Abstract

A wave-front control paradigm based on gradient-flow optimization is analyzed. In adaptive systems with gradient-flow dynamics, the output of the wave-front sensor is used to directly control high-resolution wave-front correctors without the need for wave-front phase reconstruction (direct-control systems). Here, adaptive direct-control systems with advanced phase-contrast wave-front sensors are analyzed theoretically, through numerical simulations, and experimentally. Adaptive system performance is studied for atmospheric- turbulence-induced phase distortions in the presence of input field intensity scintillations. The results demonstrate the effectiveness of this approach for high-resolution adaptive optics.

© 2001 Optical Society of America

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References

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  1. M. A. Vorontsov, E. W. Justh, Leonid A. Beresnev, “Adaptive Optics with advanced phase-contrast techniques: 1.High-resolution wave-front sensing,” J. Opt. Soc. Am. A 18, 1289–1299 (2001).
    [CrossRef]
  2. V. P. Sivokon, M. A. Vorontsov, “High-resolution adaptive phase distortion suppression based solely on intensity information,” J. Opt. Soc. Am. A 15, 234–247 (1998).
    [CrossRef]
  3. M. A. Vorontsov, “High-resolution adaptive phase distortion compensation using a diffractive-feedback system: experimental results,” J. Opt. Soc. Am. A 16, 2567–2573 (1999).
    [CrossRef]
  4. R. A. Muller, A. Buffington, “Real-time correction of atmospherically degraded telescope images through image sharpening,” J. Opt. Soc. Am. 64, 1200–1210 (1974).
    [CrossRef]
  5. T. R. O’Meara, “The multi-dither principle in adaptive optics,” J. Opt. Soc. Am. 67, 306–315 (1977).
    [CrossRef]
  6. M. A. Vorontsov, V. I. Shmalhauzen, Principles of Adaptive Optics (Nauka, Moscow, 1985).
  7. J. C. Spall, “A stochastic approximation technique for generating maximum likelihood parameter estimates,” in Proceedings of the American Control Conference (Institute of Electrical and Electronics Engineers, New York, 1987), pp. 1161-1167.
  8. G. Cauwenberghs, “A fast stochastic error-descent algorithm for supervised learning and optimization,” in Advances in Neural Information Processing Systems, S. J. Hanson, J. D. Cowan, C. L. Giles, eds. (Morgan Kaufman, San Mateo, Calif., Vol. 5, pp. 244–251, 1993).
  9. M. A. Vorontsov, G. W. Carhart, J. C. Ricklin, “Adaptive phase-distortion correction based on parallel gradient-descent optimization,” Opt. Lett. 22, 907–909 (1997).
    [CrossRef] [PubMed]
  10. M. A. Vorontsov, V. P. Sivokon, “Stochastic parallel gradient descent technique for high-resolution wavefront phase distortion correction,” J. Opt. Soc. Am. A 15, 2745–2758 (1998).
    [CrossRef]
  11. B. M. ter Haar Romey, ed., Geometry-Driven Diffusion in Computer Vision (Kluwer-Academic, Dordrecht, The Netherlands, 1994).
  12. IEEE Trans. Image Process. Special issue on partial differential equations and geometry-driven diffusion in image processing and analysis, IEEE Trans. Image Process. 7(3), (1998).
  13. M. A. Vorontsov, “Parallel image processing based on an evolution equation with anisotropic gain: integrated optoelectronic architectures,” J. Opt. Soc. Am. A 16, 1623–1637 (1999).
    [CrossRef]
  14. G. Cauwenberghs, M. A. Bayoumi, eds., Learning on Silicon (Kluwer Academic, Dordrecht, The Netherlands, 1999).
  15. A. G. Andreou, K. A. Boahen, “Translinear circuits in subthreshold MOS,” Analog Integr. Circuits Signal Process. 9, 141–166 (1996).
    [CrossRef]
  16. L. C. Andrews, “An analytic model for the refractive index power spectrum and its application to optical scintillations in the atmosphere,” J. Mod. Opt. 39, 1849–1853 (1992).
    [CrossRef]
  17. A. S. Michailov, A. Yu. Loscutov, Foundation of Synergetics (Springer-Verlag, Berlin, 1991).
  18. D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15, 2759–2768 (1998).
    [CrossRef]
  19. D. L. Fried, “Statistics of a geometric representation of wavefront distortion,” J. Opt. Soc. Am. 55, 1427–1435 (1965).
    [CrossRef]
  20. C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, J. Hermann, “Atmospheric-compensation experiments in strong-scintillation conditions,” Appl. Opt. 34, 2081–2088 (1995).
    [CrossRef] [PubMed]
  21. B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Broadband Networking Technologies, S. Civanlar, I. Widjaja, eds., Proc. SPIE3233, 221–232 (1998).
  22. F. Roddier, ed., Adaptive Optics in Astronomy (Cambridge U. Press, Cambridge, UK, 1999), pp. 91–130.
  23. M. A. Vorontsov, G. W. Carhart, 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]

