Abstract

Sampling rate and frequency content determination for optical quantities related to light propagation through turbulence are paramount experimental topics. Some papers about estimating properties of the optical turbulence seem to use ad hoc assumptions to set the sampling frequency used; this chosen sampling rate is assumed good enough to perform a proper measurement. On the other hand, other authors estimate the optimal sampling rate via fast Fourier transform of data series associated to the experiment. When possible, with the help of analytical models, cut-off frequencies, or frequency content, can be determined; yet, these approaches require prior knowledge of the optical turbulence. The aim of this paper is to propose an alternative, practical, experimental method to estimate a proper sampling rate. By means of the discrete wavelet transform, this approach can prevent any loss of information and, at the same time, avoid oversampling. Moreover, it is independent of the statistical model imposed on the turbulence.

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  1. V. I. Tatarskĭ, Wave Propagation in a Turbulent Atmosphere(Nauka Press, Moscow, 1967).
  2. H. T. Yura, “Physical model for strong optical-amplitude fluctuations in a turbulent medium,” J. Opt. Soc. Am.64, 59–67 (1974).
    [CrossRef]
  3. A. Ishimaru, Wave Propagation and Scattering in Random Media(IEEE Press & Oxford University Press, 1997).
  4. L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media(SPIE, 1998).
  5. R. L. Fante, “Mutual coherence function and frequency spectrum of a laser beam propagating through atmospheric turbulence,” J. Opt. Soc. Am.64, 592–598 (1974).
    [CrossRef]
  6. S. F. Clifford, “Temporal-frequency spectra for a spherical wave propagating through atmospheric turbulence,” J. Opt. Soc. Am.61, 1285–1292 (1971).
    [CrossRef]
  7. D. P. Greenwood, “Bandwidth specification for adaptive optics systems,” J. Opt. Soc. Am.67, 390–393 (1977).
    [CrossRef]
  8. G. A. Tyler, “Bandwidth considerations for tracking through turbulence,” J. Opt. Soc. Am. A11, 358–367 (1994).
    [CrossRef]
  9. L. R. Bissonnette, “Atmospheric scintillation of optical and infrared waves: a laboratory simulation,” Appl. Opt.16, 2242–2251 (1977).
    [CrossRef] [PubMed]
  10. A. Consortini, C. Innocenti, and G. Paoli, “Estimate method for outer scale of atmospheric turbulence,” Opt. Commun.214, 9–14 (2002).
    [CrossRef]
  11. V. P. Lukin and V. V. Pokasov, “Optical wave phase fluctuations,” Appl. Opt.20, 121–135 (1981).
    [CrossRef] [PubMed]
  12. N. Ben-Yosef and E. Goldner, “Sample size influence on optical scintillation analysis. Analytical treatment of the higher-order irradiance moments,” Appl. Opt.27, 2167–2171 (1988).
    [CrossRef] [PubMed]
  13. F. Martin, A. Tokovinin, A. Agabi, J. Borgnino, and A. Ziad, “G.S.M.: a Grating Scale Monitor for atmospheric turbulence measurements. I. The instrument and first results of angle of arrival measurements,” Astron. Astrophys. Sup.108, 173–180 (1994).
  14. F. S. Vetelino, B. Clare, K. Corbett, C. Young, K. Grant, and L. Andrews, “Characterizing the propagation path in moderate to strong optical turbulence,” Appl. Opt.45, 3534–3543 (2006).
    [CrossRef] [PubMed]
  15. H. T. Yura and D. A. Kozlowski, “Low Earth orbit satellite-to-ground optical scintillation: comparison of experimental observations and theoretical predictions,” Opt. Lett.36, 2507–2509 (2011).
    [CrossRef] [PubMed]
  16. J. A. Anguita and J. E. Cisternas, “Influence of turbulence strength on temporal correlation of scintillation,” Opt. Lett.36, 1725–1727 (2011).
    [CrossRef] [PubMed]
  17. L. Kral, I. Prochazka, and K. Hamal, “Optical signal path delay fluctuations caused by atmospheric turbulence,” Opt. Lett.30, 1767–1769 (2005).
    [CrossRef] [PubMed]
  18. L. P. Poggio, M. Furger, A. H. Prévôt, W. K. Graber, and E. L. Andreas, “Scintillometer Wind Measurements over Complex Terrain,” J. Atmos. Oceanic Technol.17, 17–26 (2000).
    [CrossRef]
  19. G. Potvin, D. Dion, and J. L. Forand, “Wind effects on scintillation decorrelation times,” Opt. Eng.44, 016001 (2005).
    [CrossRef]
  20. S. Mallat, A Wavelet Tour of Signal Processing(Academic Press, Elsevier, 2009).
  21. D. Percival and A. Walden, Wavelet Methods for Time Series Analysis, Cambridge Series In Statistical And Probabilistic Mathematics (Cambridge University Press, 2006).
  22. C. K. Chui, An Introduction to Wavelets(Academic Press, 1992).
  23. M. Farge, “Wavelet transforms and their applications to turbulence,” Annu. Rev. Fluid Mech.24, 395–457 (1992).
    [CrossRef]
  24. L. Hudgins, C. A. Friehe, and M. E. Mayer, “Wavelet transform and atmospheric turbulence,” Phys. Rev. Lett.71, 3279–3282 (1993).
    [CrossRef] [PubMed]
  25. D. G. Pérez, A. Fernandez, G. Funes, D. Gulich, and L. Zunino, “Retrieving atmospheric turbulence features from differential laser tracking motion data,” SPIE Proc.8535(2012).
    [CrossRef]
  26. O. Keskin, L. Jolissaint, and C. Bradley, “Hot-air optical turbulence generator for the testing of adaptive optics systems: principles and characterization”, Appl. Opt.45, 4888–4897 (2006).
    [CrossRef] [PubMed]
  27. S. Blanco, A. Figliola, R. Quian Quiroga, O. A. Rosso, and E. Serrano, “Time-frequency analysis of electroencephalogram series. III. Wavelet packets and information cost function,” Phys. Rev. E57, 932–940 (1998).
    [CrossRef]

