Abstract

We describe an adaptive optics (AO) system for correcting the aero-optical aberration of the supersonic mixing layer and test its performance with numerical simulations. The AO system is based on the measurement of distributed Strehl ratios and the stochastic parallel gradient descent (SPGD) algorithm. The aero-optical aberration is computed by the direct numerical simulation of a two-dimensional supersonic mixing layer. When the SPGD algorithm is applied directly, the AO cannot give effective corrections. This paper suggests two strategies to improve the performance of the SPGD algorithm for use in aero-optics. The first one is using an iteration process keeping finite memory, and the second is based on the frozen hypothesis. With these modifications, the performance of AO is improved and the aero-optical aberration can be corrected to some noticeable extent. The possibility of experimental implementation is also discussed.

© 2012 Optical Society of America

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  1. K. G. Gilbert and L. J. Otten, eds., Aero-Optical Phenomena (AIAA, 1982).
  2. E. J. Jumper and E. J. Fitzgerald, “Recent advances in aero-optics,” Prog. Aerosp. Sci. 37, 299–339 (2001).
    [CrossRef]
  3. R. K. Tyson, Principles of Adaptive Optics (Academic, 1991).
  4. R. M. Rennie, D. A. Duffin, and E. J. Jumper, “Characterization and aero-optical correction of a forced two-dimensional weakly compressible shear layer,” AIAA J. 46, 2787–2795 (2008).
    [CrossRef]
  5. R. M. Rennie, J. P. Siegenthaler, and E. J. Jumper, “Forcing of a two-dimensional, weakly-compressed subsonic free shear layer,” AIAA paper 2006–0561 (American Institute of Aeronautics and Astronautics, 2006).
  6. C. M. Ho and P. Huerre, “Perturbed free shear layers,” Annu. Rev. Fluid Mech. 16, 365–424 (1984).
    [CrossRef]
  7. A. P. Freeman and H. J. Catrakis, “Direction reduction of aero-optical aberrations by large structure suppression control in turbulence,” AIAA J. 46, 2582–2590 (2008).
    [CrossRef]
  8. J. Seidel, S. Seigel, and T. McLaughlin, “Feedback flow control of a shear layer for aero-optical aberrations,” AIAA paper 2010-0356 (American Institute of Aeronautics and Astronautics, 2010).
  9. G. Vdovin, S. Middelhoek, and P. M. Sarro, “Technology and applications of micromechined silicon adaptive mirrors,” Opt. Eng. 36, 1382–1390 (1997).
    [CrossRef]
  10. T. G. Bifano, J. Perreault, R. K. Mali, and M. N. Horenstein, “Microelectromechanical deformable mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 83–89 (1999).
    [CrossRef]
  11. E. J. Fernandez and P. Artal, “Membrane deformable mirror for adaptive optics: performance limits in visual optics,” Opt. Express 11, 1056–1069 (2003).
    [CrossRef]
  12. G. Vdovin, O. Soloviev, A. Samokhin, and M. Loktev, “Correction of low order aberrations using continuous deformable mirrors,” Opt. Express 16, 2859–2866 (2008).
    [CrossRef]
  13. R. A. Muller and A. Buffington, “Real-time correction of atmospherically degraded telescope images through imaging sharpening,” J. Opt. Soc. Am. 64, 1200–1210 (1974).
    [CrossRef]
  14. J. W. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651–697 (1978).
    [CrossRef]
  15. T. R. O’Meara, “The multidither principle in adaptive optics,” J. Opt. Soc. Am. 67, 306–315 (1977).
    [CrossRef]
  16. M. A. Vorontsov, G. W. Carhart, and J. C. Ricklin, “Adaptive phase-distortion correction based on parallel gradient-descent optimization,” Opt. Lett. 22, 907–909 (1997).
    [CrossRef]
