Abstract

We discuss several improvements in the detection of atmospheric turbulence using SLOpe Detection And Ranging (SLODAR). Frequently, SLODAR observations have shown strong ground-layer turbulence, which is beneficial to adaptive optics. We show that current methods which neglect atmospheric propagation effects can underestimate the strength of high altitude turbulence by up to ~ 30%. We show that mirror and dome seeing turbulence can be a significant fraction of measured ground-layer turbulence, some cases up to ~ 50%. We also demonstrate a novel technique to improve the nominal height resolution, by a factor of 3, called Generalized SLODAR. This can be applied when sampling high-altitude turbulence, where the nominal height resolution is the poorest, or for resolving details in the important ground-layer.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D Campbell, J. C. Y Chin, S. K. Hartman, R. E. Lafon, Jr., P. J. Stomski and D. M. Summers, "The W. M. Keck Observatory Laser Guide Star Adaptive Optics System: Performance Characterization," Publ. Astron. Soc. Pac., 118, 310-318 (2006).
    [CrossRef]
  2. G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler and G. Zins, "NAOS, the first AO system of the VLT: on-sky performance," Proc. SPIE 4839, 140-149 (2003).
  3. M. Iye, H. Takami, N. Takato, S. Oya, Y. Hayano, O. Guyon, S. A. Colley, M. Hattori, M. Watanabe, M. Eldred, Y. Saito, N. Saito, K. Akagawa, and S. Wada, "Cassegrain and Nasmyth adaptive optics systems of 8.2-m Subaru telescope," Proc. SPIE 5639, 1-10 (2004).
    [CrossRef]
  4. J. A. Stoesz, J.-P. Veran, F. J. Rigaut, G. Herriot, L. Jolissaint, D. Frenette, J. Dunn, and M. Smith, "Evaluation of the on-sky performance of Altair," Proc. SPIE 5490, 67-78 (2004).
    [CrossRef]
  5. J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University Press, 1998).
  6. A. Tokovinin and T. Travouillon, "Model of optical turbulence profile at Cerro Pach´on," Mon. Not. R. Astron. Soc. 365, 1235-1242 (2006).
    [CrossRef]
  7. F. Rigaut, "Ground Conjugate Wide Field Adaptive Optics for the ELTs," in ESO Conference and Workshop Proceedings, 58, E. Vernet, R. Ragazzoni, S. Esposito, and N. Hubin, eds., (Garching, Germany: ESO, 2002), p. 11.
  8. A. Tokovinin, "Seeing Improvement with Ground-Layer Adaptive Optics," Publ. Astron. Soc. Pac. 116, 941-951 (2004).
    [CrossRef]

2006

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D Campbell, J. C. Y Chin, S. K. Hartman, R. E. Lafon, Jr., P. J. Stomski and D. M. Summers, "The W. M. Keck Observatory Laser Guide Star Adaptive Optics System: Performance Characterization," Publ. Astron. Soc. Pac., 118, 310-318 (2006).
[CrossRef]

A. Tokovinin and T. Travouillon, "Model of optical turbulence profile at Cerro Pach´on," Mon. Not. R. Astron. Soc. 365, 1235-1242 (2006).
[CrossRef]

2004

A. Tokovinin, "Seeing Improvement with Ground-Layer Adaptive Optics," Publ. Astron. Soc. Pac. 116, 941-951 (2004).
[CrossRef]

M. Iye, H. Takami, N. Takato, S. Oya, Y. Hayano, O. Guyon, S. A. Colley, M. Hattori, M. Watanabe, M. Eldred, Y. Saito, N. Saito, K. Akagawa, and S. Wada, "Cassegrain and Nasmyth adaptive optics systems of 8.2-m Subaru telescope," Proc. SPIE 5639, 1-10 (2004).
[CrossRef]

J. A. Stoesz, J.-P. Veran, F. J. Rigaut, G. Herriot, L. Jolissaint, D. Frenette, J. Dunn, and M. Smith, "Evaluation of the on-sky performance of Altair," Proc. SPIE 5490, 67-78 (2004).
[CrossRef]

2003

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler and G. Zins, "NAOS, the first AO system of the VLT: on-sky performance," Proc. SPIE 4839, 140-149 (2003).

Mon. Not. R. Astron. Soc.

A. Tokovinin and T. Travouillon, "Model of optical turbulence profile at Cerro Pach´on," Mon. Not. R. Astron. Soc. 365, 1235-1242 (2006).
[CrossRef]

Proc. SPIE

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler and G. Zins, "NAOS, the first AO system of the VLT: on-sky performance," Proc. SPIE 4839, 140-149 (2003).

