Abstract

Optical waves propagating through atmospheric turbulence develop spatial and temporal variations in their phase. For sufficiently strong turbulence, these phase differences can lead to interference in the propagating wave and the formation of branch points; positions of zero amplitude. Under the assumption of a layered turbulence model, we show that these branch points can be used to estimate the number and velocities of atmospheric layers. We describe how to carry out this estimation process and demonstrate its robustness in the presence of sensor noise.

© 2010 Optical Society of America

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  1. J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University Press Inc., New York, NY, USA, 1998), 1st ed.
  2. D. C. Ghiglia and M. D. Pritt, Two Dimensional Phase Unwrapping: Theory, Algorithms, and Software (John Wiley and Sons, Inc., New York, NY, 1998).
  3. M. Schöck and E. J. Spillar, "Analyzing atmospheric turbulence with a shack-hartmann wavefront sensor," Proc. SPIE 3353, 1092-1099 (1998).
  4. M. Schöck and E. J. Spillar, "Method for a quantitative investiagation of the frozen flow hypothesis," J. Opt. Soc. Am. 17, 1650-1658 (2000).
    [CrossRef]
  5. D. C. Johnston and B. M. Welsh, "Estimating the contribution of different parts of the atmosphere to optical wavefront aberration," Comput. Elect. Eng. 18, 467-483 (1992).
    [CrossRef]
  6. L. Poyneer, M. van Dam, and J. P. Véran, "Experimental verification of the frozen flow atmospheric turbulence assumption with use of astronomical adaptive optics telemetry," J. Opt. Soc. Am 26, 833-846 (2009).
    [CrossRef]
  7. R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms (Bellingham, Wa, USA, 2007), 1st ed.
  8. M. C. Roggemann and A. C. Koivunen, "Branch-point reconstruction in laser beamprojection through turbulence with finite-degree-of-freedom phase-only wave-front correction," J. Opt. Soc. Am. 17, 53-62 (2000).
    [CrossRef]
  9. D. L. Fried, "Branch point problem in adaptive optics," J. Opt. Soc. Am. 15, 2759-2768 (1998).
    [CrossRef]
  10. E. O. Le Bigot and W. J. Wild, "Theory of branch-point detection and its implementation," J. Opt. Soc. Am. 16, 1724-1729 (1999).
    [CrossRef]
  11. S. V. Mantravadi, T. A. Rhoadarmer, and R. S. Glas, "Simple laboratory system for generating well-controlled atmospheric-like turbulence," in "Advanced Wavefront Control: Methods, Devices, and Applications II," presented at the Society of Photo-Optical Instrumentation Engineers (SPIE) Conference, M. K. Giles, J. D. Gonglewshi, and R. A. Carerras, eds., (2004), vol. 5553, pp. 290-300.
  12. T. A. Rhoadarmer, "Development of a self-referencing interferometer wavefront sensor," in "Advanced Wavefront Control: Methods, Devices, and Applications II," presented at the Society of Photo-Optical Instrumentation Engineers (SPIE) Conference, M. K. Giles, J. D. Gonglewshi, and R. A. Carerras, eds., (2004), vol. 5553.
  13. D. W. Oesch, D. J. Sanchez, C. M. Tewksbury-Christle, and P. R. Kelly, "The Aggregate Behavior of Branch Points - Branch Point Density as a Characteristic of an Atmospheric Turbulence Simulator," in "2009 SPIE Annual Conference," R. Carerras, T. Rhoadharmer, and D. Dayton, eds., (SPIE, 2009).

2009 (1)

L. Poyneer, M. van Dam, and J. P. Véran, "Experimental verification of the frozen flow atmospheric turbulence assumption with use of astronomical adaptive optics telemetry," J. Opt. Soc. Am 26, 833-846 (2009).
[CrossRef]

2000 (2)

M. C. Roggemann and A. C. Koivunen, "Branch-point reconstruction in laser beamprojection through turbulence with finite-degree-of-freedom phase-only wave-front correction," J. Opt. Soc. Am. 17, 53-62 (2000).
[CrossRef]

M. Schöck and E. J. Spillar, "Method for a quantitative investiagation of the frozen flow hypothesis," J. Opt. Soc. Am. 17, 1650-1658 (2000).
[CrossRef]

1999 (1)

E. O. Le Bigot and W. J. Wild, "Theory of branch-point detection and its implementation," J. Opt. Soc. Am. 16, 1724-1729 (1999).
[CrossRef]

1998 (2)

M. Schöck and E. J. Spillar, "Analyzing atmospheric turbulence with a shack-hartmann wavefront sensor," Proc. SPIE 3353, 1092-1099 (1998).

D. L. Fried, "Branch point problem in adaptive optics," J. Opt. Soc. Am. 15, 2759-2768 (1998).
[CrossRef]

1992 (1)

D. C. Johnston and B. M. Welsh, "Estimating the contribution of different parts of the atmosphere to optical wavefront aberration," Comput. Elect. Eng. 18, 467-483 (1992).
[CrossRef]

Fried, D. L.

D. L. Fried, "Branch point problem in adaptive optics," J. Opt. Soc. Am. 15, 2759-2768 (1998).
[CrossRef]

Johnston, D. C.

D. C. Johnston and B. M. Welsh, "Estimating the contribution of different parts of the atmosphere to optical wavefront aberration," Comput. Elect. Eng. 18, 467-483 (1992).
[CrossRef]

Koivunen, A. C.

M. C. Roggemann and A. C. Koivunen, "Branch-point reconstruction in laser beamprojection through turbulence with finite-degree-of-freedom phase-only wave-front correction," J. Opt. Soc. Am. 17, 53-62 (2000).
[CrossRef]

Le Bigot, E. O.

