Abstract

The atmospheric turbulence measurement has received much attention in various fields due to its effects on wave propagation. One of the interesting parameters for characterization of the atmospheric turbulence is the Fried parameter or the atmospheric correlation length. We numerically investigate the feasibility of estimating the Fried parameter using a simple and low-cost system based on the stochastic parallel gradient descent (SPGD) algorithm without the need for wavefront sensing. We simulate the atmospheric turbulence using Zernike polynomials and employ a wavefront sensor-less adaptive optics system based on the SPGD algorithm and report the estimated Fried parameter after compensating for atmospheric-turbulence-induced phase distortions. Several simulations for different atmospheric turbulence strengths are presented to validate the proposed method.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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  22. A. Dubra, J. S. Massa, and C. Paterson, “Preisach classical and nonlinear modeling of hysteresis in piezoceramic deformable mirrors,” Opt. Express 13, 9062–9070 (2005).
    [CrossRef]
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    [CrossRef]
  24. Q. Yang, C. Ftaclas, M. Chun, and D. Toomey, “Hysteresis correction in the curvature adaptive optics system,” J. Opt. Soc. Am. A 22, 142–147 (2005).
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    [CrossRef]

2013 (1)

N. Anugu and J. P. Lancelot, “Study of atmospheric turbulence with Shack-Hartmann wavefront sensor,” J. Opt. 42, 128–140 (2013).
[CrossRef]

2012 (1)

H. Ma, C. Fan, P. Zhang, J. Zhang, C. Qiao, and H. Wang, “Adaptive optics correction based on stochastic parallel gradient descent technique under various atmospheric scintillation conditions: numerical simulation,” Appl. Phys. B 106, 939–944 (2012).
[CrossRef]

2011 (1)

V. Lakshminarayanan and A. Fleck, “Zernike polynomials: a guide,” J. Mod. Opt. 58, 545–561 (2011).
[CrossRef]

2010 (1)

P. Yang, X. Lei, R. Yang, M. Ao, L. Dong, and B. Xu, “Fast and stable enhancement of the far-field peak power by use of an intracavity deformable mirror,” Appl. Phys. B 100, 591–595 (2010).
[CrossRef]

2009 (1)

2005 (2)

2004 (1)

T. Weyrauch and M. A. Vorontsov, “Free-space laser communications with adaptive optics: atmospheric compensation experiments,” J. Opt. Fiber. Commun. Rep. 1, 355–379 (2004).
[CrossRef]

2001 (1)

2000 (2)

1999 (1)

V. P. Lukin and B. V. Fortes, “Phase correction of an image turbulence broading under condition of strong intensity fluctuations,” Proc. SPIE 3763, 61–72 (1999).
[CrossRef]

1997 (1)

1995 (1)

1991 (2)

A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers,” Proc. R. Soc. A 434, 9–13 (1991).
[CrossRef]

W. H. Jiang, N. Ling, X. J. Rao, and F. Shi, “Fitting capability of deformable mirror,” Proc. SPIE 1542, 130–137 (1991).
[CrossRef]

1990 (2)

B. J. Herman and L. A. Strugala, “Method for inclusion of low-frequency contributions in numerical representation of atmospheric turbulence,” Proc. SPIE 1221, 183–192 (1990).
[CrossRef]

N. A. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

1976 (1)

1974 (1)

1967 (1)

1965 (1)

1953 (1)

H. W. Babcock, “The possibility of compensating astronomical seeing,” Astron. Soc. Pac. 65, 229–236 (1953).
[CrossRef]

Andrews, L. C.

L. C. Andrews, Field Guide to Atmospheric Optics (SPIE, 2004).

Anugu, N.

N. Anugu and J. P. Lancelot, “Study of atmospheric turbulence with Shack-Hartmann wavefront sensor,” J. Opt. 42, 128–140 (2013).
[CrossRef]

Ao, M.

