Abstract

This paper compares two control methods to predict and correct aero-optical wavefronts derived from recent flight-test data. The first is an optimal linear time-invariant controller constructed from an identified state-space model of the turbulence flow. The second control method is an adaptive controller based on a recursive least-squares lattice filter. The performance of these control schemes versus classical integrator methods is investigated in an adaptive optics experiment that reproduces the aberrations from in-flight measurements of aero-optical turbulence. Experimental results show the improvement in wavefront correction achieved by both prediction methods. Altering the flow characteristics of the disturbance wavefront during the control process illustrates the ability of the adaptive controller to track changes in the aberration statistics.

© 2012 Optical Society of America

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  1. B. L. Ellerbroek and T. A. Rhoadarmer, “Real-time adaptive optimization of wavefront reconstruction algorithms for closed-loop adaptive optical systems,” Proc. SPIE 3353, 1174–1185 (1998).
    [CrossRef]
  2. J. S. Gibson, C. C. Chang, and B. L. Ellerbroek, “Adaptive optics: wave-front correction by use of adaptive filtering and control,” Appl. Opt. 39, 2525–2538 (2000).
    [CrossRef]
  3. T. A. Rhoadarmer, L. M. Klein, J. S. Gibson, N. Chen, and Y.-T. Liu, “Adaptive control and filtering for closed-loop adaptive-optical wavefront reconstruction,” Proc. SPIE 6306, 63060E (2006).
    [CrossRef]
  4. Y. T. Liu and J. S. Gibson, “Adaptive control in adaptive optics for directed-energy systems,” Opt. Eng. 46, 046601 (2007).
    [CrossRef]
  5. S. Monirabbasi and J. S. Gibson, “Adaptive control in an adaptive optics experiment,” J. Opt. Soc. Am. A 27, A84–A96 (2010).
    [CrossRef]
  6. C. M. S. Corley, M. Nagashima, and B. N. Agrawal, “Beam control and a new laboratory testbed for adaptive optics in a maritime environment,” in Proceedings of 2010 IEEE Aerospace Conference (IEEE, 2010), pp. 1–13.
  7. C. M. S. Corley, “Maritime adaptive optics beam control,” Ph.D. thesis (Naval Post Graduate School, 2010).
  8. C. Petit, J.-M. Conan, C. Kulcsar, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla, and D. Rabaud, “Off-axis adaptive optics with optimal control: experimental and numerical validation,” Proc. SPIE 5903, 59030P (2005).
    [CrossRef]
  9. C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and P. Viaris de Lesegno, “Optimal control, observers and integrators in adaptive optics,” Opt. Express 14, 7464–7476 (2006).
    [CrossRef]
  10. K. Hinnen, M. Verhaegen, and N. Doelman, “Exploiting the spatiotemporal correlation in adaptive optics using data-driven H2 optimal control,” J. Opt. Soc. Am. A 24, 1714–1725 (2007).
    [CrossRef]
  11. K. Hinnen, M. Verhaegen, and N. Doelman, “A data-driven H2 optimal control approach for adaptive optics,” IEEE Trans. Control Syst. Technol. 16, 381–395 (2008).
    [CrossRef]
  12. C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “Linear quadratic Gaussian control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis,” J. Opt. Soc. Am. A 26, 1307–1325 (2009).
    [CrossRef]
  13. J. Tesch, J. S. Gibson, S. Gordeyev, and E. Jumper, “Identification, prediction and control of aero optical wavefronts in laser beam propagation,” in 42nd AIAA Plasmadynamics and Lasers Conference (AIAA, 2011), paper 2011-3276.
  14. J. Tesch and J. S. Gibson, “Optimal and adaptive correction of aero-optical wavefronts in an adaptive optics experiment,” Proc. SPIE 8165, 816502 (2011).
    [CrossRef]
  15. J. Tesch, “High-performance control and prediction for adaptive optics,” Ph.D. thesis (University of California, Los Angeles, 2011).
  16. C. Porter, S. Gordeyev, M. Zenk, and E. Jumper, “Flight measurements of aero-optical distortions from a flat-windowed turret on the Airborne Aero-Optics Laboratory (AAOL),” in 42nd AIAA Plasmadynamics and Lasers Conference (AIAA, 2011), paper 2011-3280.
  17. R. Fraanje, J. Rice, M. Verhaegen, and N. Doelman, “Fast reconstruction and prediction of frozen flow turbulence based on structured Kalman filtering,” J. Opt. Soc. Am. A 27, A235–A245 (2010).
    [CrossRef]
  18. A. Beghi, A. Cenedese, and A. Masiero, “A Markov-random-field-based approach to modeling and prediction of atmospheric turbulence,” in 16th Mediterranean Conference on Control and Automation (MCA, 2008), pp. 1735–1740.
  19. A. Beghi, A. Cenedese, and A. Masiero, “Stochastic realization approach to the efficient simulation of phase screens,” J. Opt. Soc. Am. A 25, 515–525 (2008).
    [CrossRef]
  20. A. Beghi, A. Cenedese, and A. Masiero, “Multiscale stochastic approach for phase screens synthesis,” Appl. Opt. 50, 4124–4133 (2011).
    [CrossRef]
  21. P. K. Orzechowski, N. Chen, J. S. Gibson, and T. C. Tsao, “Optimal suppression of laser beam jitter by high-order RLS adaptive control,” IEEE Trans. Control Syst. Technol. 16, 255–267 (2008).
    [CrossRef]
  22. S. Gordeyev and E. Jumper, “Fluid dynamics and aero-optics of turrets,” Prog. Aerosp. Sci. 46, 388–400 (2010).
    [CrossRef]
  23. S. Gordeyev, J. A. Cress, E. Jumper, and A. B. Cain, “Aero-optical environment around a cylindrical turret with a flat window,” AIAA J. 49, 308–315 (2011).
    [CrossRef]
  24. M. Weng, A. Mani, and S. Gordeyev, “Physics and computation of aero-optics,” Annu. Rev. Fluid Mech. 44, 299–321 (2012).
    [CrossRef]
  25. N. Y. Chen and J. S. Gibson, “Subspace system identification using a multichannel lattice filter,” in Proceedings of the 2004 American Control Conference (IEEE, 2004), Vol. 1, pp. 855–860.
  26. P. Van Overschee and B. De Moor, Subspace Identification for Linear Systems (Kluwer Academic, 1996).
  27. T. Katayama, Subspace Methods for System Identification (Springer-Verlag, 2005).
  28. M. Verhaegen and V. Verdult, Filtering and System Identification, a Least Squares Approach (Cambridge University, 2007).
  29. S. B. Jiang and J. S. Gibson, “An unwindowed multichannel lattice filter with orthogonal channels,” IEEE Trans. Signal Process. 43, 2831–2842 (1995).
    [CrossRef]
  30. B. Widrow and E. Walsh, Adaptive Inverse Control (Prentice Hall, 1996).
  31. N. O. Arancibia, S. Perez Gibson, and T.-C. Tsao, “Frequency-weighted minimum-variance adaptive control of laser beam jitter,” IEEE/ASME Trans. Mechatron. 14, 337–348 (2009).
    [CrossRef]
  32. A. H. Sayed, Fundamentals of Adaptive Filtering (Wiley, 2003).
  33. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980).
    [CrossRef]
  34. J. D. Mansell and B. Henderson, “Temporal and spatial characterization of polymer membrane deformable mirrors,” Proc. SPIE 7466, 74660D (2009).
    [CrossRef]