  17. M. A. Vorontsov, G. W. Carhart, M. Cohen, and G. Cauwenberghs, “Adaptive optics based on analog parallel stochastic optimization: analysis and experimental demonstration,” J. Opt. Soc. Am. 17, 1440–1453 (2000).
    [CrossRef]
  18. T. Weyrauch and M. A. Vorontsov, “Dynamic wave-front distortion compensation with a 134-control-channel submillisecond adaptive system,” Opt. Lett. 27, 751–753 (2002).
    [CrossRef]
  19. M. Cohen, G. Cauwenberghs, and M. A. Vorontsov, “Image sharpness and beam focus VLSI sensors for adaptive optics,” IEEE Sens. J. 2, 680–690 (2002).
    [CrossRef]
  20. M. A. Vorontsov, “Decoupled stochastic parallel gradient descent optimization for adaptive optics: integrated approach for wave-front sensor information fusion,” J. Opt. Soc. Am. A 19, 356–368 (2002).
    [CrossRef]
  21. M. A. Vorontsov and G. W. Carhart, “Adaptive wavefront control with asynchronous stochastic parallel gradient descent clusters,” J. Opt. Soc. Am. A. 23, 2613–2622 (2006).
    [CrossRef]
  22. S. K. Lele, “Direct numerical simulation of compressible free shear flows,” AIAA paper 1989-0374 (American Institute of Aeronautics and Astronautics, 1989).
  23. N. D. Sandham and H. C. Yee, “A numerical study of a class of TVD schemes for compressible mixing layers,” NASA TM-102194 (NASA, 1989).
  24. S. Stanley and S. Sarkar, “Simulations of spatially developing two-dimensional shear layers and jets,” Theor. Comput. Fluid Dyn. 9, 121–147 (1997).
    [CrossRef]
  25. C. Pantano and S. Sarkar, “A study of compressibility effects in the high-speed turbulent shear layer using direct simulation,” J. Fluid Mech. 451, 329–371 (2002).
    [CrossRef]
  26. J. C. Tannehill, D. A. Anderson, and R. H. Pletcher, Computational Fluid Mechanics and Heat Transfer (Taylor & Francis, 1997), Chap. 5.1.
  27. H. C. Yee, N. D. Sandham, and M. J. Djomehri, “Low-dissipative high-order shock-capturing methods using characteristic-based filters,” J. Comput. Phys. 150, 199–238 (1999).
    [CrossRef]
  28. S. Pirozzoli, “Conservative hybrid compact-WENO schemes for shock-turbulence interaction,” J. Comput. Phys. 178, 81–117 (2002).
    [CrossRef]
  29. J. L. Steger and R. F. Warming, “Flux vector splitting of the inviscid gasdynamic equations with application to finite difference method,” J. Comput. Phys. 40, 263–293 (1981).
    [CrossRef]
  30. S. K. Lele, “Compact finite difference schemes with spectral-like resolution,” J. Comput. Phys. 103, 16–42 (1992).
    [CrossRef]
  31. C. W. Shu and S. Osher, “Efficient implementation of essentially non-oscillatary shock capturing schemes,” J. Comput. Phys. 77, 439–471 (1988).
    [CrossRef]
  32. T. J. Poinsot and S. K. Lele, “Boundary conditions for direct simulations of compressible viscous flows,” J. Comput. Phys. 101, 104–129 (1992).
    [CrossRef]
  33. J. C. Spall, Introduction to Stochastic Search and Optimization (Wiley, 2003), Chap. 7.
  34. P. Piatrou and M. Roggemann, “Beaconless stochastic parallel gradient descent laser beam control: numerical experiments,” Appl. Opt. 46, 6831–6842 (2007).
    [CrossRef]
  35. Q. Gao, Z. F. Jiang, S. H. Yi, and Y. X. Zhao, “Optical path difference of the supersonic mixing layer,” Appl. Opt. 49, 3786–3792 (2010).
    [CrossRef]

2010 (1)

2008 (3)

G. Vdovin, O. Soloviev, A. Samokhin, and M. Loktev, “Correction of low order aberrations using continuous deformable mirrors,” Opt. Express 16, 2859–2866 (2008).
[CrossRef]

R. M. Rennie, D. A. Duffin, and E. J. Jumper, “Characterization and aero-optical correction of a forced two-dimensional weakly compressible shear layer,” AIAA J. 46, 2787–2795 (2008).
[CrossRef]

