On the normalization of scintillation
autocovariance for generalized SCIDAR

doi:10.1364/OE.17.010926

On the normalization of scintillation autocovariance for generalized SCIDAR

Remy Avila and Salvador Cuevas »View Author Affiliations

Optics Express, Vol. 17, Issue 13, pp. 10926-10938 (2009)
http://dx.doi.org/10.1364/OE.17.010926

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Abstract

The Generalized SCIDAR (Scintillation Detection and Ranging) technique consists in the computation of the mean autocorrelation of double-star scintillation images taken on a virtual plane located a few kilometers below the telescope pupil. This autocorrelation is normalized by the autocorrelation of the mean image. Johnston et al. in 2002 [1] pointed out that this normalization leads to an inexact estimate of the optical-turbulence strength C²_N. Those authors restricted their analysis to turbulence at ground level. Here we generalize that study by calculating analytically the error induced by that normalization, for a turbulent layer at any altitude. An exact expression is given for any telescope–pupil shape and an approximate simple formula is provided for a full circular pupil. We show that the effect of the inexact normalization is to overestimate the C² _N values. The error is larger for higher turbulent layers, smaller telescopes, longer distances of the analysis plane from the pupil, wider double-star separations, and larger differences of stellar magnitudes. Depending on the observational parameters and the turbulence altitude, the relative error can take values from zero up to a factor of 4, in which case the real C² _N value is only 0.2 times the erroneous one. Our results can be applied to correct the C² _N profiles that have been measured using the Generalized SCIDAR technique.

OCIS Codes
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(280.7060) Remote sensing and sensors : Turbulence
(290.5930) Scattering : Scintillation

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: April 15, 2009
Revised Manuscript: May 20, 2009
Manuscript Accepted: June 9, 2009
Published: June 16, 2009

Citation
Remy Avila and Salvador Cuevas, "On the normalization of scintillation autocovariance for generalized SCIDAR," Opt. Express 17, 10926-10938 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-13-10926