2012 (1)

M. Weng, A. Mani, and S. Gordeyev, “Physics and computation of aero-optics,” Annu. Rev. Fluid Mech. 44, 299–321 (2012).
[CrossRef]

2011 (3)

J. Tesch and J. S. Gibson, “Optimal and adaptive correction of aero-optical wavefronts in an adaptive optics experiment,” Proc. SPIE 8165, 816502 (2011).
[CrossRef]

A. Beghi, A. Cenedese, and A. Masiero, “Multiscale stochastic approach for phase screens synthesis,” Appl. Opt. 50, 4124–4133 (2011).
[CrossRef]

S. Gordeyev, J. A. Cress, E. Jumper, and A. B. Cain, “Aero-optical environment around a cylindrical turret with a flat window,” AIAA J. 49, 308–315 (2011).
[CrossRef]

2010 (3)

2009 (3)

C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “Linear quadratic Gaussian control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis,” J. Opt. Soc. Am. A 26, 1307–1325 (2009).
[CrossRef]

N. O. Arancibia, S. Perez Gibson, and T.-C. Tsao, “Frequency-weighted minimum-variance adaptive control of laser beam jitter,” IEEE/ASME Trans. Mechatron. 14, 337–348 (2009).
[CrossRef]

J. D. Mansell and B. Henderson, “Temporal and spatial characterization of polymer membrane deformable mirrors,” Proc. SPIE 7466, 74660D (2009).
[CrossRef]

2008 (3)

K. Hinnen, M. Verhaegen, and N. Doelman, “A data-driven H2 optimal control approach for adaptive optics,” IEEE Trans. Control Syst. Technol. 16, 381–395 (2008).
[CrossRef]

A. Beghi, A. Cenedese, and A. Masiero, “Stochastic realization approach to the efficient simulation of phase screens,” J. Opt. Soc. Am. A 25, 515–525 (2008).
[CrossRef]