2012 (1)

D. G. Pérez, A. Fernandez, G. Funes, D. Gulich, and L. Zunino, “Retrieving atmospheric turbulence features from differential laser tracking motion data,” SPIE Proc.8535(2012).
[CrossRef]

2011 (2)

2006 (2)

2005 (2)

G. Potvin, D. Dion, and J. L. Forand, “Wind effects on scintillation decorrelation times,” Opt. Eng.44, 016001 (2005).
[CrossRef]

L. Kral, I. Prochazka, and K. Hamal, “Optical signal path delay fluctuations caused by atmospheric turbulence,” Opt. Lett.30, 1767–1769 (2005).
[CrossRef] [PubMed]

2002 (1)

A. Consortini, C. Innocenti, and G. Paoli, “Estimate method for outer scale of atmospheric turbulence,” Opt. Commun.214, 9–14 (2002).
[CrossRef]

2000 (1)

L. P. Poggio, M. Furger, A. H. Prévôt, W. K. Graber, and E. L. Andreas, “Scintillometer Wind Measurements over Complex Terrain,” J. Atmos. Oceanic Technol.17, 17–26 (2000).
[CrossRef]

1998 (1)

S. Blanco, A. Figliola, R. Quian Quiroga, O. A. Rosso, and E. Serrano, “Time-frequency analysis of electroencephalogram series. III. Wavelet packets and information cost function,” Phys. Rev. E57, 932–940 (1998).
[CrossRef]

1994 (2)

F. Martin, A. Tokovinin, A. Agabi, J. Borgnino, and A. Ziad, “G.S.M.: a Grating Scale Monitor for atmospheric turbulence measurements. I. The instrument and first results of angle of arrival measurements,” Astron. Astrophys. Sup.108, 173–180 (1994).

G. A. Tyler, “Bandwidth considerations for tracking through turbulence,” J. Opt. Soc. Am. A11, 358–367 (1994).
[CrossRef]

1993 (1)

L. Hudgins, C. A. Friehe, and M. E. Mayer, “Wavelet transform and atmospheric turbulence,” Phys. Rev. Lett.71, 3279–3282 (1993).
[CrossRef] [PubMed]

1992 (1)

M. Farge, “Wavelet transforms and their applications to turbulence,” Annu. Rev. Fluid Mech.24, 395–457 (1992).
[CrossRef]

1988 (1)

1981 (1)

1977 (2)

1974 (2)

1971 (1)

Agabi, A.

