Abstract

We analyze the anisoplanatic adaptive receiver system field of view (FOV) and the possibility of controlling the system FOV by using an adaptive optics system with multiple wave-front sensors that sense wave-front phase aberrations of reference waves with different arrival angles. The conventional decoupled stochastic parallel gradient descent (D-SPGD) technique is generalized to include output signals from multiple wave-front sensors. The multiple-reference D-SPGD control algorithm introduced here is applied to obtain an anisotropic FOV in adaptive receiver systems by using two and three reference waves.

© 2004 Optical Society of America

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  1. M. Yu, M. A. Vorontsov, “Compensation of distant phase-distorting layers. I. Narrow-field-of-view adaptive receiver,” J. Opt. Soc. Am. A 21, 1645–1658 (2004).
    [CrossRef]
  2. M. A. Vorontsov, V. P. Sivokon, “Stochastic parallel-gradient-descent technique for high-resolution wave-front phase-distortion correction,” J. Opt. Soc. Am. A 15, 2745–2758 (1998).
    [CrossRef]
  3. M. A. Vorontsov, G. W. Garhart, M. Cohen, G. Cauwenberghs, “Adaptive optics based on analog parallel stochastic optimization: analysis and experimental demonstration,” J. Opt. Soc. Am. A 17, 1440–1453 (2000).
    [CrossRef]
  4. 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]
  5. J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, New York, 1998).
  6. D. L. Fried, “Anisoplanatism in adaptive optics,” J. Opt. Soc. Am. 72, 52–56 (1982).
    [CrossRef]
  7. F. Roddier, Adaptive Optics in Astronomy (Cambridge U. Press, New York, 1999).
  8. T. Fusco, J. M. Conan, L. M. Mugnier, V. Michau, G. Rousset, “Characterization of adaptive optics point spread function for anisoplanatic imaging: application to stellar field deconvolution,” Astron. Astrophys. 142, 149–156 (2000).
  9. B. L. Ellerbroek, “First-order performance evaluation of adaptive-optics systems for atmospheric-turbulence compensation in extended-field-of-view astronomical telescopes,” J. Opt. Soc. Am. A 11, 783–805 (1994).
    [CrossRef]
  10. B. L. Ellerbroek, F. Rigaut, “Methods for correcting tilt anisoplanatism in laser-guide-star-based multiconjugate adaptive optics,” J. Opt. Soc. Am. A 18, 2539–2547 (2001).
    [CrossRef]
  11. D. C. Johnson, B. M. Welsh, “Analysis of multiconjugate adaptive optics,” J. Opt. Soc. Am. A 11, 394–408 (1994).
    [CrossRef]
  12. V. V. Voitsekhovich, S. Bara, “Effect of anisotropic imaging in off-axis adaptive astronomical systems,” Astron. Astrophys., Suppl. Ser. 137, 385–389 (1999).
    [CrossRef]
  13. N. Ageorges, C. Dainty, Laser Guide Star Adaptive Optics for Astronomy (Kluwer Academic, Dordrecht, The Netherlands, 2000).
  14. J. L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazallet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 meter telescope,” in Adaptive Optics in Astronomy, F. Merkle, ed., Proc. SPIE2201, 955–960 (1994).
    [CrossRef]
  15. E. Kibblewhite, “Laser beacons for astronomy,” in Laser Guide Star Adaptive Optics, R. Q. Fugate, ed. (Philips Laboratory, Kirtland Air Force Base, N.M., 1992), pp. 24–36.
  16. M. Tallon, R. Foy, “Adaptive telescope with laser probe: isoplanatism and cone effect,” Astron. Astrophys. 235, 549–557 (1990).
  17. B. M. Welsh, C. S. Gardner, “Effects of turbulence-induced anisoplanatism on the imaging performance of adaptive-astronomical telescopes using laser guide stars,” J. Opt. Soc. Am. A 8, 69–80 (1991).
    [CrossRef]
  18. M. Le Louarn, “Multi-conjugated adaptive optics with laser guide stars: performance in the infrared and visible,” Mon. Not. R. Astron. Soc. 334, 865–874 (2002).
    [CrossRef]
  19. M. Le Louarn, M. Tallon, “Analysis of modes and behavior of a multiconjugate adaptive optics system,” J. Opt. Soc. Am. A 19, 912–925 (2002).
    [CrossRef]
  20. T. R. O’Meara, “The multi-dither principle in adaptive optics,” J. Opt. Soc. Am. 67, 306–315 (1977).
    [CrossRef]
  21. J. C. Spall, Introduction to Stochastic Search and Optimization (Wiley, New York, 2003).
  22. A. Cichocki, R. Unbehauen, Neural Networks for Optimization and Signal Processing (Wiley, New York, 1993).
  23. C. Flicker, “Sequence of phase correction in multiconjugate adaptive optics,” Opt. Lett. 26, 1743–1745 (2001).
    [CrossRef]
  24. A. Tokovinin, M. Le Louarn, M. Sarazin, “Isoplanatism in multi-conjugate adaptive optics systems,” J. Opt. Soc. Am. A 17, 1819–1827 (2000).
    [CrossRef]