P. K. Orzechowski, N. Chen, J. S. Gibson, and T. C. Tsao, “Optimal suppression of laser beam jitter by high-order RLS adaptive control,” IEEE Trans. Control Syst. Technol. 16, 255–267 (2008).
[CrossRef]

2007 (2)

2006 (2)

T. A. Rhoadarmer, L. M. Klein, J. S. Gibson, N. Chen, and Y.-T. Liu, “Adaptive control and filtering for closed-loop adaptive-optical wavefront reconstruction,” Proc. SPIE 6306, 63060E (2006).
[CrossRef]

C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and P. Viaris de Lesegno, “Optimal control, observers and integrators in adaptive optics,” Opt. Express 14, 7464–7476 (2006).
[CrossRef]

2005 (1)

C. Petit, J.-M. Conan, C. Kulcsar, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla, and D. Rabaud, “Off-axis adaptive optics with optimal control: experimental and numerical validation,” Proc. SPIE 5903, 59030P (2005).
[CrossRef]

2000 (1)

1998 (1)

B. L. Ellerbroek and T. A. Rhoadarmer, “Real-time adaptive optimization of wavefront reconstruction algorithms for closed-loop adaptive optical systems,” Proc. SPIE 3353, 1174–1185 (1998).
[CrossRef]

1995 (1)

S. B. Jiang and J. S. Gibson, “An unwindowed multichannel lattice filter with orthogonal channels,” IEEE Trans. Signal Process. 43, 2831–2842 (1995).
[CrossRef]

1980 (1)

Agrawal, B. N.

C. M. S. Corley, M. Nagashima, and B. N. Agrawal, “Beam control and a new laboratory testbed for adaptive optics in a maritime environment,” in Proceedings of 2010 IEEE Aerospace Conference (IEEE, 2010), pp. 1–13.

Arancibia, N. O.

N. O. Arancibia, S. Perez Gibson, and T.-C. Tsao, “Frequency-weighted minimum-variance adaptive control of laser beam jitter,” IEEE/ASME Trans. Mechatron. 14, 337–348 (2009).
[CrossRef]

Beghi, A.

A. Beghi, A. Cenedese, and A. Masiero, “Multiscale stochastic approach for phase screens synthesis,” Appl. Opt. 50, 4124–4133 (2011).
[CrossRef]

A. Beghi, A. Cenedese, and A. Masiero, “Stochastic realization approach to the efficient simulation of phase screens,” J. Opt. Soc. Am. A 25, 515–525 (2008).
[CrossRef]

A. Beghi, A. Cenedese, and A. Masiero, “A Markov-random-field-based approach to modeling and prediction of atmospheric turbulence,” in 16th Mediterranean Conference on Control and Automation (MCA, 2008), pp. 1735–1740.

Cain, A. B.

S. Gordeyev, J. A. Cress, E. Jumper, and A. B. Cain, “Aero-optical environment around a cylindrical turret with a flat window,” AIAA J. 49, 308–315 (2011).
[CrossRef]

Cenedese, A.

A. Beghi, A. Cenedese, and A. Masiero, “Multiscale stochastic approach for phase screens synthesis,” Appl. Opt. 50, 4124–4133 (2011).
[CrossRef]

A. Beghi, A. Cenedese, and A. Masiero, “Stochastic realization approach to the efficient simulation of phase screens,” J. Opt. Soc. Am. A 25, 515–525 (2008).
[CrossRef]

A. Beghi, A. Cenedese, and A. Masiero, “A Markov-random-field-based approach to modeling and prediction of atmospheric turbulence,” in 16th Mediterranean Conference on Control and Automation (MCA, 2008), pp. 1735–1740.

Chang, C. C.

Chemla, F.

C. Petit, J.-M. Conan, C. Kulcsar, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla, and D. Rabaud, “Off-axis adaptive optics with optimal control: experimental and numerical validation,” Proc. SPIE 5903, 59030P (2005).
[CrossRef]

Chen, N.

P. K. Orzechowski, N. Chen, J. S. Gibson, and T. C. Tsao, “Optimal suppression of laser beam jitter by high-order RLS adaptive control,” IEEE Trans. Control Syst. Technol. 16, 255–267 (2008).
[CrossRef]

T. A. Rhoadarmer, L. M. Klein, J. S. Gibson, N. Chen, and Y.-T. Liu, “Adaptive control and filtering for closed-loop adaptive-optical wavefront reconstruction,” Proc. SPIE 6306, 63060E (2006).
[CrossRef]

Chen, N. Y.

N. Y. Chen and J. S. Gibson, “Subspace system identification using a multichannel lattice filter,” in Proceedings of the 2004 American Control Conference (IEEE, 2004), Vol. 1, pp. 855–860.

Conan, J.-M.

Corley, C. M. S.

