Abstract

The slope detection and ranging (slodar) method recovers atmospheric turbulence profiles from time averaged spatial cross correlations of wavefront slopes measured by Shack–Hartmann wavefront sensors. The Palomar multiple guide star unit (MGSU) was set up to test tomographic multiple guide star adaptive optics and provided an ideal test bed for slodar turbulence altitude profiling. We present the data reduction methods and slodar results from MGSU observations made in 2006. Wind profiling is also performed using delayed wavefront cross correlations along with slodar analysis. The wind profiling analysis is shown to improve the height resolution of the slodar method and in addition gives the wind velocities of the turbulent layers.

© 2008 Optical Society of America

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References

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  1. B. L. Ellerbroek and F. J. Rigaut, “Scaling multiconjugate adaptive optics performance estimates to extremely large telescopes,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE, 4007, 1088-1099 (2000).
  2. A. Tokovinin, “Seeing improvement with ground-layer adaptive optics,” Publ. Astron. Soc. Pac. 116, 941-951 (2004).
    [CrossRef]
  3. R. W. Wilson, “slodar: measuring optical turbulence altitude with a Shack-Hartmann wavefront sensor,” Mon. Not. R. Astron. Soc. 337, 103-108 (2002).
    [CrossRef]
  4. T. Butterley, R. W. Wilson, and M. Sarazin, “Determination of the profile of atmospheric optical turbulence strength from slodar data,” Mon. Not. R. Astron. Soc. 369, 835-845 (2006).
    [CrossRef]
  5. R. W. Wilson, J. Bate, J. C. Guerra, N. N. Hubin, M. Sarazin, and C. D. Saunter, “Development of a portable slodar turbulence profiler,” in Advancements in Adaptive Optics, D. B. Calia, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE 5490, 758-765 (2004).
  6. L. Jolissaint, O. Keskin, C. Bradley, B. Wallace, and A. Hilton, “Multiple-layer optical turbulence generator principle and slodar characterization: preliminary results,” in ,i>Optics in Atmospheric Propagation and Adaptive Systems VII, J. D. Gonglewski and K. Stein, eds., Proc. SPIE 5572, 256-261(2004).
  7. G. D. Love, C. N. Dunlop, S. Patrick, C. D. Saunter, R. W. Wilson, and C. Wright, “Horizontal turbulence measurements using slodar,” in Atmospheric Optical Modeling, Measurement, and Simulation, S. M. Doss-Hammel and A. Kohnle, eds., Proc. SPIE 5891, 27-32 (2005).
  8. V. Velur, R. C. Flicker, B. C. Platt, M. C. Britton, R. G. Dekany, M. Troy, J. E. Roberts, J. C. Shelton, and J. Hickey, “Multiple guide star tomography demonstration at Palomar observatory,” in Advances in Adaptive Optics II, B. L. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, 627258 (2006).
  9. P. B. Stetson, “daophot--a computer program for crowded-field stellar photometry,” Publ. Astron. Soc. Pac. 99, 191-222(1987).
    [CrossRef]
  10. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN. The Art of Scientific Computing, 2nd ed. (Cambridge Press, 1992).
  11. D. L. Fried, “Statistics of a geometric representation of wavefront distortion,” J. Opt. Soc. Am. 55, 1427-1435 (1965).
  12. V. Kornilov, A. A. Tokovinin, O. Vozyakova, A. Zaitsev, N. Shatsky, S. F. Potanin, and M. S. Sarazin, “mass: a monitor of the vertical turbulence distribution,” in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 837-845 (2003).
  13. G. I. Taylor, “The spectrum of turbulence,” Proc. R. Soc. London, Ser. A 164, 476-490 (1938).
  14. M. Schöck and E. J. Spillar, “Method for a quantitative investigation of the frozen flow hypothesis,” J. Opt. Soc. Am. A 17, 1650-1658 (2000).
    [CrossRef]

2006 (1)

T. Butterley, R. W. Wilson, and M. Sarazin, “Determination of the profile of atmospheric optical turbulence strength from slodar data,” Mon. Not. R. Astron. Soc. 369, 835-845 (2006).
[CrossRef]