A. P. Freeman and H. J. Catrakis, “Direction reduction of aero-optical aberrations by large structure suppression control in turbulence,” AIAA J. 46, 2582–2590 (2008).
[CrossRef]

2007 (1)

2006 (1)

2003 (1)

2002 (5)

M. A. Vorontsov, “Decoupled stochastic parallel gradient descent optimization for adaptive optics: integrated approach for wave-front sensor information fusion,” J. Opt. Soc. Am. A 19, 356–368 (2002).
[CrossRef]

T. Weyrauch and M. A. Vorontsov, “Dynamic wave-front distortion compensation with a 134-control-channel submillisecond adaptive system,” Opt. Lett. 27, 751–753 (2002).
[CrossRef]

M. Cohen, G. Cauwenberghs, and M. A. Vorontsov, “Image sharpness and beam focus VLSI sensors for adaptive optics,” IEEE Sens. J. 2, 680–690 (2002).
[CrossRef]

C. Pantano and S. Sarkar, “A study of compressibility effects in the high-speed turbulent shear layer using direct simulation,” J. Fluid Mech. 451, 329–371 (2002).
[CrossRef]

S. Pirozzoli, “Conservative hybrid compact-WENO schemes for shock-turbulence interaction,” J. Comput. Phys. 178, 81–117 (2002).
[CrossRef]

2001 (1)

E. J. Jumper and E. J. Fitzgerald, “Recent advances in aero-optics,” Prog. Aerosp. Sci. 37, 299–339 (2001).
[CrossRef]

2000 (1)

M. A. Vorontsov, G. W. Carhart, M. Cohen, and G. Cauwenberghs, “Adaptive optics based on analog parallel stochastic optimization: analysis and experimental demonstration,” J. Opt. Soc. Am. 17, 1440–1453 (2000).
[CrossRef]

1999 (2)

T. G. Bifano, J. Perreault, R. K. Mali, and M. N. Horenstein, “Microelectromechanical deformable mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 83–89 (1999).
[CrossRef]

H. C. Yee, N. D. Sandham, and M. J. Djomehri, “Low-dissipative high-order shock-capturing methods using characteristic-based filters,” J. Comput. Phys. 150, 199–238 (1999).
[CrossRef]

1997 (3)

S. Stanley and S. Sarkar, “Simulations of spatially developing two-dimensional shear layers and jets,” Theor. Comput. Fluid Dyn. 9, 121–147 (1997).
[CrossRef]

G. Vdovin, S. Middelhoek, and P. M. Sarro, “Technology and applications of micromechined silicon adaptive mirrors,” Opt. Eng. 36, 1382–1390 (1997).
[CrossRef]

M. A. Vorontsov, G. W. Carhart, and J. C. Ricklin, “Adaptive phase-distortion correction based on parallel gradient-descent optimization,” Opt. Lett. 22, 907–909 (1997).
[CrossRef]

1992 (2)

T. J. Poinsot and S. K. Lele, “Boundary conditions for direct simulations of compressible viscous flows,” J. Comput. Phys. 101, 104–129 (1992).
[CrossRef]

S. K. Lele, “Compact finite difference schemes with spectral-like resolution,” J. Comput. Phys. 103, 16–42 (1992).
[CrossRef]

1988 (1)

C. W. Shu and S. Osher, “Efficient implementation of essentially non-oscillatary shock capturing schemes,” J. Comput. Phys. 77, 439–471 (1988).
[CrossRef]

1984 (1)

C. M. Ho and P. Huerre, “Perturbed free shear layers,” Annu. Rev. Fluid Mech. 16, 365–424 (1984).
[CrossRef]

1981 (1)

J. L. Steger and R. F. Warming, “Flux vector splitting of the inviscid gasdynamic equations with application to finite difference method,” J. Comput. Phys. 40, 263–293 (1981).
[CrossRef]

1978 (1)

J. W. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651–697 (1978).
[CrossRef]

1977 (1)

1974 (1)

Anderson, D. A.

J. C. Tannehill, D. A. Anderson, and R. H. Pletcher, Computational Fluid Mechanics and Heat Transfer (Taylor & Francis, 1997), Chap. 5.1.

