Abstract

A laboratory demonstration of an adaptive optics system using a point-diffraction interferometer and a continuous MEMs mirror is presented. The dynamic performance of the system was investigated experimentally using a holographic optical aberration generator. The system was tested both in conditions corresponding to weak phase only aberrations and for horizontal propagation through uniform turbulence giving scintillation and optical vortices. The system was shown to work well in weak turbulence and gave correction for the strong turbulence regime up to the highest scintillation strength tested, σ R 2 = 3.3.

© 2007 Optical Society of America

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  2. M. C. Roggemann and B. Welsh, Imaging through turbulence (CRC Press, 1996).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. B. M. Levine, E. A. Martinsen, A. Wirth, A. Jankevics, M. Toledo-Quinones, F. Landers, and T. L. Bruno, "Horizontal line-of-sight turbulence over near-ground paths and implications for adaptive optics corrections in laser communications," Appl. Opt. 37, 4553-4560 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  21. M. Langlois, R. Angel, M. Lloyd-Hart, F. Wildi, G. Love, and A. Naumov, "High Order, Reconstructor-Free Adaptive Optics For 6-8 meter class Telescopes," in Venice 2001: Beyond Conventional Adaptive Optics (2001).
  22. G. D. Love, T. J. D. Oag, and A. K. Kirby, "Common path interferometric wavefront sensor for extreme adaptive optics," Opt. Express 13, 3491-3499 (2005).
    [CrossRef] [PubMed]
  23. J. Notaras and C. Paterson, "Point-diffraction interferometer for atmospheric adaptive optics in strong scintillation," Opt. Commun.(accepted2007).
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    [CrossRef]
  26. W. H. Lee, "Computer-generated holograms; techniques and applications," in Prog. Opt., E. Wolf, ed., vol. XVI, pp. 121-232 (North-Holland, Amsterdam, 1978).
  27. K. Creath, "Phase-measurement interferometry techniques," in Prog. Opt., E.Wolf, ed., vol. XXVI, pp. 350-393 (North-Holland, Amsterdam, 1988).
  28. T. G. Bifano, J. Perreault, R. Krishnamoorthy, and M. N. Horenstein, "Microelectromechanical Deformable mirrors," IEEE J. Sel. Top. Quantum Electron. 5, 83-89 (1999).
    [CrossRef]
  29. C. Paterson, I. Munro, and J. C. Dainty, "A low cost adaptive optics system using a membrane mirror," Opt. Express 6, 175-185 (2000).
    [CrossRef] [PubMed]
  30. A. Glindemann, R. G. Lane, and J. C. Dainty, "Simulation of time-evolving speckle patterns using Kolmogorov statistics," J. Mod. Opt. 40, 2381-2388 (1993).
    [CrossRef]
  31. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

2007

J. Notaras and C. Paterson, "Point-diffraction interferometer for atmospheric adaptive optics in strong scintillation," Opt. Commun.(accepted2007).

2005

2004

2003

2002

2001

2000

1999

T. G. Bifano, J. Perreault, R. Krishnamoorthy, and M. N. Horenstein, "Microelectromechanical Deformable mirrors," IEEE J. Sel. Top. Quantum Electron. 5, 83-89 (1999).
[CrossRef]

1998

1997

M. C. Roggemann, B. M. Welsh, and R. Q. Fugate, "Improving the resolution of ground-based telescopes," Rev. Mod. Phys. 69, 437-505 (1997).
[CrossRef]

1996

1995

1994

1993

A. Glindemann, R. G. Lane, and J. C. Dainty, "Simulation of time-evolving speckle patterns using Kolmogorov statistics," J. Mod. Opt. 40, 2381-2388 (1993).
[CrossRef]

1992

1975

R. N. Smartt and W. H. Steel, "Theory and application of point-diffraction interferometers," Jpn. J. Appl. Phys. 14, 351-356 (1975).

Azucena, O.

Baker, K. L.

Barchers, J. D.

Barclay, H. T.

Beresnev, L. A.

Bifano, T. G.

T. G. Bifano, J. Perreault, R. Krishnamoorthy, and M. N. Horenstein, "Microelectromechanical Deformable mirrors," IEEE J. Sel. Top. Quantum Electron. 5, 83-89 (1999).
[CrossRef]

Birch, P. M.

Booth, M. J.

Bruno, T. L.

Carhart, G. W.