F. Martin, A. Tokovinin, A. Agabi, J. Borgnino, and A. Ziad, “G.S.M.: a Grating Scale Monitor for atmospheric turbulence measurements. I. The instrument and first results of angle of arrival measurements,” Astron. Astrophys. Sup.108, 173–180 (1994).

Andreas, E. L.

L. P. Poggio, M. Furger, A. H. Prévôt, W. K. Graber, and E. L. Andreas, “Scintillometer Wind Measurements over Complex Terrain,” J. Atmos. Oceanic Technol.17, 17–26 (2000).
[CrossRef]

Andrews, L.

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media(SPIE, 1998).

Anguita, J. A.

Ben-Yosef, N.

Bissonnette, L. R.

Blanco, S.

S. Blanco, A. Figliola, R. Quian Quiroga, O. A. Rosso, and E. Serrano, “Time-frequency analysis of electroencephalogram series. III. Wavelet packets and information cost function,” Phys. Rev. E57, 932–940 (1998).
[CrossRef]

Borgnino, J.

F. Martin, A. Tokovinin, A. Agabi, J. Borgnino, and A. Ziad, “G.S.M.: a Grating Scale Monitor for atmospheric turbulence measurements. I. The instrument and first results of angle of arrival measurements,” Astron. Astrophys. Sup.108, 173–180 (1994).

Bradley, C.

Chui, C. K.

C. K. Chui, An Introduction to Wavelets(Academic Press, 1992).

Cisternas, J. E.

Clare, B.

Clifford, S. F.

Consortini, A.

A. Consortini, C. Innocenti, and G. Paoli, “Estimate method for outer scale of atmospheric turbulence,” Opt. Commun.214, 9–14 (2002).
[CrossRef]

Corbett, K.

Dion, D.

G. Potvin, D. Dion, and J. L. Forand, “Wind effects on scintillation decorrelation times,” Opt. Eng.44, 016001 (2005).
[CrossRef]

Fante, R. L.

Farge, M.

M. Farge, “Wavelet transforms and their applications to turbulence,” Annu. Rev. Fluid Mech.24, 395–457 (1992).
[CrossRef]

Fernandez, A.

D. G. Pérez, A. Fernandez, G. Funes, D. Gulich, and L. Zunino, “Retrieving atmospheric turbulence features from differential laser tracking motion data,” SPIE Proc.8535(2012).
[CrossRef]

Figliola, A.

S. Blanco, A. Figliola, R. Quian Quiroga, O. A. Rosso, and E. Serrano, “Time-frequency analysis of electroencephalogram series. III. Wavelet packets and information cost function,” Phys. Rev. E57, 932–940 (1998).
[CrossRef]

Forand, J. L.

G. Potvin, D. Dion, and J. L. Forand, “Wind effects on scintillation decorrelation times,” Opt. Eng.44, 016001 (2005).
[CrossRef]

Friehe, C. A.

L. Hudgins, C. A. Friehe, and M. E. Mayer, “Wavelet transform and atmospheric turbulence,” Phys. Rev. Lett.71, 3279–3282 (1993).
[CrossRef] [PubMed]

Funes, G.

D. G. Pérez, A. Fernandez, G. Funes, D. Gulich, and L. Zunino, “Retrieving atmospheric turbulence features from differential laser tracking motion data,” SPIE Proc.8535(2012).
[CrossRef]

Furger, M.

L. P. Poggio, M. Furger, A. H. Prévôt, W. K. Graber, and E. L. Andreas, “Scintillometer Wind Measurements over Complex Terrain,” J. Atmos. Oceanic Technol.17, 17–26 (2000).
[CrossRef]

Goldner, E.

Graber, W. K.

L. P. Poggio, M. Furger, A. H. Prévôt, W. K. Graber, and E. L. Andreas, “Scintillometer Wind Measurements over Complex Terrain,” J. Atmos. Oceanic Technol.17, 17–26 (2000).
[CrossRef]

Grant, K.

Greenwood, D. P.

Gulich, D.

D. G. Pérez, A. Fernandez, G. Funes, D. Gulich, and L. Zunino, “Retrieving atmospheric turbulence features from differential laser tracking motion data,” SPIE Proc.8535(2012).
[CrossRef]

Hamal, K.

