Abstract

An adaptive optics (AO) system with Stochastic Parallel Gradient Descent (SPGD) algorithm and a 61-element deformable mirror is simulated to restore the image of a turbulence-degraded extended object. SPGD is used to search the optimum voltages for the actuators of the deformable mirror. We try to find a convenient image performance metric, which is needed by SPGD, merely from a gray level distorted image and without any additional optics elements. Simulation results show the gray level variance function acts more promising than other metrics, such as metrics based on the gray level gradient of each pixel. The restoration capability of the AO system is investigated with different images and different turbulence strength wave-front aberrations using SPGD with the above resultant image quality criterion. Numerical simulation results verify the performance metric is effective and the AO system can restore those images degraded by different turbulence strengths successfully.

© 2009 Optical Society of America

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References

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  1. R. K. Tyson, Principle of Adaptive Optics (Academic Press, 1991).
  2. R. A. Muller and A. Buffington, "Real-time correction of atmospherically degraded telescope images through image sharpening," J. Opt. Am. A. 64, 1200 -1210 (1974).
    [CrossRef]
  3. S. Zommer, E. N. Ribak, S. G. Lipson and J. Adler, "Simulated annealing in ocular adaptive optics," Opt. Lett. 31, 1-3 (2000).
  4. P. Yang, M. W. Ao, Y. Li, B. Xu, and W. H. Jiang, "Intracavity transverse modes controlled by a genetic algorithm based on Zernike mode coefficients," Opt. Express 15, 17051-17062 (2007).
    [CrossRef] [PubMed]
  5. M. A. Vorontsov and G. W. Carhart, "Adaptive optics based on analog parallel stochastic optimization: analysis and experimental demonstration," J. Opt. Soc. Am. A. 17, 1440 -1453 (2000)
    [CrossRef]
  6. M. S. Zakynthinaki and Y. G. Saridakis, "Stochastic optimization for a tip-tilt adaptive correcting system," Comput. Phys. Commun. 150, 274 -292 (2003)
    [CrossRef]
  7. J. W. Goodman. Introduction to Fourier Optics (Publishing House of Electronics Industry, 2006).
  8. N. Roddier, "Atmospheric wavefront simulation using Zernike polynomials," Opt. Eng. 29, 1174 -1180 (1990).
    [CrossRef]
  9. W. H. Jiang, N. Ling, X. J. Rao, and F. Shi. "Fitting capability of deformable mirror," Proc. SPIE 1542, 130 -137 (1991).
    [CrossRef]
  10. J. C. Spall, "Multivariate stochastic approximation using a simultaneous perturbation gradient approximation," IEEE Trans. Autom. Control. 37, 332 -341 (1992).
    [CrossRef]

2007

2003

M. S. Zakynthinaki and Y. G. Saridakis, "Stochastic optimization for a tip-tilt adaptive correcting system," Comput. Phys. Commun. 150, 274 -292 (2003)
[CrossRef]

2000

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

S. Zommer, E. N. Ribak, S. G. Lipson and J. Adler, "Simulated annealing in ocular adaptive optics," Opt. Lett. 31, 1-3 (2000).

1992

J. C. Spall, "Multivariate stochastic approximation using a simultaneous perturbation gradient approximation," IEEE Trans. Autom. Control. 37, 332 -341 (1992).
[CrossRef]

1991

W. H. Jiang, N. Ling, X. J. Rao, and F. Shi. "Fitting capability of deformable mirror," Proc. SPIE 1542, 130 -137 (1991).
[CrossRef]

1990

N. Roddier, "Atmospheric wavefront simulation using Zernike polynomials," Opt. Eng. 29, 1174 -1180 (1990).
[CrossRef]

1974

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

Adler, J.

S. Zommer, E. N. Ribak, S. G. Lipson and J. Adler, "Simulated annealing in ocular adaptive optics," Opt. Lett. 31, 1-3 (2000).

Ao, M. W.

Buffington, A.

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

Carhart, G. W.

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

Jiang, W. H.

Li, Y.

Ling, N.

W. H. Jiang, N. Ling, X. J. Rao, and F. Shi. "Fitting capability of deformable mirror," Proc. SPIE 1542, 130 -137 (1991).
[CrossRef]

Lipson, S. G.

S. Zommer, E. N. Ribak, S. G. Lipson and J. Adler, "Simulated annealing in ocular adaptive optics," Opt. Lett. 31, 1-3 (2000).

Muller, R. A.

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

Rao, X. J.

W. H. Jiang, N. Ling, X. J. Rao, and F. Shi. "Fitting capability of deformable mirror," Proc. SPIE 1542, 130 -137 (1991).
[CrossRef]

Ribak, E. N.

S. Zommer, E. N. Ribak, S. G. Lipson and J. Adler, "Simulated annealing in ocular adaptive optics," Opt. Lett. 31, 1-3 (2000).

Roddier, N.

N. Roddier, "Atmospheric wavefront simulation using Zernike polynomials," Opt. Eng. 29, 1174 -1180 (1990).
[CrossRef]

Saridakis, Y. G.