Crawford, J.

Creath, K.

Dainty, J. C.

C. Paterson, I. Munro, and J. C. Dainty, "A low cost adaptive optics system using a membrane mirror," Opt. Express 6, 175-185 (2000).
[CrossRef] [PubMed]

A. Glindemann, R. G. Lane, and J. C. Dainty, "Simulation of time-evolving speckle patterns using Kolmogorov statistics," J. Mod. Opt. 40, 2381-2388 (1993).
[CrossRef]

Dimotakis, P. E.

Dunsby, C.

Flath, L.M.

French, P. M. W.

Fried, D. L.

Fugate, R. Q.

M. C. Roggemann, B. M. Welsh, and R. Q. Fugate, "Improving the resolution of ground-based telescopes," Rev. Mod. Phys. 69, 437-505 (1997).
[CrossRef]

Gavel, D.

Glindemann, A.

A. Glindemann, R. G. Lane, and J. C. Dainty, "Simulation of time-evolving speckle patterns using Kolmogorov statistics," J. Mod. Opt. 40, 2381-2388 (1993).
[CrossRef]

Gourlay, J.

Gu, Y.

Herrmann, J.

Horenstein, M. N.

T. G. Bifano, J. Perreault, R. Krishnamoorthy, and M. N. Horenstein, "Microelectromechanical Deformable mirrors," IEEE J. Sel. Top. Quantum Electron. 5, 83-89 (1999).
[CrossRef]

Humphreys, R. A.

Jankevics, A.

Justh, E. W.

Kartz, M.W.

Kern, B.

Kirby, A. K.

Krishnamoorthy, R.

T. G. Bifano, J. Perreault, R. Krishnamoorthy, and M. N. Horenstein, "Microelectromechanical Deformable mirrors," IEEE J. Sel. Top. Quantum Electron. 5, 83-89 (1999).
[CrossRef]

Krishnaprasad, P. S.

Kruelevitch, P.

Landers, F.

Lane, R. G.

A. Glindemann, R. G. Lane, and J. C. Dainty, "Simulation of time-evolving speckle patterns using Kolmogorov statistics," J. Mod. Opt. 40, 2381-2388 (1993).
[CrossRef]

Lang, D. B.

Levine, B. M.

Link, D. J.

J. D. Barchers, D. L. Fried, and D. J. Link, "Evaluation of the performance of a shearing interferometer in strong scintillation in the absence of additive measurement noise," Appl. Opt. 41, 3647-3684 (2002).
[CrossRef]

J. D. Barchers, D. L. Fried, and D. J. Link, "Evaluation of the performance of Hartmann sensors in strong scintillation," Appl. Opt. 41, 1012-1021 (2002).
[CrossRef] [PubMed]

Love, G. D.

Martin, C.

Martinsen, E. A.

Mercer, C. R.

Munro, I.

Neil, M. A. A.

Notaras, J.

J. Notaras and C. Paterson, "Point-diffraction interferometer for atmospheric adaptive optics in strong scintillation," Opt. Commun.(accepted2007).

Oag, T. J. D.

Olivier, S. S.

Olsen, J.

Paterson, C.

J. Notaras and C. Paterson, "Point-diffraction interferometer for atmospheric adaptive optics in strong scintillation," Opt. Commun.(accepted2007).

C. Paterson, I. Munro, and J. C. Dainty, "A low cost adaptive optics system using a membrane mirror," Opt. Express 6, 175-185 (2000).
[CrossRef] [PubMed]

Perreault, J.

T. G. Bifano, J. Perreault, R. Krishnamoorthy, and M. N. Horenstein, "Microelectromechanical Deformable mirrors," IEEE J. Sel. Top. Quantum Electron. 5, 83-89 (1999).
[CrossRef]

Price, T. R.

Primmerman, C. A.

Purvis, A.

Rhoadarmer, T. A.

Roggemann, M. C.

M. C. Roggemann, B. M. Welsh, and R. Q. Fugate, "Improving the resolution of ground-based telescopes," Rev. Mod. Phys. 69, 437-505 (1997).
[CrossRef]

Silva, D. A.

Smartt, R. N.

R. N. Smartt and W. H. Steel, "Theory and application of point-diffraction interferometers," Jpn. J. Appl. Phys. 14, 351-356 (1975).

Stappaerts, E. A.

Steel, W. H.