2001 (1)

2000 (1)

1999 (2)

1998 (4)

1997 (1)

1996 (1)

A. G. Andreou, K. A. Boahen, “Translinear circuits in subthreshold MOS,” Analog Integr. Circuits Signal Process. 9, 141–166 (1996).
[CrossRef]

1995 (1)

1992 (1)

L. C. Andrews, “An analytic model for the refractive index power spectrum and its application to optical scintillations in the atmosphere,” J. Mod. Opt. 39, 1849–1853 (1992).
[CrossRef]

1977 (1)

1974 (1)

1965 (1)

Andreou, A. G.

A. G. Andreou, K. A. Boahen, “Translinear circuits in subthreshold MOS,” Analog Integr. Circuits Signal Process. 9, 141–166 (1996).
[CrossRef]

Andrews, L. C.

L. C. Andrews, “An analytic model for the refractive index power spectrum and its application to optical scintillations in the atmosphere,” J. Mod. Opt. 39, 1849–1853 (1992).
[CrossRef]

Barbier, P. R.

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Broadband Networking Technologies, S. Civanlar, I. Widjaja, eds., Proc. SPIE3233, 221–232 (1998).

Barclay, H. T.

Beresnev, Leonid A.

Boahen, K. A.

A. G. Andreou, K. A. Boahen, “Translinear circuits in subthreshold MOS,” Analog Integr. Circuits Signal Process. 9, 141–166 (1996).
[CrossRef]

Bruno, T. L.

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Broadband Networking Technologies, S. Civanlar, I. Widjaja, eds., Proc. SPIE3233, 221–232 (1998).

Buffington, A.

Burdge, G. L.

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Broadband Networking Technologies, S. Civanlar, I. Widjaja, eds., Proc. SPIE3233, 221–232 (1998).

Carhart, G. W.

Cauwenberghs, G.

M. A. Vorontsov, G. W. Carhart, 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]

G. Cauwenberghs, “A fast stochastic error-descent algorithm for supervised learning and optimization,” in Advances in Neural Information Processing Systems, S. J. Hanson, J. D. Cowan, C. L. Giles, eds. (Morgan Kaufman, San Mateo, Calif., Vol. 5, pp. 244–251, 1993).

Cohen, M.

DaSilva, H.

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Broadband Networking Technologies, S. Civanlar, I. Widjaja, eds., Proc. SPIE3233, 221–232 (1998).

Fried, D. L.

Hermann, J.

Humphreys, R. A.

Justh, E. W.

Kahalas, S.

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Broadband Networking Technologies, S. Civanlar, I. Widjaja, eds., Proc. SPIE3233, 221–232 (1998).

Landers, F. M.

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Broadband Networking Technologies, S. Civanlar, I. Widjaja, eds., Proc. SPIE3233, 221–232 (1998).

Levine, B. M.

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Broadband Networking Technologies, S. Civanlar, I. Widjaja, eds., Proc. SPIE3233, 221–232 (1998).

Looze, D. P.

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Broadband Networking Technologies, S. Civanlar, I. Widjaja, eds., Proc. SPIE3233, 221–232 (1998).

Loscutov, A. Yu.

A. S. Michailov, A. Yu. Loscutov, Foundation of Synergetics (Springer-Verlag, Berlin, 1991).

Michailov, A. S.

A. S. Michailov, A. Yu. Loscutov, Foundation of Synergetics (Springer-Verlag, Berlin, 1991).

Muller, R. A.

O’Meara, T. R.

Polak-Dingels, P.

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Broadband Networking Technologies, S. Civanlar, I. Widjaja, eds., Proc. SPIE3233, 221–232 (1998).

Price, T. R.

Primmerman, C. A.

Ricklin, J. C.

Rush, D. W.

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Broadband Networking Technologies, S. Civanlar, I. Widjaja, eds., Proc. SPIE3233, 221–232 (1998).

Shmalhauzen, V. I.

M. A. Vorontsov, V. I. Shmalhauzen, Principles of Adaptive Optics (Nauka, Moscow, 1985).

Sivokon, V. P.

Spall, J. C.

J. C. Spall, “A stochastic approximation technique for generating maximum likelihood parameter estimates,” in Proceedings of the American Control Conference (Institute of Electrical and Electronics Engineers, New York, 1987), pp. 1161-1167.

Vorontsov, M. A.

Wirth, A.

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Broadband Networking Technologies, S. Civanlar, I. Widjaja, eds., Proc. SPIE3233, 221–232 (1998).

Zollars, B. G.