Artal, P.

Bifano, T. G.

T. G. Bifano, J. Perreault, R. K. Mali, and M. N. Horenstein, “Microelectromechanical deformable mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 83–89 (1999).
[CrossRef]

Buffington, A.

Carhart, G. W.

Catrakis, H. J.

A. P. Freeman and H. J. Catrakis, “Direction reduction of aero-optical aberrations by large structure suppression control in turbulence,” AIAA J. 46, 2582–2590 (2008).
[CrossRef]

Cauwenberghs, G.

M. Cohen, G. Cauwenberghs, and M. A. Vorontsov, “Image sharpness and beam focus VLSI sensors for adaptive optics,” IEEE Sens. J. 2, 680–690 (2002).
[CrossRef]

M. A. Vorontsov, G. W. Carhart, M. Cohen, and G. Cauwenberghs, “Adaptive optics based on analog parallel stochastic optimization: analysis and experimental demonstration,” J. Opt. Soc. Am. 17, 1440–1453 (2000).
[CrossRef]

Cohen, M.

M. Cohen, G. Cauwenberghs, and M. A. Vorontsov, “Image sharpness and beam focus VLSI sensors for adaptive optics,” IEEE Sens. J. 2, 680–690 (2002).
[CrossRef]

M. A. Vorontsov, G. W. Carhart, M. Cohen, and G. Cauwenberghs, “Adaptive optics based on analog parallel stochastic optimization: analysis and experimental demonstration,” J. Opt. Soc. Am. 17, 1440–1453 (2000).
[CrossRef]

Djomehri, M. J.

H. C. Yee, N. D. Sandham, and M. J. Djomehri, “Low-dissipative high-order shock-capturing methods using characteristic-based filters,” J. Comput. Phys. 150, 199–238 (1999).
[CrossRef]

Duffin, D. A.

R. M. Rennie, D. A. Duffin, and E. J. Jumper, “Characterization and aero-optical correction of a forced two-dimensional weakly compressible shear layer,” AIAA J. 46, 2787–2795 (2008).
[CrossRef]

Fernandez, E. J.

Fitzgerald, E. J.

E. J. Jumper and E. J. Fitzgerald, “Recent advances in aero-optics,” Prog. Aerosp. Sci. 37, 299–339 (2001).
[CrossRef]

Freeman, A. P.

A. P. Freeman and H. J. Catrakis, “Direction reduction of aero-optical aberrations by large structure suppression control in turbulence,” AIAA J. 46, 2582–2590 (2008).
[CrossRef]

Gao, Q.

Gilbert, K. G.

K. G. Gilbert and L. J. Otten, eds., Aero-Optical Phenomena (AIAA, 1982).

Hardy, J. W.

J. W. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651–697 (1978).
[CrossRef]

Ho, C. M.

C. M. Ho and P. Huerre, “Perturbed free shear layers,” Annu. Rev. Fluid Mech. 16, 365–424 (1984).
[CrossRef]

Horenstein, M. N.

T. G. Bifano, J. Perreault, R. K. Mali, and M. N. Horenstein, “Microelectromechanical deformable mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 83–89 (1999).
[CrossRef]

Huerre, P.

C. M. Ho and P. Huerre, “Perturbed free shear layers,” Annu. Rev. Fluid Mech. 16, 365–424 (1984).
[CrossRef]

Jiang, Z. F.

Jumper, E. J.

R. M. Rennie, D. A. Duffin, and E. J. Jumper, “Characterization and aero-optical correction of a forced two-dimensional weakly compressible shear layer,” AIAA J. 46, 2787–2795 (2008).
[CrossRef]

E. J. Jumper and E. J. Fitzgerald, “Recent advances in aero-optics,” Prog. Aerosp. Sci. 37, 299–339 (2001).
[CrossRef]

R. M. Rennie, J. P. Siegenthaler, and E. J. Jumper, “Forcing of a two-dimensional, weakly-compressed subsonic free shear layer,” AIAA paper 2006–0561 (American Institute of Aeronautics and Astronautics, 2006).

