 2309–2319 (2012).

G. Kirchengast and S. Schweitzer, “Climate benchmark profiling of greenhouse gases and thermodynamic structure and wind from space,” Geophys. Res. Lett. 38, L13701 (2011).
[CrossRef]

Snyder, J. R.

Stevenson, E.

M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149  km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.

Tatarskii, V. I.

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Keter, 1971).

S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarskii, Elements of Random Fields, Vol. 3 of Principles of Statistical Radiophysics (Springer-Verlag, 1987).

Taylor, G. I.

G. I. Taylor, “The spectrum of turbulence,” Proc. R. Soc. Lond. Ser. A 164, 476–490 (1938).
[CrossRef]

Tereszchuk, K. A.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144  km open path in the Canary Islands,” Atmos. Meas. Tech. 5, 2309–2319 (2012).

A. S. Gurvich, M. E. Gorbunov, O. V. Fedorova, G. Kirchengast, V. Proschek, G. González Abad, and K. A. Tereszchuk, “Spatiotemporal structure of a laser beam over 144  km in a Canary Islands experiment,” Appl. Opt. 51, 7374–7383 (2012).
[CrossRef]

Thomas, C. B.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144  km open path in the Canary Islands,” Atmos. Meas. Tech. 5, 2309–2319 (2012).

Vorontsov, M. A.

M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149  km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.

Wang, J.-G.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144  km open path in the Canary Islands,” Atmos. Meas. Tech. 5, 2309–2319 (2012).

Weyrauch, T.

M. A. Vorontsov, G. W. Carhart, V. S. Rao Gudimetla, T. Weyrauch, E. Stevenson, S. L. Lachinova, L. A. Beresnev, J. Liu, K. Rehder, and J. F. Riker, “Characterization of atmospheric turbulence effects over 149  km propagation path using multi-wavelength laser beacons,” in Proceedings of the 2010 AMOS Conference (2010), p. E18.

Yaglom, A. M.

A. M. Yaglom, Correlation Theory of Stationary and Related Random Functions (Springer-Verlag, 1987), Vols. 1 and 2.

A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence, Vol. 2 (Dover Publications, 2007).

Zettl, K.

N. Perlot, D. Giggenbach, H. Henniger, J. Horwath, M. Knapek, and K. Zettl, “Measurements of the beam-wave fluctuations over a 142  km atmospheric path,” Proc. SPIE 6304, 63041O (2006).
[CrossRef]

Appl. Opt.

Atmos. Meas. Tech.

J. S. A. Brooke, P. F. Bernath, G. Kirchengast, C. B. Thomas, J.-G. Wang, K. A. Tereszchuk, G. González Abad, R. J. Hargreaves, C. A. Beale, J. J. Harrison, S. Schweitzer, V. Proschek, P. A. Martin, V. L. Kasyutich, C. Gerbig, O. Kolle, and A. Loescher, “Greenhouse gas measurements over a 144  km open path in the Canary Islands,” Atmos. Meas. Tech. 5, 2309–2319 (2012).

Geophys. Res. Lett.

G. Kirchengast and S. Schweitzer, “Climate benchmark profiling of greenhouse gases and thermodynamic structure and wind from space,” Geophys. Res. Lett. 38, L13701 (2011).
[CrossRef]

Izv. Acad. Sci., USSR, Atmos. Oceanic Phys.

G. V. Azizyan, A. S. Gurvich, and M. Z. Kholmyanskiy, “Influence of transport velocity variation on the cross spectra of the temperature fluctuations,” Izv. Acad. Sci., USSR, Atmos. Oceanic Phys. 16, 154–159 (1980).

A. S. Gurvich, “Influence of the temporal evolution of turbulent inhomogeneities on frequency spectra,” Izv. Acad. Sci., USSR, Atmos. Oceanic Phys. 16, 231–237 (1980).

J. Opt. Soc. Am.

Proc. R. Soc. Lond. Ser. A

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Figures (3)

Fig. 1.
Fig. 1.

Phase spectra φ(κx,0,Δt). Solid lines with symbols are the phase spectra, dashed and dashed–dotted lines are the linear trends for the low wavenumbers.

Fig. 2.
Fig. 2.

Spectra V and W for ensemble A, B, and C. Notation: 1, κx(V(κx)+Vn); 2, smoothed dependency κx(V(κx)+Vn); 3, κxmin(V(κx)+Vn); 4, UIκx(W(UIκx)+Wn); 5, smoothed dependency UIκx(W(UIκx)+Wn); 6, UIκxmin(W(UIκx)+Wn).

Fig. 3.
Fig. 3.

Comparison of 1D spatial spectra V(κx) and temporal spectra UIW(κxUI).

Tables (2)

Tables Icon

Table 1. Realization Ensembles A, B, and C

Tables Icon

Table 2. Speckle Drift Velocities UI[m/s]

Equations (19)

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I(x,y,t)=I(xUIΔt,y,tΔt),
BI=I(x+Δx,y+Δy,t+Δt)I(x,y,t).
BI=BI(Δx,Δy,Δt).
F(κx,κy)=14π2BI(x,y,0)exp(i(κxx+κyy))dxdy,
V(κx)=F(κx,κy)dκy,
W(ω)=12πBI(0,0,t)exp(iωt)dt,
Ψ(κx,κy,Δt)=14π2BI(x,y,Δt)exp(i(κxx+κyy))dxdy.
F(κx,κy)=1NtlI˜(κx,κy,tl)I˜*(κx,κy,tl),Ψ(κx,κy,tl+δltl)=1NtlI˜(κx,κy,tl)I˜*(κx,κy,tl+δl),
W(ω)=1Nxyi,jI˜(xi,yj,ω)I˜*(xi,yj,ω),
Ψ(κx,κy,Δt)=|Ψ(κx,κy,Δt)|exp(iφ(κx,κy,Δt)),
ψ(κx,κy,Δt)=|Ψ(κx,κy,Δt)|F(κx,κy)
φ(κx,κy,Δt)=φ(κx,κy,Δt),φ(κx,κy,Δt)=φ(κx,κy,Δt),φ(κx,κy,Δt)=φ(κx,κy,Δt).
BI(UIΔt,0,0)=BI(0,0,Δt).
ψ(κx,κy,Δt)=1,
φ(κx,κy,Δt)=φ(κx,0,Δt)=ΔtUIκx,
UIW(κxUI)=V(κx).
φ=arctanImΨReΨ,
σφψ212Nd.
UI=φ(κx,0,Δt)Δt·κx,

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