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References

R. A. Johnston, C. Dainty, N. J. Wooder, and R. G. Lane, "Generalized scintillation detection and ranging results obtained by use of a modified inversion technique," Appl. Opt. 41(32), 6768-6772 (2002). [CrossRef]
J. Vernin and F. Roddier, "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. A 63, 270-273 (1973). [CrossRef]
A. Rocca, F. Roddier, and J. Vernin, "Detection of atmospheric turbulent layers by spatiotemporal and spatioangular correlation measurements of stellar-light scintillation," J. Opt. Soc. Am. A 64, 1000-1004 (1974). [CrossRef]
J. Vernin and M. Azouit, "Traitement d’image adapt’e au speckle atmosph’erique. I-Formation du speckle en atmosph`ere turbulente. Proprietes statistiques," J. Opt. (Paris) 14, 5-9 (1983).
J. Vernin and M. Azouit, "Traitement d’image adapte au speckle atmospherique. II-analyse multidimensionnelle appliquee au diagnostic a distance de la turbulence," J. Opt. (Paris) 14, 131-142 (1983).
V. A. Kluckers, N. J. Wooder, T. W. Nicholls, M. J. Adcock, I. Munro, and J. C. Dainty, "Profiling of Atmospheric Turbulence Strength and Velocity using a Generalised SCIDAR Technique," Astron. Astrophys. Suppl. Ser. 130, 141-155 (1998). [CrossRef]
J.-L. Prieur, G. Daigne, and R. Avila, "SCIDAR measurements at Pic du Midi," Astron. Astrophys. 371, 366-377 (2001). [CrossRef]
F. Roddier, "The Effect of Atmospheric Turbulence in Optical Astronomy," Progress in Optics XIX, 281-376 (1981). [CrossRef]
R. Avila, E. Masciadri, J. Vernin, and L. Sanchez, "Generalized SCIDAR measurements at San Pedro Martir: I. Turbulence profile statistics," Publ. Astron. Soc. Pac. 116, 682-692 (2004). [CrossRef]
M. Chun, R. Wilson, R. Avila, T. Butterley, J.-L. Aviles, D. Wier, and S. Benigni, "Mauna Kea ground-layer characterization campaign," Mon. Not. R. Astron. Soc. 394, 1121-1130 (2009). [CrossRef]
A. Fuchs, M. Tallon, and J. Vernin, "Folding of the vertical atmospheric turbulence profile using an optical technique of movable observing plane," in Atmospheric Propagation and Remote Sensing III, W. A. Flood and W. B. Miller, eds., Vol. 2222, pp. 682-692 (1994).
R. Avila, J. Vernin, and E. Masciadri, "Whole atmospheric-turbulence profiling with generalized Scidar," Appl. Opt. 36(30), 7898-7905 (1997). [CrossRef]
R. Avila, J. L. Aviles, R. Wilson, M. Chun, T. Butterley, and E. Carrasco, "LOLAS: an optical turbulence profiler in the atmospheric boundary layer with extreme altitude-resolution," Mon. Not. R. Astron. Soc. 387, 1511-1516 (2008). [CrossRef]
A. Fuchs, M. Tallon, and J. Vernin, "Focussiong on a turbulent layer: Principle of the Generalized SCIDAR," Publ. Astron. Soc. Pac. 110, 86-91 (1998). [CrossRef]
R. Avila, J. Vernin, and S. Cuevas, "Turbulence Profiles with Generalized Scidar at San Pedro M’artir Observatory and Isoplanatism Studies," Publ. Astron. Soc. Pac. 110, 1106-1116 (1998). [CrossRef]
B. Kern, T. A. Laurence, C. Martin, and P. E. Dimotakis, "Temporal coherence of individual turbulent patterns in atmospheric seeing," Appl. Opt. 39, 4879-4885 (2000). [CrossRef]
R. Avila, J. Vernin, and L. J. S’anchez, "Atmospheric turbulence and wind profiles monitoring with generalized scidar," Astron. Astrophys. 369, 364 (2001). [CrossRef]
R. W. Wilson, N. J. Wooder, F. Rigal, and J. C. Dainty, "Estimation of anisoplanatism in adaptive optics by generalized SCIDAR profiling," Mon. Not. R. Astron. Soc. 339, 491-494 (2003). [CrossRef]
A. Tokovinin, J. Vernin, A. Ziad, and M. Chun, "Optical Turbulence Profiles at Mauna Kea Measured by MASS and SCIDAR," Publ. Astron. Soc. Pac. 117, 395-400 (2005). [CrossRef]
B. Garcıa-Lorenzo and J. J. Fuensalida, "Processing of turbulent-layer wind speed with Generalized SCIDAR through wavelet analysis," Mon. Not. R. Astron. Soc. 372, 1483-1495 (2006). arXiv:astro-ph/0608595. [CrossRef]
S. E. Egner, E. Masciadri, and D. McKenna, "Generalized SCIDAR Measurements at Mount Graham," Publ. Astron. Soc. Pac. 119, 669-686 (2007). [CrossRef]
J. Vernin, H. Trinquet, G. Jumper, E. Murphy, and A. Ratkowski, "OHP02 gravity wave campaign in relation to optical turbulence," Environmental Fluid Mechanics 7, 371-+ (2007). [CrossRef]
S. E. Egner and E. Masciadri, "A G-SCIDAR for Ground-Layer Turbulence Measurements at High Vertical Resolution," Publ. Astron. Soc. Pac. 119, 1441-1448 (2007). [CrossRef]
J. J. Fuensalida, B. Garcıa-Lorenzo, and C. Hoegemann, "Correction of the dome seeing contribution from generalized-SCIDAR data using evenness properties with Fourier analysis," Mon. Not. R. Astron. Soc. 389, 731-740 (2008). [CrossRef]
J. W. Goodman, Statistical Optics (Wiley-Interscience, New-York, 1985).