Lele, S. K.

T. J. Poinsot and S. K. Lele, “Boundary conditions for direct simulations of compressible viscous flows,” J. Comput. Phys. 101, 104–129 (1992).
[CrossRef]

S. K. Lele, “Compact finite difference schemes with spectral-like resolution,” J. Comput. Phys. 103, 16–42 (1992).
[CrossRef]

S. K. Lele, “Direct numerical simulation of compressible free shear flows,” AIAA paper 1989-0374 (American Institute of Aeronautics and Astronautics, 1989).

Loktev, M.

Mali, R. K.

T. G. Bifano, J. Perreault, R. K. Mali, and M. N. Horenstein, “Microelectromechanical deformable mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 83–89 (1999).
[CrossRef]

McLaughlin, T.

J. Seidel, S. Seigel, and T. McLaughlin, “Feedback flow control of a shear layer for aero-optical aberrations,” AIAA paper 2010-0356 (American Institute of Aeronautics and Astronautics, 2010).

Middelhoek, S.

G. Vdovin, S. Middelhoek, and P. M. Sarro, “Technology and applications of micromechined silicon adaptive mirrors,” Opt. Eng. 36, 1382–1390 (1997).
[CrossRef]

Muller, R. A.

O’Meara, T. R.

Osher, S.

C. W. Shu and S. Osher, “Efficient implementation of essentially non-oscillatary shock capturing schemes,” J. Comput. Phys. 77, 439–471 (1988).
[CrossRef]

Otten, L. J.

K. G. Gilbert and L. J. Otten, eds., Aero-Optical Phenomena (AIAA, 1982).

Pantano, C.

C. Pantano and S. Sarkar, “A study of compressibility effects in the high-speed turbulent shear layer using direct simulation,” J. Fluid Mech. 451, 329–371 (2002).
[CrossRef]

Perreault, J.

T. G. Bifano, J. Perreault, R. K. Mali, and M. N. Horenstein, “Microelectromechanical deformable mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 83–89 (1999).
[CrossRef]

Piatrou, P.

Pirozzoli, S.

S. Pirozzoli, “Conservative hybrid compact-WENO schemes for shock-turbulence interaction,” J. Comput. Phys. 178, 81–117 (2002).
[CrossRef]

Pletcher, R. H.

J. C. Tannehill, D. A. Anderson, and R. H. Pletcher, Computational Fluid Mechanics and Heat Transfer (Taylor & Francis, 1997), Chap. 5.1.

Poinsot, T. J.

T. J. Poinsot and S. K. Lele, “Boundary conditions for direct simulations of compressible viscous flows,” J. Comput. Phys. 101, 104–129 (1992).
[CrossRef]

Rennie, R. M.

R. M. Rennie, D. A. Duffin, and E. J. Jumper, “Characterization and aero-optical correction of a forced two-dimensional weakly compressible shear layer,” AIAA J. 46, 2787–2795 (2008).
[CrossRef]

R. M. Rennie, J. P. Siegenthaler, and E. J. Jumper, “Forcing of a two-dimensional, weakly-compressed subsonic free shear layer,” AIAA paper 2006–0561 (American Institute of Aeronautics and Astronautics, 2006).

Ricklin, J. C.

Roggemann, M.

Samokhin, A.

Sandham, N. D.

H. C. Yee, N. D. Sandham, and M. J. Djomehri, “Low-dissipative high-order shock-capturing methods using characteristic-based filters,” J. Comput. Phys. 150, 199–238 (1999).
[CrossRef]

N. D. Sandham and H. C. Yee, “A numerical study of a class of TVD schemes for compressible mixing layers,” NASA TM-102194 (NASA, 1989).

Sarkar, S.

C. Pantano and S. Sarkar, “A study of compressibility effects in the high-speed turbulent shear layer using direct simulation,” J. Fluid Mech. 451, 329–371 (2002).
[CrossRef]

S. Stanley and S. Sarkar, “Simulations of spatially developing two-dimensional shear layers and jets,” Theor. Comput. Fluid Dyn. 9, 121–147 (1997).
[CrossRef]

Sarro, P. M.

