Abstract

A scalable adaptive optics (AO) control system architecture composed of asynchronous control clusters based on the stochastic parallel gradient descent (SPGD) optimization technique is discussed. It is shown that subdivision of the control channels into asynchronous SPGD clusters improves the AO system performance by better utilizing individual and/or group characteristics of adaptive system components. Results of numerical simulations are presented for two different adaptive receiver systems based on asynchronous SPGD clusters—one with a single deformable mirror with Zernike response functions and a second with tip–tilt and segmented wavefront correctors. We also discuss adaptive wavefront control based on asynchronous parallel optimization of several local performance metrics—a control architecture referred to as distributed adaptive optics (DAO). Analysis of the DAO system architecture demonstrated the potential for significant increase of the adaptation process convergence rate that occurs due to partial decoupling of the system control clusters optimizing individual performance metrics.

© 2006 Optical Society of America

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References

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  1. J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, 1998).
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  4. G. W. Carhart, M. A. Vorontsov, L. A. Beresnev, P. S. Paicopolis, and F. K. Beil, "Atmospheric laser communication system with wide angle tracking and adaptive compensation," in Free-Space Laser Communication V, Proc. SPIE 5892, 589211-1-589211-12 (2005).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  11. S. L. Lachinova and M. A. Vorontsov, "Performance analysis of an adaptive phase-locked tiled fiber array in atmospheric turbulence conditions," in Target In the Loop: Atmospheric Tracking, Imaging and Compensation, Proc. SPIE 5895, 58950O-1-58950O-09 (2005).
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    [CrossRef]
  13. J. C. Spall, Introduction to Stochastic Search and Optimization (Wiley, 2003).
    [CrossRef]
  14. A. N. Kolmogorov, "The local structure of turbulence in incompressible viscous fluids for very large Reynolds numbers," Dokl. Akad. Nauk SSSR 30, 301ff (1941).
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    [CrossRef]

2005 (1)

T. Weyrauch and M. A. Vorontsov, "Atmospheric compensation with a speckle beacon under strong scintillation conditions: directed energy and laser communication applications," Appl. Opt. 44, 1-14 (2005).
[CrossRef]

2004 (2)

N. Nicolle, T. Fusco, G. Rousset, and V. Michau, "Improvement of Shack-Hartmann wavefront sensor measurement for extreme adaptive optics," Opt. Lett. 29, 2743-2745 (2004).
[CrossRef] [PubMed]

T. Weyrauch and M. A. Vorontsov, "Free-space laser communications with adaptive optics: atmospheric compensation experiments," in J. Opt. Fiber. Commun. Rep. 1, 355-379 (2004).
[CrossRef]

2002 (1)

2000 (1)

1998 (1)

1997 (1)

1994 (1)

1974 (1)

1966 (1)

1941 (1)

A. N. Kolmogorov, "The local structure of turbulence in incompressible viscous fluids for very large Reynolds numbers," Dokl. Akad. Nauk SSSR 30, 301ff (1941).

Beil, F. K.

G. W. Carhart, M. A. Vorontsov, L. A. Beresnev, P. S. Paicopolis, and F. K. Beil, "Atmospheric laser communication system with wide angle tracking and adaptive compensation," in Free-Space Laser Communication V, Proc. SPIE 5892, 589211-1-589211-12 (2005).

Beresnev, L. A.

G. W. Carhart, M. A. Vorontsov, L. A. Beresnev, P. S. Paicopolis, and F. K. Beil, "Atmospheric laser communication system with wide angle tracking and adaptive compensation," in Free-Space Laser Communication V, Proc. SPIE 5892, 589211-1-589211-12 (2005).

Buffington, A.

Carhart, G. W.

Cauwenberghs, G.

Cohen, M.

Fried, D. L.

Fusco, T.

Hardy, J. W.

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

Johnston, D. C.

Kolmogorov, A. N.

A. N. Kolmogorov, "The local structure of turbulence in incompressible viscous fluids for very large Reynolds numbers," Dokl. Akad. Nauk SSSR 30, 301ff (1941).

Lachinova, S. L.

S. L. Lachinova and M. A. Vorontsov, "Performance analysis of an adaptive phase-locked tiled fiber array in atmospheric turbulence conditions," in Target In the Loop: Atmospheric Tracking, Imaging and Compensation, Proc. SPIE 5895, 58950O-1-58950O-09 (2005).

Madec, P.

P. Madec, "Control techniques," in Adaptive Optics in Astronomy, F.Roddier, ed. (Cambridge U. Press, 1999), pp. 131-154.
[CrossRef]

Michau, V.

Muller, R. A.

Nicolle, N.

Paicopolis, P. S.

G. W. Carhart, M. A. Vorontsov, L. A. Beresnev, P. S. Paicopolis, and F. K. Beil, "Atmospheric laser communication system with wide angle tracking and adaptive compensation," in Free-Space Laser Communication V, Proc. SPIE 5892, 589211-1-589211-12 (2005).

Ricklin, J. C.

Rousset, G.

Sivokon, V. P.