E. O. Le Bigot and W. J. Wild, "Theory of branch-point detection and its implementation," J. Opt. Soc. Am. 16, 1724-1729 (1999).
[CrossRef]

Poyneer, L.

L. Poyneer, M. van Dam, and J. P. Véran, "Experimental verification of the frozen flow atmospheric turbulence assumption with use of astronomical adaptive optics telemetry," J. Opt. Soc. Am 26, 833-846 (2009).
[CrossRef]

Roggemann, M. C.

M. C. Roggemann and A. C. Koivunen, "Branch-point reconstruction in laser beamprojection through turbulence with finite-degree-of-freedom phase-only wave-front correction," J. Opt. Soc. Am. 17, 53-62 (2000).
[CrossRef]

Schöck, M.

M. Schöck and E. J. Spillar, "Method for a quantitative investiagation of the frozen flow hypothesis," J. Opt. Soc. Am. 17, 1650-1658 (2000).
[CrossRef]

M. Schöck and E. J. Spillar, "Analyzing atmospheric turbulence with a shack-hartmann wavefront sensor," Proc. SPIE 3353, 1092-1099 (1998).

Spillar, E. J.

M. Schöck and E. J. Spillar, "Method for a quantitative investiagation of the frozen flow hypothesis," J. Opt. Soc. Am. 17, 1650-1658 (2000).
[CrossRef]

M. Schöck and E. J. Spillar, "Analyzing atmospheric turbulence with a shack-hartmann wavefront sensor," Proc. SPIE 3353, 1092-1099 (1998).

van Dam, M.

L. Poyneer, M. van Dam, and J. P. Véran, "Experimental verification of the frozen flow atmospheric turbulence assumption with use of astronomical adaptive optics telemetry," J. Opt. Soc. Am 26, 833-846 (2009).
[CrossRef]

Véran, J. P.

L. Poyneer, M. van Dam, and J. P. Véran, "Experimental verification of the frozen flow atmospheric turbulence assumption with use of astronomical adaptive optics telemetry," J. Opt. Soc. Am 26, 833-846 (2009).
[CrossRef]

Welsh, B. M.

D. C. Johnston and B. M. Welsh, "Estimating the contribution of different parts of the atmosphere to optical wavefront aberration," Comput. Elect. Eng. 18, 467-483 (1992).
[CrossRef]

Wild, W. J.

E. O. Le Bigot and W. J. Wild, "Theory of branch-point detection and its implementation," J. Opt. Soc. Am. 16, 1724-1729 (1999).
[CrossRef]

Comput. Elect. Eng. (1)

D. C. Johnston and B. M. Welsh, "Estimating the contribution of different parts of the atmosphere to optical wavefront aberration," Comput. Elect. Eng. 18, 467-483 (1992).
[CrossRef]

J. Opt. Soc. Am (1)

L. Poyneer, M. van Dam, and J. P. Véran, "Experimental verification of the frozen flow atmospheric turbulence assumption with use of astronomical adaptive optics telemetry," J. Opt. Soc. Am 26, 833-846 (2009).
[CrossRef]

J. Opt. Soc. Am. (4)

M. Schöck and E. J. Spillar, "Method for a quantitative investiagation of the frozen flow hypothesis," J. Opt. Soc. Am. 17, 1650-1658 (2000).
[CrossRef]

M. C. Roggemann and A. C. Koivunen, "Branch-point reconstruction in laser beamprojection through turbulence with finite-degree-of-freedom phase-only wave-front correction," J. Opt. Soc. Am. 17, 53-62 (2000).
[CrossRef]

D. L. Fried, "Branch point problem in adaptive optics," J. Opt. Soc. Am. 15, 2759-2768 (1998).
[CrossRef]

E. O. Le Bigot and W. J. Wild, "Theory of branch-point detection and its implementation," J. Opt. Soc. Am. 16, 1724-1729 (1999).
[CrossRef]

Proc. SPIE (1)

M. Schöck and E. J. Spillar, "Analyzing atmospheric turbulence with a shack-hartmann wavefront sensor," Proc. SPIE 3353, 1092-1099 (1998).

Other (6)

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University Press Inc., New York, NY, USA, 1998), 1st ed.

D. C. Ghiglia and M. D. Pritt, Two Dimensional Phase Unwrapping: Theory, Algorithms, and Software (John Wiley and Sons, Inc., New York, NY, 1998).

S. V. Mantravadi, T. A. Rhoadarmer, and R. S. Glas, "Simple laboratory system for generating well-controlled atmospheric-like turbulence," in "Advanced Wavefront Control: Methods, Devices, and Applications II," presented at the Society of Photo-Optical Instrumentation Engineers (SPIE) Conference, M. K. Giles, J. D. Gonglewshi, and R. A. Carerras, eds., (2004), vol. 5553, pp. 290-300.

T. A. Rhoadarmer, "Development of a self-referencing interferometer wavefront sensor," in "Advanced Wavefront Control: Methods, Devices, and Applications II," presented at the Society of Photo-Optical Instrumentation Engineers (SPIE) Conference, M. K. Giles, J. D. Gonglewshi, and R. A. Carerras, eds., (2004), vol. 5553.

D. W. Oesch, D. J. Sanchez, C. M. Tewksbury-Christle, and P. R. Kelly, "The Aggregate Behavior of Branch Points - Branch Point Density as a Characteristic of an Atmospheric Turbulence Simulator," in "2009 SPIE Annual Conference," R. Carerras, T. Rhoadharmer, and D. Dayton, eds., (SPIE, 2009).

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms (Bellingham, Wa, USA, 2007), 1st ed.

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