G. Vdovin, S. Middelhoek, and P. M. Sarro, “Technology and applications of micromechined silicon adaptive mirrors,” Opt. Eng. 36, 1382–1390 (1997).
[CrossRef]

Seidel, J.

J. Seidel, S. Seigel, and T. McLaughlin, “Feedback flow control of a shear layer for aero-optical aberrations,” AIAA paper 2010-0356 (American Institute of Aeronautics and Astronautics, 2010).

Seigel, S.

J. Seidel, S. Seigel, and T. McLaughlin, “Feedback flow control of a shear layer for aero-optical aberrations,” AIAA paper 2010-0356 (American Institute of Aeronautics and Astronautics, 2010).

Shu, C. W.

C. W. Shu and S. Osher, “Efficient implementation of essentially non-oscillatary shock capturing schemes,” J. Comput. Phys. 77, 439–471 (1988).
[CrossRef]

Siegenthaler, J. P.

R. M. Rennie, J. P. Siegenthaler, and E. J. Jumper, “Forcing of a two-dimensional, weakly-compressed subsonic free shear layer,” AIAA paper 2006–0561 (American Institute of Aeronautics and Astronautics, 2006).

Soloviev, O.

Spall, J. C.

J. C. Spall, Introduction to Stochastic Search and Optimization (Wiley, 2003), Chap. 7.

Stanley, S.

S. Stanley and S. Sarkar, “Simulations of spatially developing two-dimensional shear layers and jets,” Theor. Comput. Fluid Dyn. 9, 121–147 (1997).
[CrossRef]

Steger, J. L.

J. L. Steger and R. F. Warming, “Flux vector splitting of the inviscid gasdynamic equations with application to finite difference method,” J. Comput. Phys. 40, 263–293 (1981).
[CrossRef]

Tannehill, J. C.

J. C. Tannehill, D. A. Anderson, and R. H. Pletcher, Computational Fluid Mechanics and Heat Transfer (Taylor & Francis, 1997), Chap. 5.1.

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics (Academic, 1991).

Vdovin, G.

G. Vdovin, O. Soloviev, A. Samokhin, and M. Loktev, “Correction of low order aberrations using continuous deformable mirrors,” Opt. Express 16, 2859–2866 (2008).
[CrossRef]

G. Vdovin, S. Middelhoek, and P. M. Sarro, “Technology and applications of micromechined silicon adaptive mirrors,” Opt. Eng. 36, 1382–1390 (1997).
[CrossRef]

Vorontsov, M. A.

Warming, R. F.

J. L. Steger and R. F. Warming, “Flux vector splitting of the inviscid gasdynamic equations with application to finite difference method,” J. Comput. Phys. 40, 263–293 (1981).
[CrossRef]

Weyrauch, T.

Yee, H. C.

H. C. Yee, N. D. Sandham, and M. J. Djomehri, “Low-dissipative high-order shock-capturing methods using characteristic-based filters,” J. Comput. Phys. 150, 199–238 (1999).
[CrossRef]

N. D. Sandham and H. C. Yee, “A numerical study of a class of TVD schemes for compressible mixing layers,” NASA TM-102194 (NASA, 1989).

Yi, S. H.

Zhao, Y. X.

AIAA J. (2)

R. M. Rennie, D. A. Duffin, and E. J. Jumper, “Characterization and aero-optical correction of a forced two-dimensional weakly compressible shear layer,” AIAA J. 46, 2787–2795 (2008).
[CrossRef]

A. P. Freeman and H. J. Catrakis, “Direction reduction of aero-optical aberrations by large structure suppression control in turbulence,” AIAA J. 46, 2582–2590 (2008).
[CrossRef]

Annu. Rev. Fluid Mech. (1)

C. M. Ho and P. Huerre, “Perturbed free shear layers,” Annu. Rev. Fluid Mech. 16, 365–424 (1984).
[CrossRef]

Appl. Opt. (2)

IEEE J. Sel. Top. Quantum Electron. (1)

T. G. Bifano, J. Perreault, R. K. Mali, and M. N. Horenstein, “Microelectromechanical deformable mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 83–89 (1999).
[CrossRef]