2004 (1)

A. Tokovinin, “Seeing improvement with ground-layer adaptive optics,” Publ. Astron. Soc. Pac. 116, 941-951 (2004).
[CrossRef]

2002 (1)

R. W. Wilson, “slodar: measuring optical turbulence altitude with a Shack-Hartmann wavefront sensor,” Mon. Not. R. Astron. Soc. 337, 103-108 (2002).
[CrossRef]

2000 (1)

1987 (1)

P. B. Stetson, “daophot--a computer program for crowded-field stellar photometry,” Publ. Astron. Soc. Pac. 99, 191-222(1987).
[CrossRef]

1965 (1)

1938 (1)

G. I. Taylor, “The spectrum of turbulence,” Proc. R. Soc. London, Ser. A 164, 476-490 (1938).

Bate, J.

R. W. Wilson, J. Bate, J. C. Guerra, N. N. Hubin, M. Sarazin, and C. D. Saunter, “Development of a portable slodar turbulence profiler,” in Advancements in Adaptive Optics, D. B. Calia, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE 5490, 758-765 (2004).

Bradley, C.

L. Jolissaint, O. Keskin, C. Bradley, B. Wallace, and A. Hilton, “Multiple-layer optical turbulence generator principle and slodar characterization: preliminary results,” in ,i>Optics in Atmospheric Propagation and Adaptive Systems VII, J. D. Gonglewski and K. Stein, eds., Proc. SPIE 5572, 256-261(2004).

Britton, M. C.

V. Velur, R. C. Flicker, B. C. Platt, M. C. Britton, R. G. Dekany, M. Troy, J. E. Roberts, J. C. Shelton, and J. Hickey, “Multiple guide star tomography demonstration at Palomar observatory,” in Advances in Adaptive Optics II, B. L. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, 627258 (2006).

Butterley, T.

T. Butterley, R. W. Wilson, and M. Sarazin, “Determination of the profile of atmospheric optical turbulence strength from slodar data,” Mon. Not. R. Astron. Soc. 369, 835-845 (2006).
[CrossRef]

Dekany, R. G.

V. Velur, R. C. Flicker, B. C. Platt, M. C. Britton, R. G. Dekany, M. Troy, J. E. Roberts, J. C. Shelton, and J. Hickey, “Multiple guide star tomography demonstration at Palomar observatory,” in Advances in Adaptive Optics II, B. L. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, 627258 (2006).

Dunlop, C. N.

G. D. Love, C. N. Dunlop, S. Patrick, C. D. Saunter, R. W. Wilson, and C. Wright, “Horizontal turbulence measurements using slodar,” in Atmospheric Optical Modeling, Measurement, and Simulation, S. M. Doss-Hammel and A. Kohnle, eds., Proc. SPIE 5891, 27-32 (2005).

Ellerbroek, B. L.

B. L. Ellerbroek and F. J. Rigaut, “Scaling multiconjugate adaptive optics performance estimates to extremely large telescopes,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE, 4007, 1088-1099 (2000).

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN. The Art of Scientific Computing, 2nd ed. (Cambridge Press, 1992).

Flicker, R. C.

V. Velur, R. C. Flicker, B. C. Platt, M. C. Britton, R. G. Dekany, M. Troy, J. E. Roberts, J. C. Shelton, and J. Hickey, “Multiple guide star tomography demonstration at Palomar observatory,” in Advances in Adaptive Optics II, B. L. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, 627258 (2006).

Fried, D. L.

Guerra, J. C.

R. W. Wilson, J. Bate, J. C. Guerra, N. N. Hubin, M. Sarazin, and C. D. Saunter, “Development of a portable slodar turbulence profiler,” in Advancements in Adaptive Optics, D. B. Calia, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE 5490, 758-765 (2004).

Hickey, J.

V. Velur, R. C. Flicker, B. C. Platt, M. C. Britton, R. G. Dekany, M. Troy, J. E. Roberts, J. C. Shelton, and J. Hickey, “Multiple guide star tomography demonstration at Palomar observatory,” in Advances in Adaptive Optics II, B. L. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, 627258 (2006).

Hilton, A.

