Abstract

The design of future single-altitude conjugated adaptive optics (AO) systems may include at least two deformable mirrors (DMs) instead of one as in the current AO system. Each DM will have to correct for a specific spatial frequency range. A method is presented to derive a DM modal basis based on the influence functions of the DM. The modal bases are derived such that they are orthogonal to a given set of modes that restrict the DM correction to a spatial frequency domain. The modal bases have been tested on the woofer–tweeter test bench at the University of Victoria. It has been shown that the rms amplitude of the woofer DM and tweeter DM stroke can be reduced by factors of 3 and 9, respectively, when making the transition from a zonal-driven closed loop to a modal-driven closed loop with the same performance in both cases.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Roggemann and D. Lee, "Two-deformable-mirror concept for correcting scintillation effects in laser beam projection through the turbulent atmosphere," Appl. Opt. 37, 4577-4585 (1998).
    [CrossRef]
  2. J. D. Barchers, "Application of the parallel generalized projection algorithm to the control of two finite-resolution deformable mirrors for scintillation compensation," J. Opt. Soc. Am. A 19, 54-63 (2002).
    [CrossRef]
  3. J. D. Barchers, "Closed-loop stable control of two deformable mirrors for compensation of amplitude and phase fluctuations," J. Opt. Soc. Am. A 19, 926-945 (2002).
    [CrossRef]
  4. J. D. Barchers, "Convergence rates for iterative vector space projection methods for control of two deformable mirrors for compensation of both amplitude and phase fluctuations," Appl. Opt. 41, 2213-2218 (2002).
    [CrossRef] [PubMed]
  5. H. Baumhacker, G. Pretzler, K. J. Witte, M. Hegelich, M. Kaluza, S. Karsch, A. Kudryashov, V. Samarkin, and A. Roukossouev, "Correction of strong phase and amplitude modulations by two deformable mirrors in a multistaged Ti:sapphire laser," Opt. Lett. 27, 1570-1572 (2002).
    [CrossRef]
  6. B. Ellerbroek, "First-order performance evaluation of adaptiveoptics systems for atmospheric-turbulence compensation in extended-field-of-view astronomical telescopes," J. Opt. Soc. Am. A 11, 783-805 (1994).
    [CrossRef]
  7. T. Fusco, J. Conan, G. Rousset, L. M. Mugnier, and V. Michan, "Optimal wave-front reconstruction strategies for multiconjugate adaptive optics," J. Opt. Soc. Am. A 18, 2527-2538 (2001).
    [CrossRef]
  8. F. Rigaut, "Atmospheric tomography with multi-conjugate adaptive optics," in Signal Recovery and Synthesis, Vol. 67 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001).
  9. R. C. Flicker, "Sequence of phase correction in multiconjugate adaptive optics," Opt. Lett. 26, 1743-1745 (2001).
    [CrossRef]
  10. M. Le Louarn, "Multi-conjugate adaptive optics with laser guide stars: performance in the infrared and visible," Mon. Not. R. Astron. Soc. 334, 865-874 (2002).
    [CrossRef]
  11. S. Hu, B. Xu, X. Zhang, J. Hou, J. Wu, and W. Jiang, "Double-deformable-mirror concept for correcting scintillation effects in laser beam projection through the turbulent atmosphere," Appl. Opt. 45, 2638-2642 (2006).
    [CrossRef] [PubMed]
  12. O. Keskin, L. Jolissaint, and C. Bradley, "Hot-air optical turbulence generator for the testing of adaptive optics systems: principles and characterization," Appl. Opt. 45, 4888-4897 (2006).
    [CrossRef] [PubMed]
  13. O. Cugat, S. Basrour, C. Divoux, P. Mounaix, and G. Reyne, "Deformable magnetic mirror for adaptive optics: technological aspects," Sens. Actuators A 89, 1-9 (2001).
    [CrossRef]
  14. http://www.alpao.fr/.
  15. W. J. Vetter, "Derivative operations on matrices," IEEE Trans. Auto. Control 15, 241-244 (1970).
    [CrossRef]
  16. R. Noll, "Zernike polynomials and atmospheric turbulence," J. Opt. Soc. Am. 66, 207-211 (1976).
    [CrossRef]
  17. J. Beckers, P. Lena, O. Lai, P. Madec, G. Rousset, M. Sechand, M. Northcott, F. Roddier, J. Beuzit, F. Rigaut, and D. Sandler, Adaptive Optics in Astronomy (Cambridge U. Press, 1999).