IEEE Sens. J. (1)

M. Cohen, G. Cauwenberghs, and M. A. Vorontsov, “Image sharpness and beam focus VLSI sensors for adaptive optics,” IEEE Sens. J. 2, 680–690 (2002).
[CrossRef]

J. Comput. Phys. (6)

H. C. Yee, N. D. Sandham, and M. J. Djomehri, “Low-dissipative high-order shock-capturing methods using characteristic-based filters,” J. Comput. Phys. 150, 199–238 (1999).
[CrossRef]

S. Pirozzoli, “Conservative hybrid compact-WENO schemes for shock-turbulence interaction,” J. Comput. Phys. 178, 81–117 (2002).
[CrossRef]

J. L. Steger and R. F. Warming, “Flux vector splitting of the inviscid gasdynamic equations with application to finite difference method,” J. Comput. Phys. 40, 263–293 (1981).
[CrossRef]

S. K. Lele, “Compact finite difference schemes with spectral-like resolution,” J. Comput. Phys. 103, 16–42 (1992).
[CrossRef]

C. W. Shu and S. Osher, “Efficient implementation of essentially non-oscillatary shock capturing schemes,” J. Comput. Phys. 77, 439–471 (1988).
[CrossRef]

T. J. Poinsot and S. K. Lele, “Boundary conditions for direct simulations of compressible viscous flows,” J. Comput. Phys. 101, 104–129 (1992).
[CrossRef]

J. Fluid Mech. (1)

C. Pantano and S. Sarkar, “A study of compressibility effects in the high-speed turbulent shear layer using direct simulation,” J. Fluid Mech. 451, 329–371 (2002).
[CrossRef]

J. Opt. Soc. Am. (3)

M. A. Vorontsov, G. W. Carhart, M. Cohen, and G. Cauwenberghs, “Adaptive optics based on analog parallel stochastic optimization: analysis and experimental demonstration,” J. Opt. Soc. Am. 17, 1440–1453 (2000).
[CrossRef]

R. A. Muller and A. Buffington, “Real-time correction of atmospherically degraded telescope images through imaging sharpening,” J. Opt. Soc. Am. 64, 1200–1210 (1974).
[CrossRef]

T. R. O’Meara, “The multidither principle in adaptive optics,” J. Opt. Soc. Am. 67, 306–315 (1977).
[CrossRef]

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

Opt. Eng. (1)

G. Vdovin, S. Middelhoek, and P. M. Sarro, “Technology and applications of micromechined silicon adaptive mirrors,” Opt. Eng. 36, 1382–1390 (1997).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Proc. IEEE (1)

J. W. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651–697 (1978).
[CrossRef]

Prog. Aerosp. Sci. (1)

E. J. Jumper and E. J. Fitzgerald, “Recent advances in aero-optics,” Prog. Aerosp. Sci. 37, 299–339 (2001).
[CrossRef]

Theor. Comput. Fluid Dyn. (1)

S. Stanley and S. Sarkar, “Simulations of spatially developing two-dimensional shear layers and jets,” Theor. Comput. Fluid Dyn. 9, 121–147 (1997).
[CrossRef]

Other (8)

J. C. Spall, Introduction to Stochastic Search and Optimization (Wiley, 2003), Chap. 7.

R. K. Tyson, Principles of Adaptive Optics (Academic, 1991).

R. M. Rennie, J. P. Siegenthaler, and E. J. Jumper, “Forcing of a two-dimensional, weakly-compressed subsonic free shear layer,” AIAA paper 2006–0561 (American Institute of Aeronautics and Astronautics, 2006).

K. G. Gilbert and L. J. Otten, eds., Aero-Optical Phenomena (AIAA, 1982).

J. Seidel, S. Seigel, and T. McLaughlin, “Feedback flow control of a shear layer for aero-optical aberrations,” AIAA paper 2010-0356 (American Institute of Aeronautics and Astronautics, 2010).

J. C. Tannehill, D. A. Anderson, and R. H. Pletcher, Computational Fluid Mechanics and Heat Transfer (Taylor & Francis, 1997), Chap. 5.1.