Spall, J. C.

J. C. Spall, Introduction to Stochastic Search and Optimization (Wiley, 2003).
[CrossRef]

Vorontsov, M. A.

T. Weyrauch and M. A. Vorontsov, "Atmospheric compensation with a speckle beacon under strong scintillation conditions: directed energy and laser communication applications," Appl. Opt. 44, 1-14 (2005).
[CrossRef]

T. Weyrauch and M. A. Vorontsov, "Free-space laser communications with adaptive optics: atmospheric compensation experiments," in J. Opt. Fiber. Commun. Rep. 1, 355-379 (2004).
[CrossRef]

M. A. Vorontsov, "Decoupled stochastic gradient descent optimization for adaptive optics: integrated approach for wave-front sensor information fusion," J. Opt. Soc. Am. A 19, 356-368 (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. A 17, 1440-1453 (2000).
[CrossRef]

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

S. L. Lachinova and M. A. Vorontsov, "Performance analysis of an adaptive phase-locked tiled fiber array in atmospheric turbulence conditions," in Target In the Loop: Atmospheric Tracking, Imaging and Compensation, Proc. SPIE 5895, 58950O-1-58950O-09 (2005).

G. W. Carhart, M. A. Vorontsov, L. A. Beresnev, P. S. Paicopolis, and F. K. Beil, "Atmospheric laser communication system with wide angle tracking and adaptive compensation," in Free-Space Laser Communication V, Proc. SPIE 5892, 589211-1-589211-12 (2005).

Welsh, B. M.

Weyrauch, T.

T. Weyrauch and M. A. Vorontsov, "Atmospheric compensation with a speckle beacon under strong scintillation conditions: directed energy and laser communication applications," Appl. Opt. 44, 1-14 (2005).
[CrossRef]

T. Weyrauch and M. A. Vorontsov, "Free-space laser communications with adaptive optics: atmospheric compensation experiments," in J. Opt. Fiber. Commun. Rep. 1, 355-379 (2004).
[CrossRef]

Appl. Opt. (1)

T. Weyrauch and M. A. Vorontsov, "Atmospheric compensation with a speckle beacon under strong scintillation conditions: directed energy and laser communication applications," Appl. Opt. 44, 1-14 (2005).
[CrossRef]

Dokl. Akad. Nauk SSSR (1)

A. N. Kolmogorov, "The local structure of turbulence in incompressible viscous fluids for very large Reynolds numbers," Dokl. Akad. Nauk SSSR 30, 301ff (1941).

J. Opt. Fiber. Commun. Rep. (1)

T. Weyrauch and M. A. Vorontsov, "Free-space laser communications with adaptive optics: atmospheric compensation experiments," in J. Opt. Fiber. Commun. Rep. 1, 355-379 (2004).
[CrossRef]

J. Opt. Soc. Am. (2)

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

Opt. Lett. (2)

Other (5)

P. Madec, "Control techniques," in Adaptive Optics in Astronomy, F.Roddier, ed. (Cambridge U. Press, 1999), pp. 131-154.
[CrossRef]

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

G. W. Carhart, M. A. Vorontsov, L. A. Beresnev, P. S. Paicopolis, and F. K. Beil, "Atmospheric laser communication system with wide angle tracking and adaptive compensation," in Free-Space Laser Communication V, Proc. SPIE 5892, 589211-1-589211-12 (2005).

J. C. Spall, Introduction to Stochastic Search and Optimization (Wiley, 2003).
[CrossRef]

S. L. Lachinova and M. A. Vorontsov, "Performance analysis of an adaptive phase-locked tiled fiber array in atmospheric turbulence conditions," in Target In the Loop: Atmospheric Tracking, Imaging and Compensation, Proc. SPIE 5895, 58950O-1-58950O-09 (2005).

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Figures (8)

Fig. 1
Fig. 1

Schematic of an AO receiver system with wavefront control channels distributed between AO control clusters. Propagation of optical wave A 0 through a distorting layer results in phase aberration φ ( r , t ) of received input wave A in ( r , t ) that enters the optical receiver system (shown by a cylinder). Here r = { x , y } is a coordinate vector orthogonal to the AO system’s optical axis and t is the time. The receiver system optical train contains one or more wavefront correctors (not shown). The receiver output wave A out ( r , t ) with phase δ ( r , t ) (residual phase) enters a system performance metric sensor sensitive to the residual phase aberration. The metric signal J is sent to controllers (control clusters) that compute voltages { u l , j } that are applied to the wavefront corrector’s electrodes. (a) Gray-scale images at right are examples of the pupil plane phase aberration, (b) the phase correction at each subaperture of the segmented wavefront corrector (described in the text) having seven subapertures, and (c) the residual phase distortion.

Fig. 2
Fig. 2

Operational time diagrams for two asynchronous SPGD clusters. Arrows indicate the moments of metric measurements (dashed lines) and the control voltage updates and perturbations (solid lines).

Fig. 3
Fig. 3

Characteristic diagrams of time responses { τ j } for adaptive system with N c asynchronous control clusters. (a) Definitions of time offsets Δ and Δ τ in Eq. (10), (b)–(d) correspond to the numerical simulation results as described in the text.