2004 (1)

2002 (3)

2001 (2)

2000 (3)

1999 (1)

V. V. Voitsekhovich, S. Bara, “Effect of anisotropic imaging in off-axis adaptive astronomical systems,” Astron. Astrophys., Suppl. Ser. 137, 385–389 (1999).
[CrossRef]

1998 (1)

1994 (2)

1991 (1)

1990 (1)

M. Tallon, R. Foy, “Adaptive telescope with laser probe: isoplanatism and cone effect,” Astron. Astrophys. 235, 549–557 (1990).

1982 (1)

1977 (1)

Ageorges, N.

N. Ageorges, C. Dainty, Laser Guide Star Adaptive Optics for Astronomy (Kluwer Academic, Dordrecht, The Netherlands, 2000).

Bara, S.

V. V. Voitsekhovich, S. Bara, “Effect of anisotropic imaging in off-axis adaptive astronomical systems,” Astron. Astrophys., Suppl. Ser. 137, 385–389 (1999).
[CrossRef]

Beuzit, J. L.

J. L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazallet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 meter telescope,” in Adaptive Optics in Astronomy, F. Merkle, ed., Proc. SPIE2201, 955–960 (1994).
[CrossRef]

Cauwenberghs, G.

Chazallet, F.

J. L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazallet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 meter telescope,” in Adaptive Optics in Astronomy, F. Merkle, ed., Proc. SPIE2201, 955–960 (1994).
[CrossRef]

Cichocki, A.

A. Cichocki, R. Unbehauen, Neural Networks for Optimization and Signal Processing (Wiley, New York, 1993).

Cohen, M.

Conan, J. M.

T. Fusco, J. M. Conan, L. M. Mugnier, V. Michau, G. Rousset, “Characterization of adaptive optics point spread function for anisoplanatic imaging: application to stellar field deconvolution,” Astron. Astrophys. 142, 149–156 (2000).

Dainty, C.

N. Ageorges, C. Dainty, Laser Guide Star Adaptive Optics for Astronomy (Kluwer Academic, Dordrecht, The Netherlands, 2000).

Demailly, L.

J. L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazallet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 meter telescope,” in Adaptive Optics in Astronomy, F. Merkle, ed., Proc. SPIE2201, 955–960 (1994).
[CrossRef]

Ellerbroek, B. L.

Flicker, C.

Foy, R.

M. Tallon, R. Foy, “Adaptive telescope with laser probe: isoplanatism and cone effect,” Astron. Astrophys. 235, 549–557 (1990).

Fried, D. L.

Fusco, T.

T. Fusco, J. M. Conan, L. M. Mugnier, V. Michau, G. Rousset, “Characterization of adaptive optics point spread function for anisoplanatic imaging: application to stellar field deconvolution,” Astron. Astrophys. 142, 149–156 (2000).