Hudgins, L.

L. Hudgins, C. A. Friehe, and M. E. Mayer, “Wavelet transform and atmospheric turbulence,” Phys. Rev. Lett.71, 3279–3282 (1993).
[CrossRef] [PubMed]

Innocenti, C.

A. Consortini, C. Innocenti, and G. Paoli, “Estimate method for outer scale of atmospheric turbulence,” Opt. Commun.214, 9–14 (2002).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media(IEEE Press & Oxford University Press, 1997).

Jolissaint, L.

Keskin, O.

Kozlowski, D. A.

Kral, L.

Lukin, V. P.

Mallat, S.

S. Mallat, A Wavelet Tour of Signal Processing(Academic Press, Elsevier, 2009).

Martin, F.

F. Martin, A. Tokovinin, A. Agabi, J. Borgnino, and A. Ziad, “G.S.M.: a Grating Scale Monitor for atmospheric turbulence measurements. I. The instrument and first results of angle of arrival measurements,” Astron. Astrophys. Sup.108, 173–180 (1994).

Mayer, M. E.

L. Hudgins, C. A. Friehe, and M. E. Mayer, “Wavelet transform and atmospheric turbulence,” Phys. Rev. Lett.71, 3279–3282 (1993).
[CrossRef] [PubMed]

Paoli, G.

A. Consortini, C. Innocenti, and G. Paoli, “Estimate method for outer scale of atmospheric turbulence,” Opt. Commun.214, 9–14 (2002).
[CrossRef]

Percival, D.

D. Percival and A. Walden, Wavelet Methods for Time Series Analysis, Cambridge Series In Statistical And Probabilistic Mathematics (Cambridge University Press, 2006).

Pérez, D. G.

D. G. Pérez, A. Fernandez, G. Funes, D. Gulich, and L. Zunino, “Retrieving atmospheric turbulence features from differential laser tracking motion data,” SPIE Proc.8535(2012).
[CrossRef]

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media(SPIE, 1998).

Poggio, L. P.

L. P. Poggio, M. Furger, A. H. Prévôt, W. K. Graber, and E. L. Andreas, “Scintillometer Wind Measurements over Complex Terrain,” J. Atmos. Oceanic Technol.17, 17–26 (2000).
[CrossRef]

Pokasov, V. V.

Potvin, G.

G. Potvin, D. Dion, and J. L. Forand, “Wind effects on scintillation decorrelation times,” Opt. Eng.44, 016001 (2005).
[CrossRef]

Prévôt, A. H.

L. P. Poggio, M. Furger, A. H. Prévôt, W. K. Graber, and E. L. Andreas, “Scintillometer Wind Measurements over Complex Terrain,” J. Atmos. Oceanic Technol.17, 17–26 (2000).
[CrossRef]

Prochazka, I.

Quian Quiroga, R.

S. Blanco, A. Figliola, R. Quian Quiroga, O. A. Rosso, and E. Serrano, “Time-frequency analysis of electroencephalogram series. III. Wavelet packets and information cost function,” Phys. Rev. E57, 932–940 (1998).
[CrossRef]

Rosso, O. A.

S. Blanco, A. Figliola, R. Quian Quiroga, O. A. Rosso, and E. Serrano, “Time-frequency analysis of electroencephalogram series. III. Wavelet packets and information cost function,” Phys. Rev. E57, 932–940 (1998).
[CrossRef]

Serrano, E.

S. Blanco, A. Figliola, R. Quian Quiroga, O. A. Rosso, and E. Serrano, “Time-frequency analysis of electroencephalogram series. III. Wavelet packets and information cost function,” Phys. Rev. E57, 932–940 (1998).
[CrossRef]

Tatarski?, V. I.

V. I. Tatarskĭ, Wave Propagation in a Turbulent Atmosphere(Nauka Press, Moscow, 1967).

Tokovinin, A.

F. Martin, A. Tokovinin, A. Agabi, J. Borgnino, and A. Ziad, “G.S.M.: a Grating Scale Monitor for atmospheric turbulence measurements. I. The instrument and first results of angle of arrival measurements,” Astron. Astrophys. Sup.108, 173–180 (1994).