S. K. Lele, “Direct numerical simulation of compressible free shear flows,” AIAA paper 1989-0374 (American Institute of Aeronautics and Astronautics, 1989).

N. D. Sandham and H. C. Yee, “A numerical study of a class of TVD schemes for compressible mixing layers,” NASA TM-102194 (NASA, 1989).

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Figures (8)

Fig. 1.
Fig. 1.

Schematic of spatially developing mixing layer.

Fig. 2.
Fig. 2.

(a) Density and (b) vorticity contours of the mixing layer at t = 640 .

Fig. 3.
Fig. 3.

(a) Temporal evolution of OPL at x = 291 and (b) its power spectrum.

Fig. 4.
Fig. 4.

Schematic of AO system designed for correcting the aero-optical aberration of the supersonic mixing layer.

Fig. 5.
Fig. 5.

Time diagram for one-sided averaged SPGD algorithm.

Fig. 6.
Fig. 6.

Correcting the aero-optical aberration at t = 640 with the AO we designed. (a) Comparison of the original (dashed line) and compensated OPL (solid line). (b) Evolution of global SR with Nstr = 1 , 2, 4, and 8.

Fig. 7.
Fig. 7.

Global SR curves obtained with AO correction based on traditional and modified SPGD. The parameters in the simulations are listed in the legends; more details are given in the text.

Fig. 8.
Fig. 8.

Global SR curves obtained with AO correction based SPGD with (a) finite memory and (b) the combined strategy. The parameters in the simulations are listed in the legends; more details are given in the text.

Tables (1)

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Table 1. Flow Variables in the DNS of Mixing Layer

Equations (17)

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U t + F x + G y = 0 ,
U = ( ρ , ρ ( e + u k u k / 2 ) , ρ u 1 , ρ u 2 ) , F = ( ρ u 1 , ρ ( e + u k u k / 2 ) u 1 + p u 1 τ 1 k u k + q 1 , ρ u 1 2 + p τ 11 , ρ u 1 u 2 τ 12 ) , G = ( ρ u 2 , ρ ( e + u k u k / 2 ) u 2 + p u 2 τ 2 k u k + q 2 , ρ u 1 u 2 τ 12 , ρ u 2 2 + p τ 22 ) .
Re = ρ * V * θ ω * / μ * ,
θ ω * = [ u ¯ 1 ( ) u ¯ 1 ( ) ] / ( d u ¯ 1 / d y ¯ ) max .
u 1 = U 1 + U 2 2 + U 1 U 2 2 tanh ( 2 y ) , u 2 = 0 .
M c = ( U 1 U 2 ) / ( c 1 + c 2 ) , U c = ( c 2 U 1 + c 1 U 2 ) / ( c 1 + c 2 ) ,
c 2 = c 1 2 + γ 1 2 ( u 1 2 u 2 ) .
ρ * = 0.037 kg m 3 , V * = 220 m s 1 ,
y = L y 2 sinh ( b y η ) sinh ( b y ) , b y = 3.4.
E ( f ) = ε ( f / f p ) 4 [ 1 + ( f / f p ) 2 ] 17 / 6 ,
L ( x , t ) = L y / 2 L y / 2 K GD ρ * ρ ( x , y ) d y ,
J ˜ i ( t ) = | S i A 0 exp [ i ϕ ( r , t ) ] d r | 2 ,
J i ( t ) = | 1 n A 0 exp [ i ϕ ( x k , t ) ] | 2 ,
u 1 = u 0 + γ { [ J ( t 0 + t a ) J ( t 0 ) ] δ u + [ J ( t 0 + 2 t a ) J ( t 0 + t a ) ] δ u } / 2 ,
h ( t ) = ( 1 / t m ) exp ( t / t m ) ,
u ( t ) = u 0 + ( 1 e t / t m ) ( u 1 u 0 ) .
u n + 1 = β u n + γ { [ J ( t n + t a ) J ( t n ) ] δ u + [ J ( t n + 2 t a ) J ( t n + t a ) ] δ u } / 2 ,

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