2006 (2)

2002 (5)

2001 (3)

1998 (1)

1994 (1)

1976 (1)

1970 (1)

W. J. Vetter, "Derivative operations on matrices," IEEE Trans. Auto. Control 15, 241-244 (1970).
[CrossRef]

Barchers, J. D.

Basrour, S.

O. Cugat, S. Basrour, C. Divoux, P. Mounaix, and G. Reyne, "Deformable magnetic mirror for adaptive optics: technological aspects," Sens. Actuators A 89, 1-9 (2001).
[CrossRef]

Baumhacker, H.

Beckers, J.

J. Beckers, P. Lena, O. Lai, P. Madec, G. Rousset, M. Sechand, M. Northcott, F. Roddier, J. Beuzit, F. Rigaut, and D. Sandler, Adaptive Optics in Astronomy (Cambridge U. Press, 1999).

Beuzit, J.

J. Beckers, P. Lena, O. Lai, P. Madec, G. Rousset, M. Sechand, M. Northcott, F. Roddier, J. Beuzit, F. Rigaut, and D. Sandler, Adaptive Optics in Astronomy (Cambridge U. Press, 1999).

Bradley, C.

Conan, J.

Cugat, O.

O. Cugat, S. Basrour, C. Divoux, P. Mounaix, and G. Reyne, "Deformable magnetic mirror for adaptive optics: technological aspects," Sens. Actuators A 89, 1-9 (2001).
[CrossRef]

Divoux, C.

O. Cugat, S. Basrour, C. Divoux, P. Mounaix, and G. Reyne, "Deformable magnetic mirror for adaptive optics: technological aspects," Sens. Actuators A 89, 1-9 (2001).
[CrossRef]

Ellerbroek, B.

Flicker, R. C.

Fusco, T.

Hegelich, M.

Hou, J.

Hu, S.

Jiang, W.

Jolissaint, L.

Kaluza, M.

Karsch, S.

Keskin, O.

Kudryashov, A.

Lai, O.

J. Beckers, P. Lena, O. Lai, P. Madec, G. Rousset, M. Sechand, M. Northcott, F. Roddier, J. Beuzit, F. Rigaut, and D. Sandler, Adaptive Optics in Astronomy (Cambridge U. Press, 1999).

Le Louarn, M.

M. Le Louarn, "Multi-conjugate adaptive optics with laser guide stars: performance in the infrared and visible," Mon. Not. R. Astron. Soc. 334, 865-874 (2002).
[CrossRef]

Lee, D.

Lena, P.

J. Beckers, P. Lena, O. Lai, P. Madec, G. Rousset, M. Sechand, M. Northcott, F. Roddier, J. Beuzit, F. Rigaut, and D. Sandler, Adaptive Optics in Astronomy (Cambridge U. Press, 1999).

Madec, P.

J. Beckers, P. Lena, O. Lai, P. Madec, G. Rousset, M. Sechand, M. Northcott, F. Roddier, J. Beuzit, F. Rigaut, and D. Sandler, Adaptive Optics in Astronomy (Cambridge U. Press, 1999).

Michan, V.

Mounaix, P.

O. Cugat, S. Basrour, C. Divoux, P. Mounaix, and G. Reyne, "Deformable magnetic mirror for adaptive optics: technological aspects," Sens. Actuators A 89, 1-9 (2001).
[CrossRef]

Mugnier, L. M.

Noll, R.

Northcott, M.

J. Beckers, P. Lena, O. Lai, P. Madec, G. Rousset, M. Sechand, M. Northcott, F. Roddier, J. Beuzit, F. Rigaut, and D. Sandler, Adaptive Optics in Astronomy (Cambridge U. Press, 1999).

Pretzler, G.