P. Yang, X. Lei, R. Yang, M. Ao, L. Dong, and B. Xu, “Fast and stable enhancement of the far-field peak power by use of an intracavity deformable mirror,” Appl. Phys. B 100, 591–595 (2010).
[CrossRef]

Babcock, H. W.

H. W. Babcock, “The possibility of compensating astronomical seeing,” Astron. Soc. Pac. 65, 229–236 (1953).
[CrossRef]

Barclay, H. T.

Bifano, T. G.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1986), p. 768.

Buffington, A.

Carhart, G. W.

Cauwenberghs, G.

Chun, M.

Cohen, M.

Dong, L.

P. Yang, X. Lei, R. Yang, M. Ao, L. Dong, and B. Xu, “Fast and stable enhancement of the far-field peak power by use of an intracavity deformable mirror,” Appl. Phys. B 100, 591–595 (2010).
[CrossRef]

Dubra, A.

Fan, C.

H. Ma, C. Fan, P. Zhang, J. Zhang, C. Qiao, and H. Wang, “Adaptive optics correction based on stochastic parallel gradient descent technique under various atmospheric scintillation conditions: numerical simulation,” Appl. Phys. B 106, 939–944 (2012).
[CrossRef]

Fleck, A.

V. Lakshminarayanan and A. Fleck, “Zernike polynomials: a guide,” J. Mod. Opt. 58, 545–561 (2011).
[CrossRef]

Fortes, B. V.

V. P. Lukin and B. V. Fortes, “Phase correction of an image turbulence broading under condition of strong intensity fluctuations,” Proc. SPIE 3763, 61–72 (1999).
[CrossRef]

Fraanje, R.

Fried, D. L.

Ftaclas, C.

Hammer, J. A.

Herman, B. J.

B. J. Herman and L. A. Strugala, “Method for inclusion of low-frequency contributions in numerical representation of atmospheric turbulence,” Proc. SPIE 1221, 183–192 (1990).
[CrossRef]

Herrmann, J.

Humphreys, R. A.

Janocha, H.

H. Janocha and K. Kuhnen, “Real-time compensation of hysteresis and creep in piezoelectric actuators,” Sens. Actuators A 79, 83–89 (2000).
[CrossRef]

Jiang, W. H.

W. H. Jiang, N. Ling, X. J. Rao, and F. Shi, “Fitting capability of deformable mirror,” Proc. SPIE 1542, 130–137 (1991).
[CrossRef]

Kolmogorov, A. N.

A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers,” Proc. R. Soc. A 434, 9–13 (1991).
[CrossRef]

Kuhnen, K.

H. Janocha and K. Kuhnen, “Real-time compensation of hysteresis and creep in piezoelectric actuators,” Sens. Actuators A 79, 83–89 (2000).
[CrossRef]

Lakshminarayanan, V.

V. Lakshminarayanan and A. Fleck, “Zernike polynomials: a guide,” J. Mod. Opt. 58, 545–561 (2011).
[CrossRef]

Lancelot, J. P.

N. Anugu and J. P. Lancelot, “Study of atmospheric turbulence with Shack-Hartmann wavefront sensor,” J. Opt. 42, 128–140 (2013).
[CrossRef]

Lei, X.

P. Yang, X. Lei, R. Yang, M. Ao, L. Dong, and B. Xu, “Fast and stable enhancement of the far-field peak power by use of an intracavity deformable mirror,” Appl. Phys. B 100, 591–595 (2010).
[CrossRef]

Ling, N.

W. H. Jiang, N. Ling, X. J. Rao, and F. Shi, “Fitting capability of deformable mirror,” Proc. SPIE 1542, 130–137 (1991).
[CrossRef]

Lukin, V. P.

V. P. Lukin and B. V. Fortes, “Phase correction of an image turbulence broading under condition of strong intensity fluctuations,” Proc. SPIE 3763, 61–72 (1999).
[CrossRef]

Ma, H.

H. Ma, C. Fan, P. Zhang, J. Zhang, C. Qiao, and H. Wang, “Adaptive optics correction based on stochastic parallel gradient descent technique under various atmospheric scintillation conditions: numerical simulation,” Appl. Phys. B 106, 939–944 (2012).
[CrossRef]

Massa, J. S.