M. S. Zakynthinaki and Y. G. Saridakis, "Stochastic optimization for a tip-tilt adaptive correcting system," Comput. Phys. Commun. 150, 274 -292 (2003)
[CrossRef]

Spall, J. C.

J. C. Spall, "Multivariate stochastic approximation using a simultaneous perturbation gradient approximation," IEEE Trans. Autom. Control. 37, 332 -341 (1992).
[CrossRef]

Vorontsov, M. A.

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

Xu, B.

Yang, P.

Zakynthinaki, M. S.

M. S. Zakynthinaki and Y. G. Saridakis, "Stochastic optimization for a tip-tilt adaptive correcting system," Comput. Phys. Commun. 150, 274 -292 (2003)
[CrossRef]

Zommer, S.

S. Zommer, E. N. Ribak, S. G. Lipson and J. Adler, "Simulated annealing in ocular adaptive optics," Opt. Lett. 31, 1-3 (2000).

Comput. Phys. Commun.

M. S. Zakynthinaki and Y. G. Saridakis, "Stochastic optimization for a tip-tilt adaptive correcting system," Comput. Phys. Commun. 150, 274 -292 (2003)
[CrossRef]

IEEE Trans. Autom. Control.

J. C. Spall, "Multivariate stochastic approximation using a simultaneous perturbation gradient approximation," IEEE Trans. Autom. Control. 37, 332 -341 (1992).
[CrossRef]

J. Opt. Am. A.

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

J. Opt. Soc. Am. A.

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

Opt. Eng.

N. Roddier, "Atmospheric wavefront simulation using Zernike polynomials," Opt. Eng. 29, 1174 -1180 (1990).
[CrossRef]

Opt. Express

Opt. Lett.

S. Zommer, E. N. Ribak, S. G. Lipson and J. Adler, "Simulated annealing in ocular adaptive optics," Opt. Lett. 31, 1-3 (2000).

SPIE

W. H. Jiang, N. Ling, X. J. Rao, and F. Shi. "Fitting capability of deformable mirror," Proc. SPIE 1542, 130 -137 (1991).
[CrossRef]

Other

J. W. Goodman. Introduction to Fourier Optics (Publishing House of Electronics Industry, 2006).

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

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Figures (13)

Fig. 1.
Fig. 1.

Original image A (a), with clear edges and Background; Original image B (b), more complicated and almost fills the image plane; ideal imaging result (c) of Image A and that (d) of Image B when the FOV is about 24 times the size of diffraction limit angle.

Fig. 2.
Fig. 2.

Schematic diagram of a high resolution imaging model.

Fig. 3.
Fig. 3.

Actuator distribution of 61-element DM.

Fig. 4.
Fig. 4.

Averaged curve of F 1 (a), the corresponding standard deviation curves (b) and SR curves(c) during 1500 iterations.

Fig. 5.
Fig. 5.

Averaged curve of F 2 (a), the corresponding standard deviation curves (b) and SR curves(c) during 1500 iterations.

Fig. 6.
Fig. 6.

Averaged curve of F 3 (a), the corresponding standard deviation curves (b) and SR curves(c) during 1500 iterations.

Fig. 7.
Fig. 7.

Averaged curve of F 4 (a), the corresponding standard deviation curves (b) and SR curves(c) during 1500 iterations.

Fig. 8.
Fig. 8.

Comparison of Zernike coefficients 3-104 before correction (a) and after correction with F 1 (c), F 2 (d), F 3 (e) and F 4 (f) ; (b) is Zernike coefficients of the residual wave-front with the least squares fitting.

Fig. 9.
Fig. 9.

Comparison of PSF before correction (a) and after correction with F 1 (c), F 2 (d), F 3 (e) and F 4 (f); (b) is PSF of the residual wave-front with the least squares fitting.

Fig. 10.
Fig. 10.

Imaging results comparison of Image A before correction (A) and after correction (B), (C), (D) and (E) with F 1, F 2 F 3 ,and F 4 respectively.

Fig. 11.
Fig. 11.

Imaging results comparison of Image B before correction (A) and after correction (B), (C), (D) and (E) with F 1, F 2 F3 ,and F 4 respectively.

Fig. 12.
Fig. 12.

Comparison of four image-quality metrics and the least squares fitting on correction ability

Fig. 13.
Fig. 13.

Different image metrics versus D/r 0.

Equations (8)

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f ( x , y ) = I ( x , y ) * h ( x , y )
F 1 = x y [ f ( x , y ) A ] 2
F 2 = x y { [ f ( x , y ) f ( x + 1 , y ) ] 2 + [ f ( x , y ) f ( x , y + 1 ) ] 2 }
F 3 = x y { 4 f ( x , y ) f ( x , y + 1 ) f ( x + 1 , y ) f ( x 1 , y ) f ( x , y 1 ) } 2
F 4 = u v ( u 2 + v 2 ) P ( u , v )
m ( x , y ) = j = 1 61 u j S j ( x , y )
S j ( r ) = S j ( x , y ) = exp { In ω [ ( x x j ) 2 + ( y y j ) 2 / d ] α }
u ( k + 1 ) = u ( k ) + γ Δ u ( k ) Δ F ( k ) , k = 0,1 ,

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