Adcock, M. J.
Avil’es, J. L.
Avila, R.
Aviles, J.-L.
Azouit, M.
Benigni, S.
Butterley, T.
Carrasco, E.
Chun, M.
Cuevas, S.
Daigne, G.
Dainty, C.
Dainty, J. C.
Dimotakis, P. E.
Egner, S. E.
Fuchs, A.
Fuensalida, J. J.
Garcia-Lorenzo, B.
Hoegemann, C.
Johnston, R. A.
Kern, B.
Kl¨uckers, V. A.
Lane, R. G.
Laurence, T. A.
Martin, C.
Masciadri, E.
McKenna, D.
Munro, I.
Nicholls, T. W.
Prieur, J.-L.
Rigal, F.
Rocca, A.
Roddier, F.
Tallon, M.
Tokovinin, A.
Vernin, J.
Wier, D.
Wilson, R.
Wilson, R. W.
Wooder, N. J.
Ziad, A.

Appl. Opt.

Astron. Astrophys.

R. Avila, J. Vernin, and L. J. S’anchez, "Atmospheric turbulence and wind profiles monitoring with generalized scidar," Astron. Astrophys. 369, 364 (2001). [CrossRef]
J.-L. Prieur, G. Daigne, and R. Avila, "SCIDAR measurements at Pic du Midi," Astron. Astrophys. 371, 366-377 (2001). [CrossRef]

Astron. Astrophys. Suppl. Ser.

V. A. Kluckers, N. J. Wooder, T. W. Nicholls, M. J. Adcock, I. Munro, and J. C. Dainty, "Profiling of Atmospheric Turbulence Strength and Velocity using a Generalised SCIDAR Technique," Astron. Astrophys. Suppl. Ser. 130, 141-155 (1998). [CrossRef]

J. Opt. (Paris)

J. Vernin and M. Azouit, "Traitement d’image adapt’e au speckle atmosph’erique. I-Formation du speckle en atmosph`ere turbulente. Proprietes statistiques," J. Opt. (Paris) 14, 5-9 (1983).
J. Vernin and M. Azouit, "Traitement d’image adapte au speckle atmospherique. II-analyse multidimensionnelle appliquee au diagnostic a distance de la turbulence," J. Opt. (Paris) 14, 131-142 (1983).

J. Opt. Soc. Am. A

J. Vernin and F. Roddier, "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. A 63, 270-273 (1973). [CrossRef]
A. Rocca, F. Roddier, and J. Vernin, "Detection of atmospheric turbulent layers by spatiotemporal and spatioangular correlation measurements of stellar-light scintillation," J. Opt. Soc. Am. A 64, 1000-1004 (1974). [CrossRef]

Mon. Not. R. Astron. Soc.

M. Chun, R. Wilson, R. Avila, T. Butterley, J.-L. Aviles, D. Wier, and S. Benigni, "Mauna Kea ground-layer characterization campaign," Mon. Not. R. Astron. Soc. 394, 1121-1130 (2009). [CrossRef]
R. W. Wilson, N. J. Wooder, F. Rigal, and J. C. Dainty, "Estimation of anisoplanatism in adaptive optics by generalized SCIDAR profiling," Mon. Not. R. Astron. Soc. 339, 491-494 (2003). [CrossRef]
R. Avila, J. L. Aviles, R. Wilson, M. Chun, T. Butterley, and E. Carrasco, "LOLAS: an optical turbulence profiler in the atmospheric boundary layer with extreme altitude-resolution," Mon. Not. R. Astron. Soc. 387, 1511-1516 (2008). [CrossRef]
B. Garcıa-Lorenzo and J. J. Fuensalida, "Processing of turbulent-layer wind speed with Generalized SCIDAR through wavelet analysis," Mon. Not. R. Astron. Soc. 372, 1483-1495 (2006). arXiv:astro-ph/0608595. [CrossRef]
J. J. Fuensalida, B. Garcıa-Lorenzo, and C. Hoegemann, "Correction of the dome seeing contribution from generalized-SCIDAR data using evenness properties with Fourier analysis," Mon. Not. R. Astron. Soc. 389, 731-740 (2008). [CrossRef]

Progress in Optics

F. Roddier, "The Effect of Atmospheric Turbulence in Optical Astronomy," Progress in Optics XIX, 281-376 (1981). [CrossRef]

Publ. Astron. Soc. Pac.