McGlamery, B. L.

Muller, R. A.

Noll, R.

Paterson, C.

Price, T. R.

Primmerman, C. A.

Qiao, C.

H. Ma, C. Fan, P. Zhang, J. Zhang, C. Qiao, and H. Wang, “Adaptive optics correction based on stochastic parallel gradient descent technique under various atmospheric scintillation conditions: numerical simulation,” Appl. Phys. B 106, 939–944 (2012).
[CrossRef]

Rao, X. J.

W. H. Jiang, N. Ling, X. J. Rao, and F. Shi, “Fitting capability of deformable mirror,” Proc. SPIE 1542, 130–137 (1991).
[CrossRef]

Ricklin, J. C.

Roddier, N. A.

N. A. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

Schitter, G.

Shi, F.

W. H. Jiang, N. Ling, X. J. Rao, and F. Shi, “Fitting capability of deformable mirror,” Proc. SPIE 1542, 130–137 (1991).
[CrossRef]

Song, H.

Strugala, L. A.

B. J. Herman and L. A. Strugala, “Method for inclusion of low-frequency contributions in numerical representation of atmospheric turbulence,” Proc. SPIE 1221, 183–192 (1990).
[CrossRef]

Toomey, D.

Vdovin, G.

Verhaegen, M.

Vorontsov, M. A.

Wang, H.

H. Ma, C. Fan, P. Zhang, J. Zhang, C. Qiao, and H. Wang, “Adaptive optics correction based on stochastic parallel gradient descent technique under various atmospheric scintillation conditions: numerical simulation,” Appl. Phys. B 106, 939–944 (2012).
[CrossRef]

Weyrauch, T.

T. Weyrauch and M. A. Vorontsov, “Free-space laser communications with adaptive optics: atmospheric compensation experiments,” J. Opt. Fiber. Commun. Rep. 1, 355–379 (2004).
[CrossRef]

T. Weyrauch, M. A. Vorontsov, T. G. Bifano, J. A. Hammer, M. Cohen, and G. Cauwenberghs, “Microscale adaptive optics: wave-front control with a μ-mirror array and a VLSI stochastic gradient descent controller,” Appl. Opt. 40, 4243–4253 (2001).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1986), p. 768.

Xu, B.

P. Yang, X. Lei, R. Yang, M. Ao, L. Dong, and B. Xu, “Fast and stable enhancement of the far-field peak power by use of an intracavity deformable mirror,” Appl. Phys. B 100, 591–595 (2010).
[CrossRef]

Yang, P.

P. Yang, X. Lei, R. Yang, M. Ao, L. Dong, and B. Xu, “Fast and stable enhancement of the far-field peak power by use of an intracavity deformable mirror,” Appl. Phys. B 100, 591–595 (2010).
[CrossRef]

Yang, Q.

Yang, R.

P. Yang, X. Lei, R. Yang, M. Ao, L. Dong, and B. Xu, “Fast and stable enhancement of the far-field peak power by use of an intracavity deformable mirror,” Appl. Phys. B 100, 591–595 (2010).
[CrossRef]

Zhang, J.

H. Ma, C. Fan, P. Zhang, J. Zhang, C. Qiao, and H. Wang, “Adaptive optics correction based on stochastic parallel gradient descent technique under various atmospheric scintillation conditions: numerical simulation,” Appl. Phys. B 106, 939–944 (2012).
[CrossRef]

Zhang, P.

H. Ma, C. Fan, P. Zhang, J. Zhang, C. Qiao, and H. Wang, “Adaptive optics correction based on stochastic parallel gradient descent technique under various atmospheric scintillation conditions: numerical simulation,” Appl. Phys. B 106, 939–944 (2012).
[CrossRef]

Zollars, B. G.