Analog Integr. Circuits Signal Process. (1)

A. G. Andreou, K. A. Boahen, “Translinear circuits in subthreshold MOS,” Analog Integr. Circuits Signal Process. 9, 141–166 (1996).
[CrossRef]

Appl. Opt. (1)

IEEE Trans. Image Process (1)

IEEE Trans. Image Process. Special issue on partial differential equations and geometry-driven diffusion in image processing and analysis, IEEE Trans. Image Process. 7(3), (1998).

J. Mod. Opt. (1)

L. C. Andrews, “An analytic model for the refractive index power spectrum and its application to optical scintillations in the atmosphere,” J. Mod. Opt. 39, 1849–1853 (1992).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (7)

Opt. Lett. (1)

Other (8)

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Broadband Networking Technologies, S. Civanlar, I. Widjaja, eds., Proc. SPIE3233, 221–232 (1998).

F. Roddier, ed., Adaptive Optics in Astronomy (Cambridge U. Press, Cambridge, UK, 1999), pp. 91–130.

G. Cauwenberghs, M. A. Bayoumi, eds., Learning on Silicon (Kluwer Academic, Dordrecht, The Netherlands, 1999).

A. S. Michailov, A. Yu. Loscutov, Foundation of Synergetics (Springer-Verlag, Berlin, 1991).

B. M. ter Haar Romey, ed., Geometry-Driven Diffusion in Computer Vision (Kluwer-Academic, Dordrecht, The Netherlands, 1994).

M. A. Vorontsov, V. I. Shmalhauzen, Principles of Adaptive Optics (Nauka, Moscow, 1985).

J. C. Spall, “A stochastic approximation technique for generating maximum likelihood parameter estimates,” in Proceedings of the American Control Conference (Institute of Electrical and Electronics Engineers, New York, 1987), pp. 1161-1167.

G. Cauwenberghs, “A fast stochastic error-descent algorithm for supervised learning and optimization,” in Advances in Neural Information Processing Systems, S. J. Hanson, J. D. Cowan, C. L. Giles, eds. (Morgan Kaufman, San Mateo, Calif., Vol. 5, pp. 244–251, 1993).

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Figures (9)

Fig. 1
Fig. 1

Schematic of a direct-control adaptive optics system.

Fig. 2
Fig. 2

Phase-distortion compensation in an adaptive system with conventional and optoelectronic Zernike filters: (a) input phase pattern, (b) output intensity distribution corresponding to (a) for a conventional Zernike filter, (c) residual phase pattern after ten iterations for the conventional and (d) residual phase pattern after ten iterations for the optoelectronic Zernike sensors. Parameters of the control algorithm are d=0, K=0.75, μ=1.

Fig. 3
Fig. 3

Simulation results for an adaptive system with an optoelectronic Zernike filter: (a) input phase realization; (b) stationary-state residual phase pattern obtained after 100 iterations; (c), (e), residual phase and (d), (f), intensity patterns of wave-front sensor output after N=8 (c and d), and N=32 (e and f) iterations. System parameters are σφ=2.3 rad (St=0.028), d=0.005, K=0.75, μ=1.

Fig. 4
Fig. 4

Averaged Strehl ratio achieved after N iterations of the adaptation process versus input phase standard deviation for the following adaptive system configurations: St(0) system (dashed curves), St(max) (solid curves); Stdif(max) (solid curves with dots). Numbers near the curves correspond to the number of iterations N; the curve with N=0 corresponds to K=0 (no adaptation). Other parameters are the same as in Fig. 2.

Fig. 5
Fig. 5

Simulation results for an adaptive system with a nonlinear Zernike filter for different phase-modulation coefficients α: curve 1, α=0 (no adaptation); curve 2, α=0.25π/IF0; curve 3, 0.5π/IF0; curve 4, α=1.0π/IF0. Other parameters are the same as in Fig. 2.

Fig. 6
Fig. 6

Adaptive direct-control system with an optoelectronic Zernike wave-front sensor [St(max) configuration] in the presence of input field intensity scintillations. Averaged Strehl ratio achieved after 20 iterations of the adaptation process (18) versus input phase standard deviation for different intensity fluctuation levels characterized by the intensity-fluctuation standard deviation σI: curve 1, no adaptation; curve 2, σI=0.15; curve 3, σI=0.35; curve 4, σI=0.64. Curve 5 corresponds to modified algorithm (18) with σI=0.64 and =1.25. Snapshots of the input field intensity patterns for (a) σI=0.15, (b) σI=0.35, and (c) σI=0.64. Other parameters are the same as in Fig. 2.

Fig. 7
Fig. 7

Adaptive system with a differential Zernike wave-front sensor in the presence of input field intensity scintillations: St(max) configuration (solid curves) and St(0) configuration (dashed curves). Averaged Strehl ratio achieved after N iterations of the adaptation process versus input phase standard deviation for K=0.8 and σI=0.35 (curves 2–6) and σI=0.64 (curve 7). Curve 1 corresponds to K=0 (no adaptation). The number of iterations for each curve is shown parentheses.