R. Avila, E. Masciadri, J. Vernin, and L. Sanchez, "Generalized SCIDAR measurements at San Pedro Martir: I. Turbulence profile statistics," Publ. Astron. Soc. Pac. 116, 682-692 (2004). [CrossRef]
A. Fuchs, M. Tallon, and J. Vernin, "Focussiong on a turbulent layer: Principle of the Generalized SCIDAR," Publ. Astron. Soc. Pac. 110, 86-91 (1998). [CrossRef]
R. Avila, J. Vernin, and S. Cuevas, "Turbulence Profiles with Generalized Scidar at San Pedro M’artir Observatory and Isoplanatism Studies," Publ. Astron. Soc. Pac. 110, 1106-1116 (1998). [CrossRef]
A. Tokovinin, J. Vernin, A. Ziad, and M. Chun, "Optical Turbulence Profiles at Mauna Kea Measured by MASS and SCIDAR," Publ. Astron. Soc. Pac. 117, 395-400 (2005). [CrossRef]
S. E. Egner, E. Masciadri, and D. McKenna, "Generalized SCIDAR Measurements at Mount Graham," Publ. Astron. Soc. Pac. 119, 669-686 (2007). [CrossRef]
S. E. Egner and E. Masciadri, "A G-SCIDAR for Ground-Layer Turbulence Measurements at High Vertical Resolution," Publ. Astron. Soc. Pac. 119, 1441-1448 (2007). [CrossRef]

Other

J. Vernin, H. Trinquet, G. Jumper, E. Murphy, and A. Ratkowski, "OHP02 gravity wave campaign in relation to optical turbulence," Environmental Fluid Mechanics 7, 371-+ (2007). [CrossRef]
J. W. Goodman, Statistical Optics (Wiley-Interscience, New-York, 1985).
A. Fuchs, M. Tallon, and J. Vernin, "Folding of the vertical atmospheric turbulence profile using an optical technique of movable observing plane," in Atmospheric Propagation and Remote Sensing III, W. A. Flood and W. B. Miller, eds., Vol. 2222, pp. 682-692 (1994).

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[1] R. A. Johnston, C. Dainty, N. J. Wooder, and R. G. Lane, "Generalized scintillation detection and ranging results obtained by use of a modified inversion technique," Appl. Opt. 41(32), 6768-6772 (2002). [CrossRef]

[2] J. Vernin and F. Roddier, "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. A 63, 270-273 (1973). [CrossRef]

[3] A. Rocca, F. Roddier, and J. Vernin, "Detection of atmospheric turbulent layers by spatiotemporal and spatioangular correlation measurements of stellar-light scintillation," J. Opt. Soc. Am. A 64, 1000-1004 (1974). [CrossRef]

[4] J. Vernin and M. Azouit, "Traitement d’image adapt’e au speckle atmosph’erique. I-Formation du speckle en atmosph`ere turbulente. Proprietes statistiques," J. Opt. (Paris) 14, 5-9 (1983).

[5] J. Vernin and M. Azouit, "Traitement d’image adapte au speckle atmospherique. II-analyse multidimensionnelle appliquee au diagnostic a distance de la turbulence," J. Opt. (Paris) 14, 131-142 (1983).

[6] V. A. Kluckers, N. J. Wooder, T. W. Nicholls, M. J. Adcock, I. Munro, and J. C. Dainty, "Profiling of Atmospheric Turbulence Strength and Velocity using a Generalised SCIDAR Technique," Astron. Astrophys. Suppl. Ser. 130, 141-155 (1998). [CrossRef]

[7] J.-L. Prieur, G. Daigne, and R. Avila, "SCIDAR measurements at Pic du Midi," Astron. Astrophys. 371, 366-377 (2001). [CrossRef]

[8] F. Roddier, "The Effect of Atmospheric Turbulence in Optical Astronomy," Progress in Optics XIX, 281-376 (1981). [CrossRef]

[9] R. Avila, E. Masciadri, J. Vernin, and L. Sanchez, "Generalized SCIDAR measurements at San Pedro Martir: I. Turbulence profile statistics," Publ. Astron. Soc. Pac. 116, 682-692 (2004). [CrossRef]