Appl. Opt. (2)

Appl. Phys. B (2)

H. Ma, C. Fan, P. Zhang, J. Zhang, C. Qiao, and H. Wang, “Adaptive optics correction based on stochastic parallel gradient descent technique under various atmospheric scintillation conditions: numerical simulation,” Appl. Phys. B 106, 939–944 (2012).
[CrossRef]

P. Yang, X. Lei, R. Yang, M. Ao, L. Dong, and B. Xu, “Fast and stable enhancement of the far-field peak power by use of an intracavity deformable mirror,” Appl. Phys. B 100, 591–595 (2010).
[CrossRef]

Astron. Soc. Pac. (1)

H. W. Babcock, “The possibility of compensating astronomical seeing,” Astron. Soc. Pac. 65, 229–236 (1953).
[CrossRef]

J. Mod. Opt. (1)

V. Lakshminarayanan and A. Fleck, “Zernike polynomials: a guide,” J. Mod. Opt. 58, 545–561 (2011).
[CrossRef]

J. Opt. (1)

N. Anugu and J. P. Lancelot, “Study of atmospheric turbulence with Shack-Hartmann wavefront sensor,” J. Opt. 42, 128–140 (2013).
[CrossRef]

J. Opt. Fiber. Commun. Rep. (1)

T. Weyrauch and M. A. Vorontsov, “Free-space laser communications with adaptive optics: atmospheric compensation experiments,” J. Opt. Fiber. Commun. Rep. 1, 355–379 (2004).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (2)

Opt. Eng. (1)

N. A. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Proc. R. Soc. A (1)

A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers,” Proc. R. Soc. A 434, 9–13 (1991).
[CrossRef]

Proc. SPIE (3)

B. J. Herman and L. A. Strugala, “Method for inclusion of low-frequency contributions in numerical representation of atmospheric turbulence,” Proc. SPIE 1221, 183–192 (1990).
[CrossRef]

V. P. Lukin and B. V. Fortes, “Phase correction of an image turbulence broading under condition of strong intensity fluctuations,” Proc. SPIE 3763, 61–72 (1999).
[CrossRef]

W. H. Jiang, N. Ling, X. J. Rao, and F. Shi, “Fitting capability of deformable mirror,” Proc. SPIE 1542, 130–137 (1991).
[CrossRef]

Sens. Actuators A (1)

H. Janocha and K. Kuhnen, “Real-time compensation of hysteresis and creep in piezoelectric actuators,” Sens. Actuators A 79, 83–89 (2000).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics (Pergamon, 1986), p. 768.

L. C. Andrews, Field Guide to Atmospheric Optics (SPIE, 2004).

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Figures (7)

Fig. 1.
Fig. 1.

Comparison of the averaged phase structure function computed using Zernike polynomials and Kolmogorov model for D/r0=10.

Fig. 2.
Fig. 2.

Simulated phase screens using Zernike polynomials for different D/r0 ratios.

Fig. 3.
Fig. 3.

Far-field intensity patterns of a light beam propagating through phase screens with different D/r0 ratios.

Fig. 4.
Fig. 4.

Schematic diagram of wavefront sensor-less AO system.

Fig. 5.
Fig. 5.

Actuator configuration of 61-element DM.

Fig. 6.
Fig. 6.

Zernike coefficients of a phase screen with the given D/r0 ratio and Zernike coefficients of the phase correction by the DM.

Fig. 7.
Fig. 7.

Reconstructed Fried parameter (in millimeter) for different Zernike modes.

Tables (1)

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Table 1. Simulation Results

Equations (7)

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Dϕ(r⃗)=[ϕ(r⃗1)ϕ(r⃗2)]2,
Dϕ(r⃗)=6.88(|r⃗|r0)5/3,
ϕ(r,θ)=iaiZi(r,θ).
ai2=Ni(Dr0)5/3
Ni=0.15337(1)nm(n+1)Γ(14/3)Γ(n5/6)Γ(17/6)2Γ(n+23/6),
φ(x,y)=j=1N=61ujVj(x,y),
Vj(x,y)=exp[ln(ω)((xxj)2+(yyj)2/d)α],

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