R. N. Smartt and W. H. Steel, "Theory and application of point-diffraction interferometers," Jpn. J. Appl. Phys. 14, 351-356 (1975).

Thessin, R. N.

Toledo-Quinones, M.

Tucker, J.

Vaughn, J. L.

Vorontsov, M. A.

Welsh, B. M.

M. C. Roggemann, B. M. Welsh, and R. Q. Fugate, "Improving the resolution of ground-based telescopes," Rev. Mod. Phys. 69, 437-505 (1997).
[CrossRef]

Wilks, S. C.

Wilson, T.

Wirth, A.

Young, P. E.

Zollars, B. G.

Appl. Opt.

D. L. Fried and J. L. Vaughn, "Branch cuts in the phase function," Appl. Opt. 31, 2865-2882 (1992).
[CrossRef] [PubMed]

C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, and J. Herrmann, "Atmosphericcompensation experiments in strong-scintillation conditions," Appl. Opt. 34, 2081-2088 (1995).
[CrossRef] [PubMed]

B. M. Levine, E. A. Martinsen, A. Wirth, A. Jankevics, M. Toledo-Quinones, F. Landers, and T. L. Bruno, "Horizontal line-of-sight turbulence over near-ground paths and implications for adaptive optics corrections in laser communications," Appl. Opt. 37, 4553-4560 (1998).
[CrossRef]

J. D. Barchers and T. A. Rhoadarmer, "Evaluation of phase-shifting approaches for a point-diffraction interferometer with the mutual coherence function," Appl. Opt. 41, 7499-7509 (2002).
[CrossRef]

J. D. Barchers, D. L. Fried, and D. J. Link, "Evaluation of the performance of a shearing interferometer in strong scintillation in the absence of additive measurement noise," Appl. Opt. 41, 3647-3684 (2002).
[CrossRef]

J. D. Barchers, D. L. Fried, and D. J. Link, "Evaluation of the performance of Hartmann sensors in strong scintillation," Appl. Opt. 41, 1012-1021 (2002).
[CrossRef] [PubMed]

B. Kern, P. E. Dimotakis, C. Martin, D. B. Lang, and R. N. Thessin, "Imaging through turbulence with a quadrature-phase optical interferometer," Appl. Opt. 44, 7424-7438 (2005).
[CrossRef] [PubMed]

C. R. Mercer and K. Creath, "Liquid-crystal point-diffraction interferometer for wavefront measurements," Appl. Opt. 35, 1633-1642 (1996).
[CrossRef] [PubMed]

P. M. Birch, J. Gourlay, G. D. Love, and A. Purvis, "Real-time optical aberration correction with a ferroelectric liquid-crystal spatial light modulator," Appl. Opt. 37, 2164-2169 (1998).
[CrossRef]

Automatica

E. W. Justh, P. S. Krishnaprasad, and M. A. Vorontsov, "Analysis of a high-resolution optical wave-front control system," Automatica 40, 1129-1141 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

T. G. Bifano, J. Perreault, R. Krishnamoorthy, and M. N. Horenstein, "Microelectromechanical Deformable mirrors," IEEE J. Sel. Top. Quantum Electron. 5, 83-89 (1999).
[CrossRef]

J. Mod. Opt.

A. Glindemann, R. G. Lane, and J. C. Dainty, "Simulation of time-evolving speckle patterns using Kolmogorov statistics," J. Mod. Opt. 40, 2381-2388 (1993).
[CrossRef]

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

R. N. Smartt and W. H. Steel, "Theory and application of point-diffraction interferometers," Jpn. J. Appl. Phys. 14, 351-356 (1975).

Opt. Commun.

J. Notaras and C. Paterson, "Point-diffraction interferometer for atmospheric adaptive optics in strong scintillation," Opt. Commun.(accepted2007).

Opt. Express

Opt. Lett.

Rev. Mod. Phys.

M. C. Roggemann, B. M. Welsh, and R. Q. Fugate, "Improving the resolution of ground-based telescopes," Rev. Mod. Phys. 69, 437-505 (1997).
[CrossRef]

Other

W. H. Lee, "Computer-generated holograms; techniques and applications," in Prog. Opt., E. Wolf, ed., vol. XVI, pp. 121-232 (North-Holland, Amsterdam, 1978).