Fig. 8
Fig. 8

Schematic of experimental setup for adaptive wave-front phase distortion compensation with a LCLV-based Zernike filter.

Fig. 9
Fig. 9

Experimental results for an adaptive system with a nonlinear Zernike wave-front sensor: (a) interference pattern for the aberrated beam; (b) corresponding intensity distribution in the lens focal plane registered by the camera CCD2 (Fig. 8); (c) and (d) are the same but for the corrected wave front.

Equations (34)

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u(r, t)t=G(u, Iout),
u(r, t)t=ηJ(r, t),
J[u]=St-α1[u¯(t)-u0]2-α2|u(r, t)|2d2r,
J[u]=A0(r)exp{i[u(r)+φ˜(r)]}d2r2-β1[u0-S-1u(r)d2r]2-β2 |u(r)|2d2r,
δJ=J[u+δu]-J[u]=J(r)δu(r)d2r+o(δu),
J=-2|A¯0|A0(r)sin[u(r)+φ˜(r)-Δ]-2β1(u¯-u0)+2β22u(r).
A¯0|A¯0|exp(iΔ)=A0(r)exp{i[u(r)+φ˜(r)]}d2r.
u(r, t)t=d2u(r, t)-γ|A¯0(t)|A0(r)sin[u(r, t)+φ˜(r)-Δ]-μ[u¯(t)-u0],
Idif(r, t)12[Izer(+)(r, t)-Izer(-)(r, t)]=2A0(r)|A¯0(t)|sin[u(r, t)+φ˜(r)-Δ],
J=-Idif(r, t)-2β1(u¯-u0)+2β22u(r, t).
u(r, t)t=d2u(r, t)-KIdif(r, t)-μ[u¯(t)-u0],
u(n+1)(r)=u(n)(r)+d2u(n)(r)-KIdif(n)(r)-μ[u¯(n)-u0],
u(n+1)(ri, j)=u(n)(ri, j)+d2u(n)(ri, j)-KIdif(n)(ri, j)-μ[u¯(n)-u0],
u(n+1)(ri, j)=u(n)(ri, j)+KIdif(n)(ri, j)-μ[u¯(n)-u0].
Iout(r, t)=I0(r)+2|A¯0(t)|2-2A0(r)×|A¯0(t)|{cos[u(r, t)+φ˜(r)-Δ]-sin[u(r, t)+φ˜(r)-Δ]}.
Iout(r, t)=Idif(r, t)+I0(r)+2|A¯0(t)|2-2A0(r)|A¯0(t)|cos[u(r, t)+φ˜(r)-Δ].
u(r, t)t=d2u(r, t)-KIout(r, t)-μ[u¯(t)-u0].
u(r, t)t=ηJ(r, t)-κ1I0(r)-κ2|A¯0(t)|2+κ3A0(r)|A¯0(t)|cos[u(r, t)+φ˜(r)-Δ],
-Kc1{cos[u(r)+φ˜(r)-Δ]
-sin[u(r)+φ˜(r)-Δ]}+c2=0,
u(r)=-φ˜(r)+const.+2πn.
u(n+1)(r)=u(n)(r)+d2u(n)(r)-KIout(n)(r)-μ[u¯(n)-u0].
A0(r)=[1+αamζ(r)]/χ,
A0(r)=|αamζ(r)|2/χ,
u(n+1)(r)=u(n)(r)+d2u(n)(r)-K[Iout(n)(r)-I0(r)]-μ[u¯(n)-u0],
J[u]=A0(r)exp{i[u(r)+φ˜(r)]}d2r2-β1[u0-S-1u(r)d2r]2-β2|u(r)|2d2r.
J[u]=A¯0A¯0*-β1[u¯-u0]2-β2|u(r)|2d2r,
A¯0=A0(r)exp{i[u(r)+φ˜(r)]}d2r.
δJ=A¯0δA¯0*+A¯0*δA¯0-2β1S-1[u¯-u0]×δu(r)d2r-2β2uδud2r
=|A¯0|[exp(iΔ)δA¯0*+exp(-iΔ)δA¯0]-2β1S-1[u¯-u0]δu(r)d2r+2β2(2u)δud2r.
δA¯0=iA0 exp{i[u+φ˜]}δud2r,
δA¯0*=-i  A0 exp{-i[u+φ˜]}δud2r.
δJ=-2|A¯0|A0(r)sin[u(r)+φ˜(r)-Δ]δu(r)d2r-2β1S-1[u¯-u0]δu(r)d2r+2β2u(r)δu(r)d2r.
J=-2|A¯0|A0(r)sin[u(r)+φ˜(r)-Δ]-2β1S-1(u¯-u0)+2β22u(r).

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