C. M. S. Corley, “Maritime adaptive optics beam control,” Ph.D. thesis (Naval Post Graduate School, 2010).

C. M. S. Corley, M. Nagashima, and B. N. Agrawal, “Beam control and a new laboratory testbed for adaptive optics in a maritime environment,” in Proceedings of 2010 IEEE Aerospace Conference (IEEE, 2010), pp. 1–13.

Cress, J. A.

S. Gordeyev, J. A. Cress, E. Jumper, and A. B. Cain, “Aero-optical environment around a cylindrical turret with a flat window,” AIAA J. 49, 308–315 (2011).
[CrossRef]

de Lesegno, P. Viaris

De Moor, B.

P. Van Overschee and B. De Moor, Subspace Identification for Linear Systems (Kluwer Academic, 1996).

Doelman, N.

Ellerbroek, B. L.

J. S. Gibson, C. C. Chang, and B. L. Ellerbroek, “Adaptive optics: wave-front correction by use of adaptive filtering and control,” Appl. Opt. 39, 2525–2538 (2000).
[CrossRef]

B. L. Ellerbroek and T. A. Rhoadarmer, “Real-time adaptive optimization of wavefront reconstruction algorithms for closed-loop adaptive optical systems,” Proc. SPIE 3353, 1174–1185 (1998).
[CrossRef]

Fraanje, R.

Fusco, T.

C. Petit, J.-M. Conan, C. Kulcsar, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla, and D. Rabaud, “Off-axis adaptive optics with optimal control: experimental and numerical validation,” Proc. SPIE 5903, 59030P (2005).
[CrossRef]

Gibson, J. S.

J. Tesch and J. S. Gibson, “Optimal and adaptive correction of aero-optical wavefronts in an adaptive optics experiment,” Proc. SPIE 8165, 816502 (2011).
[CrossRef]

S. Monirabbasi and J. S. Gibson, “Adaptive control in an adaptive optics experiment,” J. Opt. Soc. Am. A 27, A84–A96 (2010).
[CrossRef]

P. K. Orzechowski, N. Chen, J. S. Gibson, and T. C. Tsao, “Optimal suppression of laser beam jitter by high-order RLS adaptive control,” IEEE Trans. Control Syst. Technol. 16, 255–267 (2008).
[CrossRef]

Y. T. Liu and J. S. Gibson, “Adaptive control in adaptive optics for directed-energy systems,” Opt. Eng. 46, 046601 (2007).
[CrossRef]

T. A. Rhoadarmer, L. M. Klein, J. S. Gibson, N. Chen, and Y.-T. Liu, “Adaptive control and filtering for closed-loop adaptive-optical wavefront reconstruction,” Proc. SPIE 6306, 63060E (2006).
[CrossRef]

J. S. Gibson, C. C. Chang, and B. L. Ellerbroek, “Adaptive optics: wave-front correction by use of adaptive filtering and control,” Appl. Opt. 39, 2525–2538 (2000).
[CrossRef]

S. B. Jiang and J. S. Gibson, “An unwindowed multichannel lattice filter with orthogonal channels,” IEEE Trans. Signal Process. 43, 2831–2842 (1995).
[CrossRef]

N. Y. Chen and J. S. Gibson, “Subspace system identification using a multichannel lattice filter,” in Proceedings of the 2004 American Control Conference (IEEE, 2004), Vol. 1, pp. 855–860.

J. Tesch, J. S. Gibson, S. Gordeyev, and E. Jumper, “Identification, prediction and control of aero optical wavefronts in laser beam propagation,” in 42nd AIAA Plasmadynamics and Lasers Conference (AIAA, 2011), paper 2011-3276.

Gordeyev, S.

M. Weng, A. Mani, and S. Gordeyev, “Physics and computation of aero-optics,” Annu. Rev. Fluid Mech. 44, 299–321 (2012).
[CrossRef]

S. Gordeyev, J. A. Cress, E. Jumper, and A. B. Cain, “Aero-optical environment around a cylindrical turret with a flat window,” AIAA J. 49, 308–315 (2011).
[CrossRef]

S. Gordeyev and E. Jumper, “Fluid dynamics and aero-optics of turrets,” Prog. Aerosp. Sci. 46, 388–400 (2010).
[CrossRef]

J. Tesch, J. S. Gibson, S. Gordeyev, and E. Jumper, “Identification, prediction and control of aero optical wavefronts in laser beam propagation,” in 42nd AIAA Plasmadynamics and Lasers Conference (AIAA, 2011), paper 2011-3276.

C. Porter, S. Gordeyev, M. Zenk, and E. Jumper, “Flight measurements of aero-optical distortions from a flat-windowed turret on the Airborne Aero-Optics Laboratory (AAOL),” in 42nd AIAA Plasmadynamics and Lasers Conference (AIAA, 2011), paper 2011-3280.