M. Iye, H. Takami, N. Takato, S. Oya, Y. Hayano, O. Guyon, S. A. Colley, M. Hattori, M. Watanabe, M. Eldred, Y. Saito, N. Saito, K. Akagawa, and S. Wada, "Cassegrain and Nasmyth adaptive optics systems of 8.2-m Subaru telescope," Proc. SPIE 5639, 1-10 (2004).
[CrossRef]

J. A. Stoesz, J.-P. Veran, F. J. Rigaut, G. Herriot, L. Jolissaint, D. Frenette, J. Dunn, and M. Smith, "Evaluation of the on-sky performance of Altair," Proc. SPIE 5490, 67-78 (2004).
[CrossRef]

Publ. Astron. Soc. Pac.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D Campbell, J. C. Y Chin, S. K. Hartman, R. E. Lafon, Jr., P. J. Stomski and D. M. Summers, "The W. M. Keck Observatory Laser Guide Star Adaptive Optics System: Performance Characterization," Publ. Astron. Soc. Pac., 118, 310-318 (2006).
[CrossRef]

A. Tokovinin, "Seeing Improvement with Ground-Layer Adaptive Optics," Publ. Astron. Soc. Pac. 116, 941-951 (2004).
[CrossRef]

Other

F. Rigaut, "Ground Conjugate Wide Field Adaptive Optics for the ELTs," in ESO Conference and Workshop Proceedings, 58, E. Vernet, R. Ragazzoni, S. Esposito, and N. Hubin, eds., (Garching, Germany: ESO, 2002), p. 11.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University Press, 1998).

Supplementary Material (2)

» Media 1: AVI (579 KB)     
» Media 2: AVI (581 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1.
Fig. 1.

Diagram illustrating the geometry of the SLODAR method for a N=4 system. θ is the double star angular separation. D is the diameter of the telescope pupil and w the width of the sub-aperture of the Shack-Hartmann Wavefront Sensor (SHWFS) array. The centers of the altitude bins are given by Δδh where Δ is the lateral pupil separation (units of w) and δh = w/θ. The ground-layer can be analyzed in higher-resolution by utilization of double stars having larger θ.

Fig. 2.
Fig. 2.

Comparison of propagation effects on the covariance response function using numerical simulations (black dots with error bars) using Fresnel propagation and with theoretical values (red line with crosses) using the modified power spectrum (Eq. 1). The covariance plots are (a) longitudinal no propagation, (b) longitudinal with propagation, (c) transverse no propagation and (d) transverse with propagation. The longitudinal direction refers to direction parallel to double star separation axis, aligned along the x-direction of the SHWFS. The transverse direction refers to direction perpendicular to double star separation axis, aligned along the y-direction of the SHWFS. The comparisons are for single turbulent with Δ = 6 or height H = 7709 m and normalized by their respective Δ = 0 or height H = 0 m functions (i.e. no fitting involved). Plots (b) and (d) show that propagation effects decrease the peak covariance value (δi = 6) by ~ 20% compared to plots (a) and (c).

Fig. 3.
Fig. 3.

Comparison of propagation effects on the normalized theoretical covariance response functions for increasing height (H) and different sub-aperture sizes, w. The co-variance plots are (a) longitudinal and (b) transverse. The sub-aperture size w = 5.8 cm with no propagation (black line with crosses); w = 11.6 cm with propagation (blue line) and w = 5.8 cm with propagation (red line). The plots show that propagation effects are lessened by the larger sized sub-aperture, w = 11.6 cm, but still significant ~ 30%. The theoretical covariance functions are plotted for even Δ with H = Δδh, where δh = 1.29 km and Hmax = 20.6 km (Δ =16). The theoretical covariance functions for the SLODAR model are discrete valued, defined for integer values, δi, but plotted as continuous lines for clarity.

Fig. 4.
Fig. 4.

A comparison between using the theoretical covariance impulse functions with (a) no propagation effects and (b) propagation effects on actual observational data taken 16:19 12 April 2006 (UTC) with ANU 17×17 SLODAR instrument on the ANU 40″ telescope. The observational data was taken under excellent seeing, r 0 = 18.2 cm and exhibits significant high-altitude turbulence. The inclusion of propagation effects, (b), increases the strength of the highest turbulence, H ~ 16 km by ~ 25% relative to (a), in agreement with Fig. 3. The high-altitude turbulence H > 15 km causes a steeper increase in the cumulative turbulence of (b) by ~ 30% compared to (a) ~ 25%. The high-altitude of (b) appears more concentrated than (a).

Fig. 5.
Fig. 5.

Plots (a) and (c) are observational data containing significant amounts of mirror and dome seeing that cause over-estimating the contribution of the atmospheric ground-layer. Plots (b) and (d) are observational data with mirror and dome seeing removed by application of a high-pass filter with cut-off of 2 Hz to the centroid data streams. Plots (a) and (b) are the Spectral Energy Density of the Y-centroid slope data (top) and Y-centroid data stream (bottom) for star A sub-aperture index [i = 2, j = 5]. Plots (c) and (d) are AVI animations (size: (c) 579 KB and (d) 581 KB) of the spatial-temporal 2-D cross-covariance sequences for offset lags of 0 to 20 frames, each offset lag is 5 ms apart. The cross-covariance sequences are for X-centroid and Y-centroid data, and normalized to the zero spatial offset peak, [δi = 0, δj = 0], for zero offset lag, τ = 0 ms. The contribution of mirror and dome seeing to the ground-layer measurement ([δi = 0, δj = 0], τ = 0 ms) of plot (c) is about 48%, observed as excess residual for [δi = 0, δj = 0] for τ = 50 ms. Plots (a)-(d) reference the observational dataset of α Cen consisting of 20 s of data at 200 fps (4000 frames), taken 12:43 20 June 2006 UTC with the ANU 17×17 SLODAR instrument on the ANU 40″ telescope.