L. Jolissaint, O. Keskin, C. Bradley, B. Wallace, and A. Hilton, “Multiple-layer optical turbulence generator principle and slodar characterization: preliminary results,” in ,i>Optics in Atmospheric Propagation and Adaptive Systems VII, J. D. Gonglewski and K. Stein, eds., Proc. SPIE 5572, 256-261(2004).

Hubin, N. N.

R. W. Wilson, J. Bate, J. C. Guerra, N. N. Hubin, M. Sarazin, and C. D. Saunter, “Development of a portable slodar turbulence profiler,” in Advancements in Adaptive Optics, D. B. Calia, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE 5490, 758-765 (2004).

Jolissaint, L.

L. Jolissaint, O. Keskin, C. Bradley, B. Wallace, and A. Hilton, “Multiple-layer optical turbulence generator principle and slodar characterization: preliminary results,” in ,i>Optics in Atmospheric Propagation and Adaptive Systems VII, J. D. Gonglewski and K. Stein, eds., Proc. SPIE 5572, 256-261(2004).

Keskin, O.

L. Jolissaint, O. Keskin, C. Bradley, B. Wallace, and A. Hilton, “Multiple-layer optical turbulence generator principle and slodar characterization: preliminary results,” in ,i>Optics in Atmospheric Propagation and Adaptive Systems VII, J. D. Gonglewski and K. Stein, eds., Proc. SPIE 5572, 256-261(2004).

Kornilov, V.

V. Kornilov, A. A. Tokovinin, O. Vozyakova, A. Zaitsev, N. Shatsky, S. F. Potanin, and M. S. Sarazin, “mass: a monitor of the vertical turbulence distribution,” in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 837-845 (2003).

Love, G. D.

G. D. Love, C. N. Dunlop, S. Patrick, C. D. Saunter, R. W. Wilson, and C. Wright, “Horizontal turbulence measurements using slodar,” in Atmospheric Optical Modeling, Measurement, and Simulation, S. M. Doss-Hammel and A. Kohnle, eds., Proc. SPIE 5891, 27-32 (2005).

Patrick, S.

G. D. Love, C. N. Dunlop, S. Patrick, C. D. Saunter, R. W. Wilson, and C. Wright, “Horizontal turbulence measurements using slodar,” in Atmospheric Optical Modeling, Measurement, and Simulation, S. M. Doss-Hammel and A. Kohnle, eds., Proc. SPIE 5891, 27-32 (2005).

Platt, B. C.

V. Velur, R. C. Flicker, B. C. Platt, M. C. Britton, R. G. Dekany, M. Troy, J. E. Roberts, J. C. Shelton, and J. Hickey, “Multiple guide star tomography demonstration at Palomar observatory,” in Advances in Adaptive Optics II, B. L. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, 627258 (2006).

Potanin, S. F.

V. Kornilov, A. A. Tokovinin, O. Vozyakova, A. Zaitsev, N. Shatsky, S. F. Potanin, and M. S. Sarazin, “mass: a monitor of the vertical turbulence distribution,” in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 837-845 (2003).

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN. The Art of Scientific Computing, 2nd ed. (Cambridge Press, 1992).

Rigaut, F. J.

B. L. Ellerbroek and F. J. Rigaut, “Scaling multiconjugate adaptive optics performance estimates to extremely large telescopes,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE, 4007, 1088-1099 (2000).

Roberts, J. E.

V. Velur, R. C. Flicker, B. C. Platt, M. C. Britton, R. G. Dekany, M. Troy, J. E. Roberts, J. C. Shelton, and J. Hickey, “Multiple guide star tomography demonstration at Palomar observatory,” in Advances in Adaptive Optics II, B. L. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, 627258 (2006).

Sarazin, M.

T. Butterley, R. W. Wilson, and M. Sarazin, “Determination of the profile of atmospheric optical turbulence strength from slodar data,” Mon. Not. R. Astron. Soc. 369, 835-845 (2006).
[CrossRef]

R. W. Wilson, J. Bate, J. C. Guerra, N. N. Hubin, M. Sarazin, and C. D. Saunter, “Development of a portable slodar turbulence profiler,” in Advancements in Adaptive Optics, D. B. Calia, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE 5490, 758-765 (2004).