Reyne, G.

O. Cugat, S. Basrour, C. Divoux, P. Mounaix, and G. Reyne, "Deformable magnetic mirror for adaptive optics: technological aspects," Sens. Actuators A 89, 1-9 (2001).
[CrossRef]

Rigaut, F.

F. Rigaut, "Atmospheric tomography with multi-conjugate adaptive optics," in Signal Recovery and Synthesis, Vol. 67 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001).

J. Beckers, P. Lena, O. Lai, P. Madec, G. Rousset, M. Sechand, M. Northcott, F. Roddier, J. Beuzit, F. Rigaut, and D. Sandler, Adaptive Optics in Astronomy (Cambridge U. Press, 1999).

Roddier, F.

J. Beckers, P. Lena, O. Lai, P. Madec, G. Rousset, M. Sechand, M. Northcott, F. Roddier, J. Beuzit, F. Rigaut, and D. Sandler, Adaptive Optics in Astronomy (Cambridge U. Press, 1999).

Roggemann, M.

Roukossouev, A.

Rousset, G.

T. Fusco, J. Conan, G. Rousset, L. M. Mugnier, and V. Michan, "Optimal wave-front reconstruction strategies for multiconjugate adaptive optics," J. Opt. Soc. Am. A 18, 2527-2538 (2001).
[CrossRef]

J. Beckers, P. Lena, O. Lai, P. Madec, G. Rousset, M. Sechand, M. Northcott, F. Roddier, J. Beuzit, F. Rigaut, and D. Sandler, Adaptive Optics in Astronomy (Cambridge U. Press, 1999).

Samarkin, V.

Sandler, D.

J. Beckers, P. Lena, O. Lai, P. Madec, G. Rousset, M. Sechand, M. Northcott, F. Roddier, J. Beuzit, F. Rigaut, and D. Sandler, Adaptive Optics in Astronomy (Cambridge U. Press, 1999).

Sechand, M.

J. Beckers, P. Lena, O. Lai, P. Madec, G. Rousset, M. Sechand, M. Northcott, F. Roddier, J. Beuzit, F. Rigaut, and D. Sandler, Adaptive Optics in Astronomy (Cambridge U. Press, 1999).

Vetter, W. J.

W. J. Vetter, "Derivative operations on matrices," IEEE Trans. Auto. Control 15, 241-244 (1970).
[CrossRef]

Witte, K. J.

Wu, J.

Xu, B.

Zhang, X.

Appl. Opt. (4)

IEEE Trans. Auto. Control (1)

W. J. Vetter, "Derivative operations on matrices," IEEE Trans. Auto. Control 15, 241-244 (1970).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Mon. Not. R. Astron. Soc. (1)

M. Le Louarn, "Multi-conjugate adaptive optics with laser guide stars: performance in the infrared and visible," Mon. Not. R. Astron. Soc. 334, 865-874 (2002).
[CrossRef]

Opt. Lett. (2)

Sens. Actuators A (1)

O. Cugat, S. Basrour, C. Divoux, P. Mounaix, and G. Reyne, "Deformable magnetic mirror for adaptive optics: technological aspects," Sens. Actuators A 89, 1-9 (2001).
[CrossRef]

Other (3)

http://www.alpao.fr/.

J. Beckers, P. Lena, O. Lai, P. Madec, G. Rousset, M. Sechand, M. Northcott, F. Roddier, J. Beuzit, F. Rigaut, and D. Sandler, Adaptive Optics in Astronomy (Cambridge U. Press, 1999).

F. Rigaut, "Atmospheric tomography with multi-conjugate adaptive optics," in Signal Recovery and Synthesis, Vol. 67 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2001).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (19)

Fig. 1
Fig. 1

Schematic diagram of the woofer–tweeter bench layout.

Fig. 2
Fig. 2

Woofer, tweeter, and SH-WFS registration. The dotted squares represent the lenslets used to sample the pupil, the circles are the locations of the tweeter actuators, and the gray diamonds show the woofer actuator positions.

Fig. 3
Fig. 3

Voltage versus stroke linearity curve of the tweeter actuators.