Fig. 6.
Fig. 6.

Extension of Fig. 1 to illustrate the notation used to describe the SLODAR theoretical covariance impulse function, XL (Δ,δi,δj) (see Eq. 2) and the notation used for Generalized SLODAR.

Fig. 7.
Fig. 7.

The data reduction methodology for Generalized SLODAR

Fig. 8.
Fig. 8.

Numerical simulation of Generalized SLODAR using parameters of Tab. 1. The objective is to fully separate two thin turbulent layers with height separation, ΔH = 2δh * where δh * = δh/NG with δh = 1200 m and NG = 3 generalized datasets. Plots (a)-(d) denote the numerical results as filled circles with error bars (black). Plot (a) shows the averaged longitudinal auto-covariance profile using star A; plot (b) shows the combined super-resolution longitudinal cross-covariance profile, C *x,obs L (δm *), using star A and star B; plot (c) shows the super-resolution CN 2(h *)dh * profile obtained by fitting super resolution kernel, XL ** ,δm *), to the cross-covariance profile, plot (b), using 4000 atmospheric realizations; plot (d) is similar to plot (c) except using 2000 atmospheric realizations. Plot (a) denotes the best theoretical fit with parameters β = 3.63 and ρ 0 = 0.31 ± 0.01 m as continuous line (red); theoretical G-tilt of sub-aperture as circle (black); theoretical Z-tilt of sub-aperture as square (black). Plot (b) denotes the best theoretical fit of super-resolution CN 2(h)dh profile, plot (c), as continuous line (red). Plots (c) and (d) denote the modelled atmosphere with parameters β = 3.67 and ρ 0 = 0.3 as stem lines with asterisks (red). The numerical simulation results shown in plots (a)-(d) confirm the validity of using the methodology outlined in Section 4 and illustrated in Fig. 7.

Fig. 9.
Fig. 9.

Observational data of Generalized SLODAR, NG = 2 datasets, having fractional offsets η 1 = 0.5 and η 2 = 0.9, and nominal height resolution, δh = 1102 m. The double star is α Cen, with separation θ = 9.44″, observed 10:04 (η 1) & 10:59 (η 2) 21 June 2006 (UTC) with the ANU 17×17 SLODAR instrument on the 40″ telescope at SSO The plots denote the observation results as filled circles with error bars (black). Plot (a) shows the combined super-resolution transverse cross-covariance profile, C *x,obs T (δm *), using 4000 frames for each dataset. Plot (b) shows the super-resolution CN 2(h *)dh * profile obtained by fitting super resolution kernel, XT **,δm *), to the cross-covariance profile, shown as continuous line (red) in plot (a). The observational data gives the seeing conditions as ρ 0 =0.095 ± 0.004 m and a power law of β = 3.15 ± 0.04. Plot (b) shows a 2x improvement in nominal resolution, δh * ~ δh/2, for the CN 2(h *)dh * profile, indicating strongest turbulence is near the ground ≤ 50 m.

Tables (1)

Tables Icon

Table 1. Parameters for the numerical simulation

Equations (14)

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

P ϕ 0 ( f ) = P ϕ ( f ) cos 2 ( πλh f 2 )
X L Δ δi δj = 1 N cross valid i , j , i , j C i , j , i , j x ( Δ )
C L , k ′x,obs ( δi , δj ) = x 0 X L 0 δi δj + x 1 X L 1 δi δj + + x N 1 X L N 1 δi δj
[ col { X L 0 δi δj } col { X L 1 δi δj } col { X L N 1 δi δj } ] [ x 0 x 1 x N 1 ]
= [ col { C L , k ′x,obs ( δi , δj ) } ]
X L ( Δ , δi ) = 1 N cross valid i , j , i C i , j , i , j x ( Δ )
a k = A L , 0 ′x,obs ( δi = 0 ) A L , k ′x,obs ( δi = 0 )
C L * x , obs ( δ m * ) = k a k C L , k ′x,obs ( δ m k )
δ m * = k δ m k
δ m * = { δ m 0 δ m 1 δ m N G 1 }
Ω k = Δ + η k
Ω * = k Ω k
Ω * = { Ω 0 Ω 1 Ω N G 1 }
X L * ( Ω * , δ m * ) = 1 N cross valid m , l , m C m , l , m , l x ( Ω * )

Metrics