Sarazin, M. S.

V. Kornilov, A. A. Tokovinin, O. Vozyakova, A. Zaitsev, N. Shatsky, S. F. Potanin, and M. S. Sarazin, “mass: a monitor of the vertical turbulence distribution,” in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 837-845 (2003).

Saunter, C. D.

R. W. Wilson, J. Bate, J. C. Guerra, N. N. Hubin, M. Sarazin, and C. D. Saunter, “Development of a portable slodar turbulence profiler,” in Advancements in Adaptive Optics, D. B. Calia, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE 5490, 758-765 (2004).

G. D. Love, C. N. Dunlop, S. Patrick, C. D. Saunter, R. W. Wilson, and C. Wright, “Horizontal turbulence measurements using slodar,” in Atmospheric Optical Modeling, Measurement, and Simulation, S. M. Doss-Hammel and A. Kohnle, eds., Proc. SPIE 5891, 27-32 (2005).

Schöck, M.

Shatsky, N.

V. Kornilov, A. A. Tokovinin, O. Vozyakova, A. Zaitsev, N. Shatsky, S. F. Potanin, and M. S. Sarazin, “mass: a monitor of the vertical turbulence distribution,” in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 837-845 (2003).

Shelton, J. C.

V. Velur, R. C. Flicker, B. C. Platt, M. C. Britton, R. G. Dekany, M. Troy, J. E. Roberts, J. C. Shelton, and J. Hickey, “Multiple guide star tomography demonstration at Palomar observatory,” in Advances in Adaptive Optics II, B. L. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, 627258 (2006).

Spillar, E. J.

Stetson, P. B.

P. B. Stetson, “daophot--a computer program for crowded-field stellar photometry,” Publ. Astron. Soc. Pac. 99, 191-222(1987).
[CrossRef]

Taylor, G. I.

G. I. Taylor, “The spectrum of turbulence,” Proc. R. Soc. London, Ser. A 164, 476-490 (1938).

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN. The Art of Scientific Computing, 2nd ed. (Cambridge Press, 1992).

Tokovinin, A.

A. Tokovinin, “Seeing improvement with ground-layer adaptive optics,” Publ. Astron. Soc. Pac. 116, 941-951 (2004).
[CrossRef]

Tokovinin, A. A.

V. Kornilov, A. A. Tokovinin, O. Vozyakova, A. Zaitsev, N. Shatsky, S. F. Potanin, and M. S. Sarazin, “mass: a monitor of the vertical turbulence distribution,” in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 837-845 (2003).

Troy, M.

V. Velur, R. C. Flicker, B. C. Platt, M. C. Britton, R. G. Dekany, M. Troy, J. E. Roberts, J. C. Shelton, and J. Hickey, “Multiple guide star tomography demonstration at Palomar observatory,” in Advances in Adaptive Optics II, B. L. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, 627258 (2006).

Velur, V.

V. Velur, R. C. Flicker, B. C. Platt, M. C. Britton, R. G. Dekany, M. Troy, J. E. Roberts, J. C. Shelton, and J. Hickey, “Multiple guide star tomography demonstration at Palomar observatory,” in Advances in Adaptive Optics II, B. L. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, 627258 (2006).

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN. The Art of Scientific Computing, 2nd ed. (Cambridge Press, 1992).

Vozyakova, O.

V. Kornilov, A. A. Tokovinin, O. Vozyakova, A. Zaitsev, N. Shatsky, S. F. Potanin, and M. S. Sarazin, “mass: a monitor of the vertical turbulence distribution,” in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 837-845 (2003).

Wallace, B.

L. Jolissaint, O. Keskin, C. Bradley, B. Wallace, and A. Hilton, “Multiple-layer optical turbulence generator principle and slodar characterization: preliminary results,” in ,i>Optics in Atmospheric Propagation and Adaptive Systems VII, J. D. Gonglewski and K. Stein, eds., Proc. SPIE 5572, 256-261(2004).

Wilson, R. W.