Gardner, C. S.

Garhart, G. W.

Gendron, E.

J. L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazallet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 meter telescope,” in Adaptive Optics in Astronomy, F. Merkle, ed., Proc. SPIE2201, 955–960 (1994).
[CrossRef]

Gigan, P.

J. L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazallet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 meter telescope,” in Adaptive Optics in Astronomy, F. Merkle, ed., Proc. SPIE2201, 955–960 (1994).
[CrossRef]

Hardy, J. W.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, New York, 1998).

Hubin, N.

J. L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazallet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 meter telescope,” in Adaptive Optics in Astronomy, F. Merkle, ed., Proc. SPIE2201, 955–960 (1994).
[CrossRef]

Johnson, D. C.

Kibblewhite, E.

E. Kibblewhite, “Laser beacons for astronomy,” in Laser Guide Star Adaptive Optics, R. Q. Fugate, ed. (Philips Laboratory, Kirtland Air Force Base, N.M., 1992), pp. 24–36.

Lacombe, F.

J. L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazallet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 meter telescope,” in Adaptive Optics in Astronomy, F. Merkle, ed., Proc. SPIE2201, 955–960 (1994).
[CrossRef]

Le Louarn, M.

Michau, V.

T. Fusco, J. M. Conan, L. M. Mugnier, V. Michau, G. Rousset, “Characterization of adaptive optics point spread function for anisoplanatic imaging: application to stellar field deconvolution,” Astron. Astrophys. 142, 149–156 (2000).

Mugnier, L. M.

T. Fusco, J. M. Conan, L. M. Mugnier, V. Michau, G. Rousset, “Characterization of adaptive optics point spread function for anisoplanatic imaging: application to stellar field deconvolution,” Astron. Astrophys. 142, 149–156 (2000).

O’Meara, T. R.

Rabaud, D.

J. L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazallet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 meter telescope,” in Adaptive Optics in Astronomy, F. Merkle, ed., Proc. SPIE2201, 955–960 (1994).
[CrossRef]

Rigaut, F.

Roddier, F.

F. Roddier, Adaptive Optics in Astronomy (Cambridge U. Press, New York, 1999).

Rousset, G.

T. Fusco, J. M. Conan, L. M. Mugnier, V. Michau, G. Rousset, “Characterization of adaptive optics point spread function for anisoplanatic imaging: application to stellar field deconvolution,” Astron. Astrophys. 142, 149–156 (2000).

J. L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazallet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 meter telescope,” in Adaptive Optics in Astronomy, F. Merkle, ed., Proc. SPIE2201, 955–960 (1994).
[CrossRef]

Sarazin, M.

Sivokon, V. P.

Spall, J. C.

J. C. Spall, Introduction to Stochastic Search and Optimization (Wiley, New York, 2003).

Tallon, M.

M. Le Louarn, M. Tallon, “Analysis of modes and behavior of a multiconjugate adaptive optics system,” J. Opt. Soc. Am. A 19, 912–925 (2002).
[CrossRef]

M. Tallon, R. Foy, “Adaptive telescope with laser probe: isoplanatism and cone effect,” Astron. Astrophys. 235, 549–557 (1990).

Tokovinin, A.

Unbehauen, R.

A. Cichocki, R. Unbehauen, Neural Networks for Optimization and Signal Processing (Wiley, New York, 1993).

Voitsekhovich, V. V.

V. V. Voitsekhovich, S. Bara, “Effect of anisotropic imaging in off-axis adaptive astronomical systems,” Astron. Astrophys., Suppl. Ser. 137, 385–389 (1999).
[CrossRef]

Vorontsov, M. A.

Welsh, B. M.

Yu, M.

Astron. Astrophys. (2)

T. Fusco, J. M. Conan, L. M. Mugnier, V. Michau, G. Rousset, “Characterization of adaptive optics point spread function for anisoplanatic imaging: application to stellar field deconvolution,” Astron. Astrophys. 142, 149–156 (2000).