Henderson, B.

J. D. Mansell and B. Henderson, “Temporal and spatial characterization of polymer membrane deformable mirrors,” Proc. SPIE 7466, 74660D (2009).
[CrossRef]

Hinnen, K.

K. Hinnen, M. Verhaegen, and N. Doelman, “A data-driven H2 optimal control approach for adaptive optics,” IEEE Trans. Control Syst. Technol. 16, 381–395 (2008).
[CrossRef]

K. Hinnen, M. Verhaegen, and N. Doelman, “Exploiting the spatiotemporal correlation in adaptive optics using data-driven H2 optimal control,” J. Opt. Soc. Am. A 24, 1714–1725 (2007).
[CrossRef]

Jiang, S. B.

S. B. Jiang and J. S. Gibson, “An unwindowed multichannel lattice filter with orthogonal channels,” IEEE Trans. Signal Process. 43, 2831–2842 (1995).
[CrossRef]

Jumper, E.

S. Gordeyev, J. A. Cress, E. Jumper, and A. B. Cain, “Aero-optical environment around a cylindrical turret with a flat window,” AIAA J. 49, 308–315 (2011).
[CrossRef]

S. Gordeyev and E. Jumper, “Fluid dynamics and aero-optics of turrets,” Prog. Aerosp. Sci. 46, 388–400 (2010).
[CrossRef]

C. Porter, S. Gordeyev, M. Zenk, and E. Jumper, “Flight measurements of aero-optical distortions from a flat-windowed turret on the Airborne Aero-Optics Laboratory (AAOL),” in 42nd AIAA Plasmadynamics and Lasers Conference (AIAA, 2011), paper 2011-3280.

J. Tesch, J. S. Gibson, S. Gordeyev, and E. Jumper, “Identification, prediction and control of aero optical wavefronts in laser beam propagation,” in 42nd AIAA Plasmadynamics and Lasers Conference (AIAA, 2011), paper 2011-3276.

Katayama, T.

T. Katayama, Subspace Methods for System Identification (Springer-Verlag, 2005).

Klein, L. M.

T. A. Rhoadarmer, L. M. Klein, J. S. Gibson, N. Chen, and Y.-T. Liu, “Adaptive control and filtering for closed-loop adaptive-optical wavefront reconstruction,” Proc. SPIE 6306, 63060E (2006).
[CrossRef]

Kulcsar, C.

C. Petit, J.-M. Conan, C. Kulcsar, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla, and D. Rabaud, “Off-axis adaptive optics with optimal control: experimental and numerical validation,” Proc. SPIE 5903, 59030P (2005).
[CrossRef]

Kulcsár, C.

Liu, Y. T.

Y. T. Liu and J. S. Gibson, “Adaptive control in adaptive optics for directed-energy systems,” Opt. Eng. 46, 046601 (2007).
[CrossRef]

Liu, Y.-T.

T. A. Rhoadarmer, L. M. Klein, J. S. Gibson, N. Chen, and Y.-T. Liu, “Adaptive control and filtering for closed-loop adaptive-optical wavefront reconstruction,” Proc. SPIE 6306, 63060E (2006).
[CrossRef]

Mani, A.

M. Weng, A. Mani, and S. Gordeyev, “Physics and computation of aero-optics,” Annu. Rev. Fluid Mech. 44, 299–321 (2012).
[CrossRef]

Mansell, J. D.

J. D. Mansell and B. Henderson, “Temporal and spatial characterization of polymer membrane deformable mirrors,” Proc. SPIE 7466, 74660D (2009).
[CrossRef]

Masiero, A.

A. Beghi, A. Cenedese, and A. Masiero, “Multiscale stochastic approach for phase screens synthesis,” Appl. Opt. 50, 4124–4133 (2011).
[CrossRef]

A. Beghi, A. Cenedese, and A. Masiero, “Stochastic realization approach to the efficient simulation of phase screens,” J. Opt. Soc. Am. A 25, 515–525 (2008).
[CrossRef]

A. Beghi, A. Cenedese, and A. Masiero, “A Markov-random-field-based approach to modeling and prediction of atmospheric turbulence,” in 16th Mediterranean Conference on Control and Automation (MCA, 2008), pp. 1735–1740.

Monirabbasi, S.

Montri, J.

C. Petit, J.-M. Conan, C. Kulcsar, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla, and D. Rabaud, “Off-axis adaptive optics with optimal control: experimental and numerical validation,” Proc. SPIE 5903, 59030P (2005).
[CrossRef]

Nagashima, M.

C. M. S. Corley, M. Nagashima, and B. N. Agrawal, “Beam control and a new laboratory testbed for adaptive optics in a maritime environment,” in Proceedings of 2010 IEEE Aerospace Conference (IEEE, 2010), pp. 1–13.