T. Butterley, R. W. Wilson, and M. Sarazin, “Determination of the profile of atmospheric optical turbulence strength from slodar data,” Mon. Not. R. Astron. Soc. 369, 835-845 (2006).
[CrossRef]

R. W. Wilson, “slodar: measuring optical turbulence altitude with a Shack-Hartmann wavefront sensor,” Mon. Not. R. Astron. Soc. 337, 103-108 (2002).
[CrossRef]

G. D. Love, C. N. Dunlop, S. Patrick, C. D. Saunter, R. W. Wilson, and C. Wright, “Horizontal turbulence measurements using slodar,” in Atmospheric Optical Modeling, Measurement, and Simulation, S. M. Doss-Hammel and A. Kohnle, eds., Proc. SPIE 5891, 27-32 (2005).

R. W. Wilson, J. Bate, J. C. Guerra, N. N. Hubin, M. Sarazin, and C. D. Saunter, “Development of a portable slodar turbulence profiler,” in Advancements in Adaptive Optics, D. B. Calia, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE 5490, 758-765 (2004).

Wright, C.

G. D. Love, C. N. Dunlop, S. Patrick, C. D. Saunter, R. W. Wilson, and C. Wright, “Horizontal turbulence measurements using slodar,” in Atmospheric Optical Modeling, Measurement, and Simulation, S. M. Doss-Hammel and A. Kohnle, eds., Proc. SPIE 5891, 27-32 (2005).

Zaitsev, A.

V. Kornilov, A. A. Tokovinin, O. Vozyakova, A. Zaitsev, N. Shatsky, S. F. Potanin, and M. S. Sarazin, “mass: a monitor of the vertical turbulence distribution,” in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 837-845 (2003).

J. Opt. Soc. Am. (1)

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

Mon. Not. R. Astron. Soc. (2)

R. W. Wilson, “slodar: measuring optical turbulence altitude with a Shack-Hartmann wavefront sensor,” Mon. Not. R. Astron. Soc. 337, 103-108 (2002).
[CrossRef]

T. Butterley, R. W. Wilson, and M. Sarazin, “Determination of the profile of atmospheric optical turbulence strength from slodar data,” Mon. Not. R. Astron. Soc. 369, 835-845 (2006).
[CrossRef]

Proc. R. Soc. London, Ser. A (1)

G. I. Taylor, “The spectrum of turbulence,” Proc. R. Soc. London, Ser. A 164, 476-490 (1938).

Publ. Astron. Soc. Pac. (2)

A. Tokovinin, “Seeing improvement with ground-layer adaptive optics,” Publ. Astron. Soc. Pac. 116, 941-951 (2004).
[CrossRef]

P. B. Stetson, “daophot--a computer program for crowded-field stellar photometry,” Publ. Astron. Soc. Pac. 99, 191-222(1987).
[CrossRef]

Other (7)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN. The Art of Scientific Computing, 2nd ed. (Cambridge Press, 1992).

V. Kornilov, A. A. Tokovinin, O. Vozyakova, A. Zaitsev, N. Shatsky, S. F. Potanin, and M. S. Sarazin, “mass: a monitor of the vertical turbulence distribution,” in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 837-845 (2003).

B. L. Ellerbroek and F. J. Rigaut, “Scaling multiconjugate adaptive optics performance estimates to extremely large telescopes,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE, 4007, 1088-1099 (2000).

R. W. Wilson, J. Bate, J. C. Guerra, N. N. Hubin, M. Sarazin, and C. D. Saunter, “Development of a portable slodar turbulence profiler,” in Advancements in Adaptive Optics, D. B. Calia, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE 5490, 758-765 (2004).

L. Jolissaint, O. Keskin, C. Bradley, B. Wallace, and A. Hilton, “Multiple-layer optical turbulence generator principle and slodar characterization: preliminary results,” in ,i>Optics in Atmospheric Propagation and Adaptive Systems VII, J. D. Gonglewski and K. Stein, eds., Proc. SPIE 5572, 256-261(2004).