Tyler, G. A.

Vetelino, F. S.

Walden, A.

D. Percival and A. Walden, Wavelet Methods for Time Series Analysis, Cambridge Series In Statistical And Probabilistic Mathematics (Cambridge University Press, 2006).

Young, C.

Yura, H. T.

Ziad, A.

F. Martin, A. Tokovinin, A. Agabi, J. Borgnino, and A. Ziad, “G.S.M.: a Grating Scale Monitor for atmospheric turbulence measurements. I. The instrument and first results of angle of arrival measurements,” Astron. Astrophys. Sup.108, 173–180 (1994).

Zunino, L.

D. G. Pérez, A. Fernandez, G. Funes, D. Gulich, and L. Zunino, “Retrieving atmospheric turbulence features from differential laser tracking motion data,” SPIE Proc.8535(2012).
[CrossRef]

Annu. Rev. Fluid Mech. (1)

M. Farge, “Wavelet transforms and their applications to turbulence,” Annu. Rev. Fluid Mech.24, 395–457 (1992).
[CrossRef]

Appl. Opt. (5)

Astron. Astrophys. Sup. (1)

F. Martin, A. Tokovinin, A. Agabi, J. Borgnino, and A. Ziad, “G.S.M.: a Grating Scale Monitor for atmospheric turbulence measurements. I. The instrument and first results of angle of arrival measurements,” Astron. Astrophys. Sup.108, 173–180 (1994).

J. Atmos. Oceanic Technol. (1)

L. P. Poggio, M. Furger, A. H. Prévôt, W. K. Graber, and E. L. Andreas, “Scintillometer Wind Measurements over Complex Terrain,” J. Atmos. Oceanic Technol.17, 17–26 (2000).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

A. Consortini, C. Innocenti, and G. Paoli, “Estimate method for outer scale of atmospheric turbulence,” Opt. Commun.214, 9–14 (2002).
[CrossRef]

Opt. Eng. (1)

G. Potvin, D. Dion, and J. L. Forand, “Wind effects on scintillation decorrelation times,” Opt. Eng.44, 016001 (2005).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. E (1)

S. Blanco, A. Figliola, R. Quian Quiroga, O. A. Rosso, and E. Serrano, “Time-frequency analysis of electroencephalogram series. III. Wavelet packets and information cost function,” Phys. Rev. E57, 932–940 (1998).
[CrossRef]

Phys. Rev. Lett. (1)

L. Hudgins, C. A. Friehe, and M. E. Mayer, “Wavelet transform and atmospheric turbulence,” Phys. Rev. Lett.71, 3279–3282 (1993).
[CrossRef] [PubMed]

SPIE Proc. (1)

D. G. Pérez, A. Fernandez, G. Funes, D. Gulich, and L. Zunino, “Retrieving atmospheric turbulence features from differential laser tracking motion data,” SPIE Proc.8535(2012).
[CrossRef]

Other (6)

V. I. Tatarskĭ, Wave Propagation in a Turbulent Atmosphere(Nauka Press, Moscow, 1967).

A. Ishimaru, Wave Propagation and Scattering in Random Media(IEEE Press & Oxford University Press, 1997).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media(SPIE, 1998).

S. Mallat, A Wavelet Tour of Signal Processing(Academic Press, Elsevier, 2009).

D. Percival and A. Walden, Wavelet Methods for Time Series Analysis, Cambridge Series In Statistical And Probabilistic Mathematics (Cambridge University Press, 2006).

C. K. Chui, An Introduction to Wavelets(Academic Press, 1992).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Density plots of the WES for the horizontal displacements for different sampling rates showing the temporal evolution.

Fig. 3
Fig. 3

a) WES and b) PSD at a sampling rate of 800Hz, c) and d) idem for 2kHz, e) and f) idem for 6kHz, g) and h) idem for 12kHz. For the wavelet spectra the frequency bands were marked. The red curve is the thrend of the PSD obtained via wavelets. Also, the theoretical Kolmogorov slopes −2/3 and −11/3 are shown in h).

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

W = W ˜ S ,
S 2 = W 2 = J , k C J ( k ) 2 .
f J = 2 J f s ,
E J = k C J ( k ) 2 J , k C J ( k ) 2 ,

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