[10] M. Chun, R. Wilson, R. Avila, T. Butterley, J.-L. Aviles, D. Wier, and S. Benigni, "Mauna Kea ground-layer characterization campaign," Mon. Not. R. Astron. Soc. 394, 1121-1130 (2009). [CrossRef]

[11] A. Fuchs, M. Tallon, and J. Vernin, "Folding of the vertical atmospheric turbulence profile using an optical technique of movable observing plane," in Atmospheric Propagation and Remote Sensing III, W. A. Flood and W. B. Miller, eds., Vol. 2222, pp. 682-692 (1994).

[12] R. Avila, J. Vernin, and E. Masciadri, "Whole atmospheric-turbulence profiling with generalized Scidar," Appl. Opt. 36(30), 7898-7905 (1997). [CrossRef]

[13] R. Avila, J. L. Aviles, R. Wilson, M. Chun, T. Butterley, and E. Carrasco, "LOLAS: an optical turbulence profiler in the atmospheric boundary layer with extreme altitude-resolution," Mon. Not. R. Astron. Soc. 387, 1511-1516 (2008). [CrossRef]

[14] A. Fuchs, M. Tallon, and J. Vernin, "Focussiong on a turbulent layer: Principle of the Generalized SCIDAR," Publ. Astron. Soc. Pac. 110, 86-91 (1998). [CrossRef]

[15] R. Avila, J. Vernin, and S. Cuevas, "Turbulence Profiles with Generalized Scidar at San Pedro M’artir Observatory and Isoplanatism Studies," Publ. Astron. Soc. Pac. 110, 1106-1116 (1998). [CrossRef]

[16] B. Kern, T. A. Laurence, C. Martin, and P. E. Dimotakis, "Temporal coherence of individual turbulent patterns in atmospheric seeing," Appl. Opt. 39, 4879-4885 (2000). [CrossRef]

[17] R. Avila, J. Vernin, and L. J. S’anchez, "Atmospheric turbulence and wind profiles monitoring with generalized scidar," Astron. Astrophys. 369, 364 (2001). [CrossRef]

[18] R. W. Wilson, N. J. Wooder, F. Rigal, and J. C. Dainty, "Estimation of anisoplanatism in adaptive optics by generalized SCIDAR profiling," Mon. Not. R. Astron. Soc. 339, 491-494 (2003). [CrossRef]

[19] A. Tokovinin, J. Vernin, A. Ziad, and M. Chun, "Optical Turbulence Profiles at Mauna Kea Measured by MASS and SCIDAR," Publ. Astron. Soc. Pac. 117, 395-400 (2005). [CrossRef]

[20] B. Garcıa-Lorenzo and J. J. Fuensalida, "Processing of turbulent-layer wind speed with Generalized SCIDAR through wavelet analysis," Mon. Not. R. Astron. Soc. 372, 1483-1495 (2006). arXiv:astro-ph/0608595. [CrossRef]

[21] S. E. Egner, E. Masciadri, and D. McKenna, "Generalized SCIDAR Measurements at Mount Graham," Publ. Astron. Soc. Pac. 119, 669-686 (2007). [CrossRef]

[22] J. Vernin, H. Trinquet, G. Jumper, E. Murphy, and A. Ratkowski, "OHP02 gravity wave campaign in relation to optical turbulence," Environmental Fluid Mechanics 7, 371-+ (2007). [CrossRef]

[23] S. E. Egner and E. Masciadri, "A G-SCIDAR for Ground-Layer Turbulence Measurements at High Vertical Resolution," Publ. Astron. Soc. Pac. 119, 1441-1448 (2007). [CrossRef]

[24] J. J. Fuensalida, B. Garcıa-Lorenzo, and C. Hoegemann, "Correction of the dome seeing contribution from generalized-SCIDAR data using evenness properties with Fourier analysis," Mon. Not. R. Astron. Soc. 389, 731-740 (2008). [CrossRef]

[25] J. W. Goodman, Statistical Optics (Wiley-Interscience, New-York, 1985).

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