G. D. Love, C. N. Dunlop, S. Patrick, C. D. Saunter, R. W. Wilson, and C. Wright, “Horizontal turbulence measurements using slodar,” in Atmospheric Optical Modeling, Measurement, and Simulation, S. M. Doss-Hammel and A. Kohnle, eds., Proc. SPIE 5891, 27-32 (2005).

V. Velur, R. C. Flicker, B. C. Platt, M. C. Britton, R. G. Dekany, M. Troy, J. E. Roberts, J. C. Shelton, and J. Hickey, “Multiple guide star tomography demonstration at Palomar observatory,” in Advances in Adaptive Optics II, B. L. Ellerbroek and D. Bonaccini Calia, eds., Proc. SPIE 6272, 627258 (2006).

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Figures (14)

Fig. 1
Fig. 1

Flow chart of the wavefront gradient calculation.

Fig. 2
Fig. 2

Flow chart of the slodar and wind profiling analysis. MGSUs A and B refer to any pair of MGSU cameras.

Fig. 3
Fig. 3

Top left panel shows the original response of the centroids in each subaperture to the global wavefront tilt set by the TT mirror during the calibration process for MGSU 1. Significant scatter of the measured centroids across the subapertures for a given global wavefront tip–tilt is caused by cross talk between subapertures and optical aberrations. To work around this problem, certain subapertures, which are well-illuminated and have less cross talk or aberration, are selected (top right panel) to construct the response curve of centroids to wavefront gradients (bottom left panel). Centroid results from experimental data are then rescaled based on this response curve. The bottom right panel shows the much improved linearity achieved with the rescaled centroids. The rescaled data show more scatter when the wavefront slope is large because the slope in the response curve is smaller and thus scatter in centroids causes more scatter in measured wavefront slopes.

Fig. 4
Fig. 4

Comparison of centroid histograms from different centroiding methods (UT 06:40 dataset, MGSU 2, 48000 frame, CCD pixel scale is 0.75   arcsec ). Results for a particular subaperture (4,12) are shown. Although the histograms from the center of mass method look Gaussian, the range is severely limited. The histograms from the iterative center of mass method and the daophot Find method show unphysical departures from a Gaussian shape and are rejected. The histograms from the Gauss two-dimensional fitting have an approximately Gaussian shape and there is no indication of an artificially limited range.

Fig. 5
Fig. 5

This example of a time averaged frame shows how subapertures are divided when static aberrations are present (UT 06:40, MGSU 2). The plus signs show the nominal centers of each subaperture; the boxes show how the actual subapertures are divided to calculate wavefront gradients. Due to the static aberrations, nominal and actual subapertures do not agree very well, making this irregular division necessary. Note also that the fluxes in the subapertures are not uniform. The mean flux is 334 e with a standard deviation of 81 e .

Fig. 6
Fig. 6

Histogram of the fitted Gaussian surface FWHM for the MGSU 2 UT 06:40 dataset.

Fig. 7
Fig. 7

Left panel: the comparison between the measured centroids and the true wavefront slopes generated by the tip–tilt mirror. Right panel: the comparison between the subaperture averaged centroids and the wavefront slopes. The averaged centroids are close to linearly proportional to the actual wavefront slopes.

Fig. 8
Fig. 8

Left panel: the global tip–tilt in the x direction at UT 03:55 for all four MGSU cameras. Right panel: corresponding y centroids. The curves are smoothed with a boxcar average of 1000 frames. The four TT curves show a similar pattern. This confirms that the synchronization between cameras has been done correctly.

Fig. 9
Fig. 9

Left panel shows the two-dimensional deconvolution frame of the cross correlation between MGSUs 1 and 2 for UT03:55, 10 February 2006. Darker areas mean greater turbulence strength. The x and y axes are the directions of the rows and columns of the WFS. The right panel shows a one-dimensional cut of the left panel through the center and along the tail, whose direction is coincident with the direction of the two corresponding guide stars. The right-hand side (height > 0 ) of the curve shows the turbulence strength profile of the atmosphere.

Fig. 10
Fig. 10

Top panels: slodar results from the UT 06:40 dataset. The six curves in the top plots show turbulence profile results from slodar analysis for the six baselines, as indicated in the key in the upper right of each plot. Bottom left panel: the averaged slodar results from four different baselines (excluding the short baselines 1–2 and 1–4) with δ h = 0.5 km . In the averaged data we can clearly see the ground layer and a layer at 4 km . The bottom right panel shows results for the same time (averaged over 10 min ) from the Palomar mass instrument.