M. Tallon, R. Foy, “Adaptive telescope with laser probe: isoplanatism and cone effect,” Astron. Astrophys. 235, 549–557 (1990).

Astron. Astrophys., Suppl. Ser. (1)

V. V. Voitsekhovich, S. Bara, “Effect of anisotropic imaging in off-axis adaptive astronomical systems,” Astron. Astrophys., Suppl. Ser. 137, 385–389 (1999).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (10)

M. Le Louarn, M. Tallon, “Analysis of modes and behavior of a multiconjugate adaptive optics system,” J. Opt. Soc. Am. A 19, 912–925 (2002).
[CrossRef]

A. Tokovinin, M. Le Louarn, M. Sarazin, “Isoplanatism in multi-conjugate adaptive optics systems,” J. Opt. Soc. Am. A 17, 1819–1827 (2000).
[CrossRef]

B. M. Welsh, C. S. Gardner, “Effects of turbulence-induced anisoplanatism on the imaging performance of adaptive-astronomical telescopes using laser guide stars,” J. Opt. Soc. Am. A 8, 69–80 (1991).
[CrossRef]

B. L. Ellerbroek, “First-order performance evaluation of adaptive-optics systems for atmospheric-turbulence compensation in extended-field-of-view astronomical telescopes,” J. Opt. Soc. Am. A 11, 783–805 (1994).
[CrossRef]

B. L. Ellerbroek, F. Rigaut, “Methods for correcting tilt anisoplanatism in laser-guide-star-based multiconjugate adaptive optics,” J. Opt. Soc. Am. A 18, 2539–2547 (2001).
[CrossRef]

D. C. Johnson, B. M. Welsh, “Analysis of multiconjugate adaptive optics,” J. Opt. Soc. Am. A 11, 394–408 (1994).
[CrossRef]

M. Yu, M. A. Vorontsov, “Compensation of distant phase-distorting layers. I. Narrow-field-of-view adaptive receiver,” J. Opt. Soc. Am. A 21, 1645–1658 (2004).
[CrossRef]

M. A. Vorontsov, V. P. Sivokon, “Stochastic parallel-gradient-descent technique for high-resolution wave-front phase-distortion correction,” J. Opt. Soc. Am. A 15, 2745–2758 (1998).
[CrossRef]

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

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]

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

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

Opt. Lett. (1)

Other (7)

J. C. Spall, Introduction to Stochastic Search and Optimization (Wiley, New York, 2003).

A. Cichocki, R. Unbehauen, Neural Networks for Optimization and Signal Processing (Wiley, New York, 1993).

F. Roddier, Adaptive Optics in Astronomy (Cambridge U. Press, New York, 1999).

N. Ageorges, C. Dainty, Laser Guide Star Adaptive Optics for Astronomy (Kluwer Academic, Dordrecht, The Netherlands, 2000).

J. L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazallet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 meter telescope,” in Adaptive Optics in Astronomy, F. Merkle, ed., Proc. SPIE2201, 955–960 (1994).
[CrossRef]

E. Kibblewhite, “Laser beacons for astronomy,” in Laser Guide Star Adaptive Optics, R. Q. Fugate, ed. (Philips Laboratory, Kirtland Air Force Base, N.M., 1992), pp. 24–36.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, New York, 1998).

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Figures (6)

Fig. 1
Fig. 1

Schematic of adaptive system with D-SPGD controller and a single distant phase-distorting layer located at the plane z=0.

Fig. 2
Fig. 2

Angular dependence of the ensemble-averaged Strehl ratio 〈St〉 for D-SPGD adaptive on-axis compensation of a distant phase-distorting layer for different values of Dc/r0: near-field approximation (solid curves) and quasi-optical approximation (dashed curves). The uncompensated Strehl ratio values St0 are shown by diamonds. The gray-scale images at right represent focal-plane intensity distributions: a, diffraction limited and b–f for a phase-distorting layer with Dc/r0=6. Focal-plane intensity distributions are shown, b, for uncompensated and c, d, for compensated on-axis waves, where b and c are obtained in the near field and d in the quasi-optical approximation for l=0.03ld (ld=0.5ka2). Images e and f are obtained for θ=θ1=0.06θD for the near-field and the quasi-optical approximations (l=0.03ld), respectively. Each intensity distribution in a–f is normalized by its own maximum value.