Fig. 4
Fig. 4

DM space modal basis B W of the tip–tilt-free woofer.

Fig. 5
Fig. 5

DM space modal basis B T of the tip–tilt-free tweeter.

Fig. 6
Fig. 6

Projection matrix W T of the tweeter influence functions T on the woofer influence functions W.

Fig. 7
Fig. 7

Projection matrix W T of the tweeter modes T on the woofer influence functions W. Compared with the projection matrix in Fig. 6, the range of the coefficients have been reduced by a factor of 10 4 .

Fig. 8
Fig. 8

DM space modal basis B T of the tip–tilt-free and woofer-free tweeter.

Fig. 9
Fig. 9

Measured zonal interaction matrices D z = [ D T T D W D T ] of, from left to right, the tip–tilt D T T , the zonal woofer D W , and the zonal tweeter D T .

Fig. 10
Fig. 10

Measured modal interaction matrices D = [ D T T D W D T ] of, from left to right, the tip–tilt D T T , the modal woofer D W , and the modal tweeter D T .

Fig. 11
Fig. 11

Top panel, comparison between the mean of the columns of the zonal D W and modal D W interaction matrices of the woofer. Bottom panel, comparison between the mean of the columns of the zonal D T and modal D T interaction matrices of the tweeter.

Fig. 12
Fig. 12

Eigenvalues of the zonal D W and modal D W interaction matrices of the woofer.

Fig. 13
Fig. 13

Eigenvalues of the zonal D T and modal D T interaction matrices of the tweeter.

Fig. 14
Fig. 14

Eigenvalues of the zonal D z and modal D interaction matrices.

Fig. 15
Fig. 15

Saturated tweeter with tip–tilt at rest and woofer correcting low orders.

Fig. 16
Fig. 16

Modal tweeter shape after woofer and modal tweeter successive closed loops. The woofer loop is closed after the tip–tilt loop, and the tip–tilt is set back to its rest position.

Fig. 17
Fig. 17

Tweeter shape after tip–tilt closed loop and woofer at rest.

Fig. 18
Fig. 18

Woofer shape after tip–tilt and woofer successive closed loops.

Fig. 19
Fig. 19

(a) Zonal and (b) modal woofer and (c) zonal and (d) modal tweeter shapes after closed loop with the three mirrors together.

Tables (3)

Tables Icon

Table 1 WFS Measurement and DM Actuator Dimensions

Tables Icon

Table 2 Woofer–Tweeter Bench Interaction Matrices

Tables Icon

Table 3 Woofer–Tweeter Bench Command Matrices

Equations (32)

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

J F = F Z P 2
J F P = P   trace ( F F T F P T Z T Z P F T + Z P P T Z T ) = 2 Z T F + 2 Z T Z P = 0
P = ( Z T Z ) 1 Z T F = Z F ,
F = F Z P
= F Z Z F = F B F .
B F = F F = I n F P P ,
W = W B W ,
T = T B T ,
B W = I P W P W , P W = Z 1 3 W ,
B T = I P T P T , P T = Z 1 3 T .
T = T B T ,
B T = I P T P T ,
P T = ( W ) T = B W 1 W T B T .
s = D c .
D z = [ D T T D W D T ] ,
D = [ D T T D W D T ]
J s = s D c 2
J s c = c   trace ( s s T s c T D T D c s T + D c c T D T ) = 2 D T s + 2 D T D c = 0 ,
c = ( D T D ) 1 D T s = D s ,
D = U Σ V T .
D = ( D T D ) 1 D T = V Σ U T ,
c m = [ c T T c W c T ] .
K = [ 1 0 0 1 0 0 0 B W 0 0 0 B T ] .
S = [ Δ m 0 ] .
A A = V S 1 U T U S V T = V S S V T ,
A A = U S V T V S U T = U S S U T ,
S S = [ Δ m 1 0 ] [ Δ m 0 ] = I m ,
S S = [ Δ m 0 ] [ Δ m 1 0 ] = [ I m 0 0 0 ] .
A A = I m ,
A A = U m U m T ,
A A = V n V n T ,
A A = I n ,

Metrics