K. Creath, "Phase-measurement interferometry techniques," in Prog. Opt., E.Wolf, ed., vol. XXVI, pp. 350-393 (North-Holland, Amsterdam, 1988).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

M. C. Roggemann and B. Welsh, Imaging through turbulence (CRC Press, 1996).

J.W. Hardy, Adaptive Optics for Astronomical Telescopes, Oxford series in optical and imaging sciences, 1st ed., (Oxford University Press, 1998).

M. Langlois, R. Angel, M. Lloyd-Hart, F. Wildi, G. Love, and A. Naumov, "High Order, Reconstructor-Free Adaptive Optics For 6-8 meter class Telescopes," in Venice 2001: Beyond Conventional Adaptive Optics (2001).

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Figures (16)

Fig. 1.
Fig. 1.

Optical layout of the closed-loop AO system. Key: L1-15, lenses; PBS, polarizing beam-splitters; BS, non-polarizing beam-splitters; M1-8, mirrors and QW1-3, quarter-wave plates. The line colours in the quadrature PDI depict polarization (oe-15-21-13745-i001 and oe-15-21-13745-i002 are orthogonal linear polarizations).

Fig. 2.
Fig. 2.

Plots of the response of the wavefront sensor signal channels to the corresponding actuators.

Fig. 3.
Fig. 3.

Control wrapping schemes. Left, method 1; signals wrapped between -π and π. Right, method 2; using full stroke and wrapping by 2 where n = 1, or 2, or 3,...

Fig. 4.
Fig. 4.

Illustration of two possible mirror solutions to a plane wave, (a) and (b). oe-15-21-13745-i003 are the WFS sampling points.

Fig. 5.
Fig. 5.

On-axis intensity v. time for the AO system using wrapping schemes 1 and 2 (-π to π, and full stroke ±2π) for MEMs mirror on a static aberration (D/r 0 = 6). τ 0/τS = 1/10, and gain= 0.5.

Fig. 6.
Fig. 6.

Far-field image of point-source with AO on and off for two different turbulence strengths, D/r 0 = 6, and D/r 0 = 10, τ 0/τS = 1/10, and gain= 0.5 (average of 100 short exposures).

Fig. 7.
Fig. 7.

Plots of on-axis intensity v. time for uniform intensity aberrations with AO on and off. Plots: (a) D/r 0 = 6 and (b) D/r 0 = 10. For all plots τ 0/τS = 1/16, and gain= 0.5. Note the traces are not synchronized.

Fig. 8.
Fig. 8.

Strehl v. D/r 0 for AO on and off in the weak (phase-only) regime (τ 0/τS = 1/16, and gain= 0.5).

Fig. 9.
Fig. 9.

Strehl v. τ 0/τS . Plot (a) D/r 0 = 6, and plot (b) D/r 0 = 10 (gain= 0.5).

Fig. 10.
Fig. 10.

Phase and intensity distributions for an example wave, with σ R 2 = 3.3. The circle indicates the aperture size (4Lf ).

Fig. 11.
Fig. 11.

Far-field image of point-source with AO on and off for 2 different aperture sizes (D = 3Lf , and 4Lf ), with σ R 2 = 1.5, τ 0/τS = 1/24, and gain= 0.5 (average of 100 short exposures).

Fig. 12.
Fig. 12.

Example of reconstructed residual phase and corresponding phase distribution from closed-loop AO system (D = 3Lf , and σ R 2 = 2.7).

Fig. 13.
Fig. 13.

Strehl v. time for D = 3Lf (τ 0/τS = 1/24, and gain= 0.5). Note the traces are not synchronized.

Fig. 14.
Fig. 14.

Strehl v. time for D = 4Lf (τ 0/τS = 1/24, and gain= 0.5). Note the traces are not synchronized.

Fig. 15.
Fig. 15.

Strehl v. σ R 2(τ 0/τS = 1/24, and gain= 0.5).

Fig. 16.
Fig. 16.

Strehl v. τ 0/τS (gain= 0.5).

Equations (6)

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

tan [ δ ϕ x y ] = I 3 π / 2 x y I π / 2 x y I 0 x y I π x y ,
x = Cs .
C m n = 1 / g m n , m = n C m n = 0 , m n
x n = x n 1 + α x ,
σ R 2 = 1.24 k 7 / 6 C n 2 L 11 / 6 ,
r 0 = ( 0.423 k 2 C n 2 L ) 3 / 5 ,

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