Fig. 4
Fig. 4

Atmospheric-average Strehl metric evolution curves St ( t ) obtained for the conventional SPGD system (curve 1), and for the control system with seven asynchronous SPGD clusters (curves 2–4). The cluster time response parameters correspond to the diagrams are shown in Fig. 3: (b) for curve 2, (c) for curve 4, and (d) for curve 1. The compensation level ⟨St⟩ is defined as the ideal compensation is calculated using Strehl metric calculation based on residual phase aberrations δ ( r ) = φ ( r ) φ Z ( r ) , where phase function φ Z ( r ) corresponds to the approximation of function φ ( r ) with first N Z Zernike polynomials. Numerical simulations are performed for the Kolmogorov turbulence model with D r 0 = 4 .

Fig. 5
Fig. 5

Strehl ratio evolution curves St ( t ) for SPGD (dashed lines) and the SPGD cluster (solid lines) AO system architectures for different atmospheric turbulence strengths defined by the D r 0 ratio. The clusters’ time responses correspond to diagram (b) in Fig. 3.

Fig. 6
Fig. 6

Strehl ratio atmospheric-average adaptation curves St ( t ) for the control system architecture shown in Fig. 1 with a segmented mirror (seven subapertures) and a tip–tilt mirror. A single metric (Strehl ratio) is used to control all channels. Control is based on asynchronous SPGD clusters for (a)–(d) and the conventional SPGD approach for (e). Numerical simulations are performed for D r 0 = 4 , N Z = 32 , β τ = τ max τ min = 4 and β T = 2 .

Fig. 7
Fig. 7

Schematic of the AO receiver system with distributed control based on asynchronous SPGD clusters. The system includes a segmented mirror with seven subapertures and a tip–tilt mirror. For both the piston and tip–tilt control clusters the global metric J is used. The local metrics { J j } that correspond to the segmented mirror subapertures are used for controlling of low-order aberrations at the segmented mirror subapertures.

Fig. 8
Fig. 8

Strehl ratio atmospheric-average adaptation curves for the DAO control systems architectures shown in Fig. 7 [curves (a)–(c)] and for the AO system architecture in Fig. 1 with asynchronous SPGD control using a simple metric [curves (d)–(f)]. In both cases control is based on asynchronous SPGD clusters with the following time responses: τ max = τ SM τ min = τ TM = τ p (slow segmented mirror) for curves (c) and (f); τ max = τ p , τ min = τ SM = τ TM (slow piston mirror) for (b) and (e); and τ min = τ TM = τ SM = τ p (equally fast control channels) for (a) and (d). Numerical simulations are performed for the Kolmogorov turbulence model with D r 0 = 8 and N Z = 32 .

Equations (16)

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u l , j ( n + 1 ) = u l , j ( n ) + γ j ( n ) δ J ( n ) δ u l , j ( n ) ,
τ j d v j ( t ) d t + v j ( t ) = u j ( t ) , j = 1 , , N c ,
u ( r , t ) = j = 1 N c v j ( t ) S j ( r ) ,
τ J d J ( t ) d t + J ( t ) = I ( t ) ,
u ( t n + 1 , j ) = u ( t n , j ) + γ j ( n ) δ J j ( n ) δ u ( t n + 1 , j ) , j = 1 , , N c ,
δ J j δ u l , j J j u l , j ( u l , j ) 2 + k l M j J j u k , j δ J k , j δ u l , j + q j N c k = 1 M k J j u k , q δ J k , q δ u l , j + q j N c k = 1 M k J j u k , q Δ u k , q δ u l , j .
Δ u l , j ( n ) = γ j ( n ) δ J j ( n ) δ u l , j ( n ) γ j ( n ) J j ( n ) u l , j ( n ) ( u l , j ( n ) ) 2 , j = 1 , , N c .
J ( t ) = A 0 exp [ i δ ( r , t ) ] d 2 r 2 .
u ( r , t ) = k = 1 N z v k ( t ) Z k ( r ) ,
τ 1 = τ max , τ 2 = τ 1 Δ , τ j = min { τ j } + ( N c j ) Δ τ , for j = 2 , , N c ,
u j ( r , t ) u j p ( r , t ) + u j a ( r , t ) = v 0 , j ( t ) Z 0 ( r r j ) + l = 1 N z v l , j ( t ) Z l ( r r j ) .
u SM ( r , t ) = j = 1 N c u j p ( r , t ) + j = 1 N c u j a ( r , t ) ,
A out ( r , t ) = A in exp [ i δ ( r , t ) ] = A in exp [ i φ ( r , t ) + i u SM ( r , t ) + i u TM ( r , t ) ] ,
τ SM d v j ( t ) d t + v j ( t ) = u j ( t ) j = 1 , , N c ,
τ p d v 0 ( t ) d t + v 0 ( t ) = u 0 ( t ) ,
τ TM d v T ( t ) d t + v T ( t ) = u T ( t ) ,

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