Orzechowski, P. K.

P. K. Orzechowski, N. Chen, J. S. Gibson, and T. C. Tsao, “Optimal suppression of laser beam jitter by high-order RLS adaptive control,” IEEE Trans. Control Syst. Technol. 16, 255–267 (2008).
[CrossRef]

Perez Gibson, S.

N. O. Arancibia, S. Perez Gibson, and T.-C. Tsao, “Frequency-weighted minimum-variance adaptive control of laser beam jitter,” IEEE/ASME Trans. Mechatron. 14, 337–348 (2009).
[CrossRef]

Petit, C.

Porter, C.

C. Porter, S. Gordeyev, M. Zenk, and E. Jumper, “Flight measurements of aero-optical distortions from a flat-windowed turret on the Airborne Aero-Optics Laboratory (AAOL),” in 42nd AIAA Plasmadynamics and Lasers Conference (AIAA, 2011), paper 2011-3280.

Rabaud, D.

C. Petit, J.-M. Conan, C. Kulcsar, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla, and D. Rabaud, “Off-axis adaptive optics with optimal control: experimental and numerical validation,” Proc. SPIE 5903, 59030P (2005).
[CrossRef]

Raynaud, H.-F.

Rhoadarmer, T. A.

T. A. Rhoadarmer, L. M. Klein, J. S. Gibson, N. Chen, and Y.-T. Liu, “Adaptive control and filtering for closed-loop adaptive-optical wavefront reconstruction,” Proc. SPIE 6306, 63060E (2006).
[CrossRef]

B. L. Ellerbroek and T. A. Rhoadarmer, “Real-time adaptive optimization of wavefront reconstruction algorithms for closed-loop adaptive optical systems,” Proc. SPIE 3353, 1174–1185 (1998).
[CrossRef]

Rice, J.

Sayed, A. H.

A. H. Sayed, Fundamentals of Adaptive Filtering (Wiley, 2003).

Southwell, W. H.

Tesch, J.

J. Tesch and J. S. Gibson, “Optimal and adaptive correction of aero-optical wavefronts in an adaptive optics experiment,” Proc. SPIE 8165, 816502 (2011).
[CrossRef]

J. Tesch, J. S. Gibson, S. Gordeyev, and E. Jumper, “Identification, prediction and control of aero optical wavefronts in laser beam propagation,” in 42nd AIAA Plasmadynamics and Lasers Conference (AIAA, 2011), paper 2011-3276.

J. Tesch, “High-performance control and prediction for adaptive optics,” Ph.D. thesis (University of California, Los Angeles, 2011).

Tsao, T. C.

P. K. Orzechowski, N. Chen, J. S. Gibson, and T. C. Tsao, “Optimal suppression of laser beam jitter by high-order RLS adaptive control,” IEEE Trans. Control Syst. Technol. 16, 255–267 (2008).
[CrossRef]

Tsao, T.-C.

N. O. Arancibia, S. Perez Gibson, and T.-C. Tsao, “Frequency-weighted minimum-variance adaptive control of laser beam jitter,” IEEE/ASME Trans. Mechatron. 14, 337–348 (2009).
[CrossRef]

Van Overschee, P.

P. Van Overschee and B. De Moor, Subspace Identification for Linear Systems (Kluwer Academic, 1996).

Verdult, V.

M. Verhaegen and V. Verdult, Filtering and System Identification, a Least Squares Approach (Cambridge University, 2007).

Verhaegen, M.

R. Fraanje, J. Rice, M. Verhaegen, and N. Doelman, “Fast reconstruction and prediction of frozen flow turbulence based on structured Kalman filtering,” J. Opt. Soc. Am. A 27, A235–A245 (2010).
[CrossRef]

K. Hinnen, M. Verhaegen, and N. Doelman, “A data-driven H2 optimal control approach for adaptive optics,” IEEE Trans. Control Syst. Technol. 16, 381–395 (2008).
[CrossRef]

K. Hinnen, M. Verhaegen, and N. Doelman, “Exploiting the spatiotemporal correlation in adaptive optics using data-driven H2 optimal control,” J. Opt. Soc. Am. A 24, 1714–1725 (2007).
[CrossRef]

M. Verhaegen and V. Verdult, Filtering and System Identification, a Least Squares Approach (Cambridge University, 2007).

Walsh, E.

B. Widrow and E. Walsh, Adaptive Inverse Control (Prentice Hall, 1996).

Weng, M.

M. Weng, A. Mani, and S. Gordeyev, “Physics and computation of aero-optics,” Annu. Rev. Fluid Mech. 44, 299–321 (2012).
[CrossRef]

Widrow, B.

B. Widrow and E. Walsh, Adaptive Inverse Control (Prentice Hall, 1996).

Zenk, M.