Fig. 3
Fig. 3

Schematics of the D-SPGD adaptive receiver systems operating with two reference sources (A and B) and a single wave-front corrector. The two near-field wave-front sensors SensorA and SensorB are in planes conjugate to the telescope pupil plane formed by beam splitters BS and the re-imaging lenses LA and LB. Diaphragms DA and DB provide narrow FOV sensing of wave-front distortions corresponding to each of the two reference waves. Feedback control in a is based solely on information obtained from the near-field sensors (conventional D-SPGD controller). The multiple-reference (MR) D-SPGD controller in (b) is based on both far-field (StA and StB) and near-field sensor outputs. The far-field sensors are composed of pinhole diaphragms and photodetectors PDA and PDB. The wave vector geometry for the reference and off-axis waves is illustrated in c.

Fig. 4
Fig. 4

Extended-FOV D-SPGD compensation with two reference waves and a single wave-front corrector. Ensemble-averaged Strehl ratio profiles St(θx, θy=0) in a, c, and d and St(θx=0, θy) in b are obtained after MR D-SPGD compensation: a and b correspond to different angular distances θAB between the reference waves (Dc/r0=6.0), and c corresponds to different parameters Dc/r0 with θAB/θD=0.2. The dashed curves in both a and b correspond to compensation with a single reference wave. The dashed curves in c correspond to a D-SPGD process converging to a local minimum for Dc/r0=6.0. The dotted curve in a is obtained for θAB/θD=0.4 with partitioning of the wave-front corrector area into two sections, each with 16×32 actuators. Each section is controlled with a separate wave-front sensor. The Strehl ratio profiles in a–c are obtained in the near-field approximation, and d corresponds to the quasi-optical approximation for different propagation distances l/ld. The dashed curve in d corresponds to the near-field approximation. In d, the Strehl ratio profiles are shown for offset angles normalized by both the angle θD and the isoplanatic angle θ0 (indicated by arrows).

Fig. 5
Fig. 5

Effect of wave-front corrector resolution on phase-aberration compensation efficiency with two reference waves for the near-field approximation and Dc/r0=6. The ensemble-averaged Strehl ratio profiles St(θx, 0), a and St(0, θy), b, correspond to a piston-type wave-front corrector array with different numbers of actuators N. Control parameters are optimized separately for each N in a and b.

Fig. 6
Fig. 6

Extended-FOV D-SPGD compensation with three reference waves and a single wave-front corrector, for ensemble-averaged Strehl ratio profiles St(θx, 0), a; St(θx, -3θs/4), b; and St(0, θy), c. The dashed curves in a–c correspond to results obtained for two-reference compensation with an angular distance θAB/θD=0.1. The geometry indicating reference wave propagation directions is illustrated in the right top corner of a–c.

Equations (10)

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Jδ[u]1SΩC[δA2(r)+δB2(r)]d2r,
StABStA+StB.
J3AB=J3A+J3B=j=1N(I¯jA+I¯jB)=ΩCIδA(r)d2r+ΩCIδB(r)d2r.
J=j=1Ngβjjj,
jl={0,, 0,jl, 0,, 0},
uj(n+1)=uj(n)+γ(n)[βAnδI¯jA(n)+βBnδI¯jB(n)]δuj(n)
(j=1,, N).
βA(n)=StB(n)StA(n)+StB(n),βB(n)=StA(n)StA(n)+StB(n),
βj(n)=ljNgStl(n)l=1NgStl(n),
uj(n+1)=uj(n)+γ(n)l=1NgβlnδI¯j,l(n)δuj(n)(j=1,, N),

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