Fig. 11
Fig. 11

slodar results for the UT 03:55 dataset, as in Fig. 10 but without mass results because the mass was not in operation at the same time. In the averaged data we can clearly see the ground layer and a layer around 8 km .

Fig. 12
Fig. 12

These figures show a series of time-delayed cross correlations between MGSUs 1 and 2 (from the UT 03:55 dataset). Darker areas mean greater turbulence strength. The peaks corresponding to different layers are marked by plus signs and the layers are numbered 0 through 4. The positions of the peaks are determined by fitting the peaks locally to two-dimensional Gaussian surfaces. In the last five frames exact positions for peaks 3 and 4 are hard to identify due to spreading and are not shown here.

Fig. 13
Fig. 13

Positions of the peaks found in Fig. 12 are shown as plus signs. Peaks from the same layer are aligned in a straight line, corresponding to the direction of the wind in these layers (the opposite direction in reality). The intersections of these lines with the dashed line (the star separation direction) give the initial position of the layers (marked by open diamonds), which can be used to calculate the layer heights. The wind speed is calculated by dividing the distance between the plus signs and the respective diamonds by the corresponding delay time ( 150 400 ms ).

Fig. 14
Fig. 14

Wind profiling results are plotted together with the slodar results determined for the same data set (see Fig. 11). The six curves as shown in the legend are slodar results from the six baselines. The wind profiling results are shown as vertical bars with the relative strength indicated by the bar length. The two layers around 7 km as seen in the wind profiling analysis, as well as the three ground layers, are not resolved by slodar.

Tables (4)

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Table 1 Names and Coordinates (Epoch J2000.0) of the Four Stars Observed

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Table 2 Star Angular Separations (θ) of the Six Baselines and the Corresponding Height Resolution δ h and Range H max a

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Table 3 Five Successful Datasets from the Experiments, All of Which Are From 10 February 2006 a

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Table 4 Five Layers 0–4 Identified by the Wind Profiling Method for the UT 03:55 Dataset, with Their Heights, Relative Strengths, Wind Speeds, and Directions All Determined a

Equations (13)

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f ( x , y ) = a 0 e [ ( x - a 1 ) 2 / a 2 2 ] [ ( y - a 4 ) 2 / a 5 2 ] + a 3 .
C ( δ i , δ j ) = i j s i j ( t ) s i + δ i , j + δ j ( t ) O ( δ i , δ j ) ,
A ( δ i , δ j ) = i j s i j ( t ) s i + δ i , j + δ j ( t ) O ( δ i , δ j ) .
δ h = w θ sec ζ , H = Δ δ h ,
C ( δ i , δ j , δ t ) = i j s i j ( t ) s i + δ i , j + δ j ( t + δ t ) O ( δ i , δ j ) ,
y 0 = a 0 + b 0 x 0 , y 0 = a + b ( x 0 - x ¯ ) ,
H = r δ h , r = ( x 0 - 15 ) 2 + ( y 0 - 15 ) 2 ,
H a = δ h ( x 0 - 15 r + b 0 y 0 - 15 r ) 1 b 0 - b , H b = δ h ( x 0 - 15 r + b 0 y 0 - 15 r ) x 0 - x ¯ b 0 - b .
( δ H ) 2 = ( H a ) 2 ( δ a ) 2 + ( H b ) 2 ( δ b ) 2 = ( δ h ) 2 ( x 0 - 15 r + b 0 y 0 - 15 r ) 2 [ ( 1 b 0 - b ) 2 σ 2 n + ( x 0 - x ¯ b 0 - b ) 2 σ 2 i ( x i - x ¯ ) 2 ] .
θ = 180 π a tan b ,
δ θ = 180 π δ b 1 + b 2 .
v = v i = d ( x i - x 0 ) 2 + ( y i - y 0 ) 2 t i ,
δ v = i = 1 N ( v i - v ) 2 N - 1 ,

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