C. Porter, S. Gordeyev, M. Zenk, and E. Jumper, “Flight measurements of aero-optical distortions from a flat-windowed turret on the Airborne Aero-Optics Laboratory (AAOL),” in 42nd AIAA Plasmadynamics and Lasers Conference (AIAA, 2011), paper 2011-3280.

AIAA J. (1)

S. Gordeyev, J. A. Cress, E. Jumper, and A. B. Cain, “Aero-optical environment around a cylindrical turret with a flat window,” AIAA J. 49, 308–315 (2011).
[CrossRef]

Annu. Rev. Fluid Mech. (1)

M. Weng, A. Mani, and S. Gordeyev, “Physics and computation of aero-optics,” Annu. Rev. Fluid Mech. 44, 299–321 (2012).
[CrossRef]

Appl. Opt. (2)

IEEE Trans. Control Syst. Technol. (2)

K. Hinnen, M. Verhaegen, and N. Doelman, “A data-driven H2 optimal control approach for adaptive optics,” IEEE Trans. Control Syst. Technol. 16, 381–395 (2008).
[CrossRef]

P. K. Orzechowski, N. Chen, J. S. Gibson, and T. C. Tsao, “Optimal suppression of laser beam jitter by high-order RLS adaptive control,” IEEE Trans. Control Syst. Technol. 16, 255–267 (2008).
[CrossRef]

IEEE Trans. Signal Process. (1)

S. B. Jiang and J. S. Gibson, “An unwindowed multichannel lattice filter with orthogonal channels,” IEEE Trans. Signal Process. 43, 2831–2842 (1995).
[CrossRef]

IEEE/ASME Trans. Mechatron. (1)

N. O. Arancibia, S. Perez Gibson, and T.-C. Tsao, “Frequency-weighted minimum-variance adaptive control of laser beam jitter,” IEEE/ASME Trans. Mechatron. 14, 337–348 (2009).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (5)

Opt. Eng. (1)

Y. T. Liu and J. S. Gibson, “Adaptive control in adaptive optics for directed-energy systems,” Opt. Eng. 46, 046601 (2007).
[CrossRef]

Opt. Express (1)

Proc. SPIE (5)

C. Petit, J.-M. Conan, C. Kulcsar, H.-F. Raynaud, T. Fusco, J. Montri, F. Chemla, and D. Rabaud, “Off-axis adaptive optics with optimal control: experimental and numerical validation,” Proc. SPIE 5903, 59030P (2005).
[CrossRef]

B. L. Ellerbroek and T. A. Rhoadarmer, “Real-time adaptive optimization of wavefront reconstruction algorithms for closed-loop adaptive optical systems,” Proc. SPIE 3353, 1174–1185 (1998).
[CrossRef]

T. A. Rhoadarmer, L. M. Klein, J. S. Gibson, N. Chen, and Y.-T. Liu, “Adaptive control and filtering for closed-loop adaptive-optical wavefront reconstruction,” Proc. SPIE 6306, 63060E (2006).
[CrossRef]

J. Tesch and J. S. Gibson, “Optimal and adaptive correction of aero-optical wavefronts in an adaptive optics experiment,” Proc. SPIE 8165, 816502 (2011).
[CrossRef]

J. D. Mansell and B. Henderson, “Temporal and spatial characterization of polymer membrane deformable mirrors,” Proc. SPIE 7466, 74660D (2009).
[CrossRef]

Prog. Aerosp. Sci. (1)

S. Gordeyev and E. Jumper, “Fluid dynamics and aero-optics of turrets,” Prog. Aerosp. Sci. 46, 388–400 (2010).
[CrossRef]

Other (12)

B. Widrow and E. Walsh, Adaptive Inverse Control (Prentice Hall, 1996).

N. Y. Chen and J. S. Gibson, “Subspace system identification using a multichannel lattice filter,” in Proceedings of the 2004 American Control Conference (IEEE, 2004), Vol. 1, pp. 855–860.

P. Van Overschee and B. De Moor, Subspace Identification for Linear Systems (Kluwer Academic, 1996).

T. Katayama, Subspace Methods for System Identification (Springer-Verlag, 2005).

M. Verhaegen and V. Verdult, Filtering and System Identification, a Least Squares Approach (Cambridge University, 2007).

A. H. Sayed, Fundamentals of Adaptive Filtering (Wiley, 2003).

J. Tesch, “High-performance control and prediction for adaptive optics,” Ph.D. thesis (University of California, Los Angeles, 2011).

C. Porter, S. Gordeyev, M. Zenk, and E. Jumper, “Flight measurements of aero-optical distortions from a flat-windowed turret on the Airborne Aero-Optics Laboratory (AAOL),” in 42nd AIAA Plasmadynamics and Lasers Conference (AIAA, 2011), paper 2011-3280.

J. Tesch, J. S. Gibson, S. Gordeyev, and E. Jumper, “Identification, prediction and control of aero optical wavefronts in laser beam propagation,” in 42nd AIAA Plasmadynamics and Lasers Conference (AIAA, 2011), paper 2011-3276.

A. Beghi, A. Cenedese, and A. Masiero, “A Markov-random-field-based approach to modeling and prediction of atmospheric turbulence,” in 16th Mediterranean Conference on Control and Automation (MCA, 2008), pp. 1735–1740.

C. M. S. Corley, M. Nagashima, and B. N. Agrawal, “Beam control and a new laboratory testbed for adaptive optics in a maritime environment,” in Proceedings of 2010 IEEE Aerospace Conference (IEEE, 2010), pp. 1–13.

C. M. S. Corley, “Maritime adaptive optics beam control,” Ph.D. thesis (Naval Post Graduate School, 2010).

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Figures (13)

Fig. 1.
Fig. 1.

Block diagram for optimal LTI control.

Fig. 2.
Fig. 2.

Block diagram for adaptive control.

Fig. 3.
Fig. 3.

Optical layout. The primary components are the laser source, two membrane deformable mirrors (DM1 and DM2), a Shack–Hartmann wavefront sensor (SHWFS), and target camera.

Fig. 4.
Fig. 4.

Photograph of the experiment.

Fig. 5.
Fig. 5.

Block diagram of the AO experiment.

Fig. 6.
Fig. 6.

Images of the frequency-weighted DM modes for DM1.

Fig. 7.
Fig. 7.

Bode plot of the sensitivity transfer function S(z) for α=0.95 and various controller gains β. For the experiments in this paper, β=0.3 was used.

Fig. 8.
Fig. 8.

Layout of the AAOL wavefront data, with regions used to fill the central, circular obscuration. v^ is the approximate flow velocity estimated using an image correlation analysis and is equal to 0.96pixels per time step in the horizontal direction and 0.46 pixels per time step in the vertical direction.

Fig. 9.
Fig. 9.

Power spectral density for various pixels in the AAOL wavefront data compared to the same pixel in the interpolated region S.

Fig. 10.
Fig. 10.

(a) RMS value of the wavefront error computed over space and time for a 200-frame moving window; (b) maximum intensity in the average target camera image for the 200-frame moving window.

Fig. 11.
Fig. 11.

Mean target camera images for (a) time steps 300 to 4000 and (b) time steps 4000 to 8000. Target camera images are 60×60pixels, with pixel pitch size=6.7μm.

Fig. 12.
Fig. 12.

RMS values of all 31 modal time series for time steps 300 through 4000.

Fig. 13.
Fig. 13.

Power spectral densities of select modal time series for (left) time steps 300 through 4000 and (right) 4001 through 8000.

Tables (3)

Tables Icon

Table 1. Experimental Details for the Notre Dame AAOL Data Set

Tables Icon

Table 2. RMS Values of the Wavefront Error in Experiments 1–4 Computed over Space and Time Intervals T1=[3004000] and T2=[40008000]

Tables Icon

Table 3. Target Camera Performance Measures for Experiments 1–4, Computed over Time Intervals T1=[3004000] and T2=[40008000]a

Equations (29)

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

e=w+G(z)u,w^=eG^(z)u,u=F(z)w^.
J=t=1tide^*(t)e^(t),
e^=wid+G^(z)F(z)wid.
G^(z)=zmG0(z),
F(z)=G01(z)F˜(z).
e^=widzmF˜(z)wid,
x(t+1)=Ax(t)+Kε(t),wid(t)=Cx(t)+ε(t).
w˜id(t)=Cx(t),
ε(t)=wid(t)Cx(t)=wid(t)w˜id(t)
x(t+1)=[AKC]x(t)+Kwid(t),w˜id(t+1)=C[AKC]x(t)+CKwid(t).
e^a=w^+F(z)G^(z)w^.
F(z)=n=0NFnzn,
d=av2,
v=round(c+vb2),vb=1802552/2,
d=a(c+vb2).
sξ=2νπλfΔξ,sη=2νπλfΔη,
φ=φb+φ2φ1,
y=yb+Γ2c2z1Γ1c1,
E=(Γ1V)+.
e=Ey
EΓ1V=I.
C(z)=βzzα,
G^(z)=βz+βα,
G(z)=G^(z).
S(z)=zαz+βα.
w=S(z)E(y2+yb),
s(t)=a0r(0)+k=1pakr(tk)+=1qbr(t+),
s˜(t)=a0r˜(0)+k=1pakr˜(tk)+=1qbr˜(t+)+ϵ(t),
Jc=(γϕRΓ2c2)T(γϕRΓ2c2)+c2TΠc2,

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